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train · 9.9k rows

name string	atp_proof string	mizar_proof string	system string
t75_bvfunc14	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t74_bvfunc14, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>![X10]:(m1_eqrel_1(X10,X1)=>![X11]:(m1_eqrel_1(X11,X1)=>(X2=k7_enumset1(X3,X4,X5,X6,X7,X8,X9,X10,X11)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X3=X10\|(X3=X11\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X4=X10\|(X4=X11\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X5=X10\|(X5=X11\|(X6=X7\|(X6=X8\|(X6=X9\|(X6=X10\|(X6=X11\|(X7=X8\|(X7=X9\|(X7=X10\|(X7=X11\|(X8=X9\|(X8=X10\|(X8=X11\|(X9=X10\|(X9=X11\|(X10=X11\|k5_bvfunc_2(X1,X10,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X8),X9),X11))))))))))))))))))))))))))))))))))))))))))))))))), file('/scratch/mptp/predsminms1/t75_bvfunc14__0', t74_bvfunc14)). fof(t83_enumset1, axiom, ![X1, X2, X3, X4, X5, X6, X7, X8, X9]:k7_enumset1(X1,X2,X3,X4,X5,X6,X7,X8,X9)=k2_xboole_0(k5_enumset1(X1,X2,X3,X4,X5,X6,X7),k2_tarski(X8,X9)), file('/scratch/mptp/predsminms1/t75_bvfunc14__0', t83_enumset1)). fof(t75_bvfunc14, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>![X10]:(m1_eqrel_1(X10,X1)=>![X11]:(m1_eqrel_1(X11,X1)=>(X2=k7_enumset1(X3,X4,X5,X6,X7,X8,X9,X10,X11)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X3=X10\|(X3=X11\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X4=X10\|(X4=X11\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X5=X10\|(X5=X11\|(X6=X7\|(X6=X8\|(X6=X9\|(X6=X10\|(X6=X11\|(X7=X8\|(X7=X9\|(X7=X10\|(X7=X11\|(X8=X9\|(X8=X10\|(X8=X11\|(X9=X10\|(X9=X11\|(X10=X11\|k5_bvfunc_2(X1,X11,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X8),X9),X10))))))))))))))))))))))))))))))))))))))))))))))))), file('/scratch/mptp/predsminms1/t75_bvfunc14__0', t75_bvfunc14)). fof(commutativity_k2_tarski, axiom, ![X1, X2]:k2_tarski(X1,X2)=k2_tarski(X2,X1), file('/scratch/mptp/predsminms1/t75_bvfunc14__0', commutativity_k2_tarski)). fof(c_0_4, plain, ![X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11]:(epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1)<=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X3=X10\|(X3=X11\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X4=X10\|(X4=X11\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X5=X10\|(X5=X11\|(X6=X7\|(X6=X8\|(X6=X9\|(X6=X10\|(X6=X11\|(X7=X8\|(X7=X9\|(X7=X10\|(X7=X11\|(X8=X9\|(X8=X10\|(X8=X11\|(X9=X10\|(X9=X11\|(X10=X11\|k5_bvfunc_2(X1,X10,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X8),X9),X11)))))))))))))))))))))))))))))))))))))), introduced(definition)). fof(c_0_5, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>![X10]:(m1_eqrel_1(X10,X1)=>![X11]:(m1_eqrel_1(X11,X1)=>(X2=k7_enumset1(X3,X4,X5,X6,X7,X8,X9,X10,X11)=>epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1))))))))))))), inference(apply_def,[status(thm)],[t74_bvfunc14, c_0_4])). fof(c_0_6, plain, ![X34, X35, X36, X37, X38, X39, X40, X41, X42, X43, X44]:(v1_xboole_0(X34)\|(~m1_subset_1(X35,k1_zfmisc_1(k1_bvfunc_2(X34)))\|(~m1_eqrel_1(X36,X34)\|(~m1_eqrel_1(X37,X34)\|(~m1_eqrel_1(X38,X34)\|(~m1_eqrel_1(X39,X34)\|(~m1_eqrel_1(X40,X34)\|(~m1_eqrel_1(X41,X34)\|(~m1_eqrel_1(X42,X34)\|(~m1_eqrel_1(X43,X34)\|(~m1_eqrel_1(X44,X34)\|(X35!=k7_enumset1(X36,X37,X38,X39,X40,X41,X42,X43,X44)\|epred1_11(X44,X43,X42,X41,X40,X39,X38,X37,X36,X35,X34))))))))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5])])])])). fof(c_0_7, plain, ![X23, X24, X25, X26, X27, X28, X29, X30, X31]:k7_enumset1(X23,X24,X25,X26,X27,X28,X29,X30,X31)=k2_xboole_0(k5_enumset1(X23,X24,X25,X26,X27,X28,X29),k2_tarski(X30,X31)), inference(variable_rename,[status(thm)],[t83_enumset1])). fof(c_0_8, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>![X10]:(m1_eqrel_1(X10,X1)=>![X11]:(m1_eqrel_1(X11,X1)=>(X2=k7_enumset1(X3,X4,X5,X6,X7,X8,X9,X10,X11)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X3=X10\|(X3=X11\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X4=X10\|(X4=X11\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X5=X10\|(X5=X11\|(X6=X7\|(X6=X8\|(X6=X9\|(X6=X10\|(X6=X11\|(X7=X8\|(X7=X9\|(X7=X10\|(X7=X11\|(X8=X9\|(X8=X10\|(X8=X11\|(X9=X10\|(X9=X11\|(X10=X11\|k5_bvfunc_2(X1,X11,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X8),X9),X10)))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[t75_bvfunc14])). cnf(c_0_9, plain, (v1_xboole_0(X1)\|epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))\|~m1_eqrel_1(X3,X1)\|~m1_eqrel_1(X4,X1)\|~m1_eqrel_1(X5,X1)\|~m1_eqrel_1(X6,X1)\|~m1_eqrel_1(X7,X1)\|~m1_eqrel_1(X8,X1)\|~m1_eqrel_1(X9,X1)\|~m1_eqrel_1(X10,X1)\|~m1_eqrel_1(X11,X1)\|X2!=k7_enumset1(X3,X4,X5,X6,X7,X8,X9,X10,X11)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_10, plain, (k7_enumset1(X1,X2,X3,X4,X5,X6,X7,X8,X9)=k2_xboole_0(k5_enumset1(X1,X2,X3,X4,X5,X6,X7),k2_tarski(X8,X9))), inference(split_conjunct,[status(thm)],[c_0_7])). fof(c_0_11, plain, ![X32, X33]:k2_tarski(X32,X33)=k2_tarski(X33,X32), inference(variable_rename,[status(thm)],[commutativity_k2_tarski])). fof(c_0_12, negated_conjecture, (~v1_xboole_0(esk1_0)&(m1_subset_1(esk2_0,k1_zfmisc_1(k1_bvfunc_2(esk1_0)))&(m1_eqrel_1(esk3_0,esk1_0)&(m1_eqrel_1(esk4_0,esk1_0)&(m1_eqrel_1(esk5_0,esk1_0)&(m1_eqrel_1(esk6_0,esk1_0)&(m1_eqrel_1(esk7_0,esk1_0)&(m1_eqrel_1(esk8_0,esk1_0)&(m1_eqrel_1(esk9_0,esk1_0)&(m1_eqrel_1(esk10_0,esk1_0)&(m1_eqrel_1(esk11_0,esk1_0)&(esk2_0=k7_enumset1(esk3_0,esk4_0,esk5_0,esk6_0,esk7_0,esk8_0,esk9_0,esk10_0,esk11_0)&(esk3_0!=esk4_0&(esk3_0!=esk5_0&(esk3_0!=esk6_0&(esk3_0!=esk7_0&(esk3_0!=esk8_0&(esk3_0!=esk9_0&(esk3_0!=esk10_0&(esk3_0!=esk11_0&(esk4_0!=esk5_0&(esk4_0!=esk6_0&(esk4_0!=esk7_0&(esk4_0!=esk8_0&(esk4_0!=esk9_0&(esk4_0!=esk10_0&(esk4_0!=esk11_0&(esk5_0!=esk6_0&(esk5_0!=esk7_0&(esk5_0!=esk8_0&(esk5_0!=esk9_0&(esk5_0!=esk10_0&(esk5_0!=esk11_0&(esk6_0!=esk7_0&(esk6_0!=esk8_0&(esk6_0!=esk9_0&(esk6_0!=esk10_0&(esk6_0!=esk11_0&(esk7_0!=esk8_0&(esk7_0!=esk9_0&(esk7_0!=esk10_0&(esk7_0!=esk11_0&(esk8_0!=esk9_0&(esk8_0!=esk10_0&(esk8_0!=esk11_0&(esk9_0!=esk10_0&(esk9_0!=esk11_0&(esk10_0!=esk11_0&k5_bvfunc_2(esk1_0,esk11_0,esk2_0)!=k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,esk3_0,esk4_0),esk5_0),esk6_0),esk7_0),esk8_0),esk9_0),esk10_0))))))))))))))))))))))))))))))))))))))))))))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_8])])])])). cnf(c_0_13, plain, (v1_xboole_0(X1)\|epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1)\|X2!=k2_xboole_0(k5_enumset1(X3,X4,X5,X6,X7,X8,X9),k2_tarski(X10,X11))\|~m1_eqrel_1(X11,X1)\|~m1_eqrel_1(X10,X1)\|~m1_eqrel_1(X9,X1)\|~m1_eqrel_1(X8,X1)\|~m1_eqrel_1(X7,X1)\|~m1_eqrel_1(X6,X1)\|~m1_eqrel_1(X5,X1)\|~m1_eqrel_1(X4,X1)\|~m1_eqrel_1(X3,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))), inference(rw,[status(thm)],[c_0_9, c_0_10])). cnf(c_0_14, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_15, negated_conjecture, (esk2_0=k7_enumset1(esk3_0,esk4_0,esk5_0,esk6_0,esk7_0,esk8_0,esk9_0,esk10_0,esk11_0)), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_16, plain, ![X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11]:(epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X3=X10\|(X3=X11\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X4=X10\|(X4=X11\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X5=X10\|(X5=X11\|(X6=X7\|(X6=X8\|(X6=X9\|(X6=X10\|(X6=X11\|(X7=X8\|(X7=X9\|(X7=X10\|(X7=X11\|(X8=X9\|(X8=X10\|(X8=X11\|(X9=X10\|(X9=X11\|(X10=X11\|k5_bvfunc_2(X1,X10,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X8),X9),X11)))))))))))))))))))))))))))))))))))))), inference(split_equiv,[status(thm)],[c_0_4])). cnf(c_0_17, plain, (v1_xboole_0(X1)\|epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1)\|X2!=k2_xboole_0(k5_enumset1(X3,X4,X5,X6,X7,X8,X9),k2_tarski(X10,X11))\|~m1_eqrel_1(X11,X1)\|~m1_eqrel_1(X10,X1)\|~m1_eqrel_1(X9,X1)\|~m1_eqrel_1(X8,X1)\|~m1_eqrel_1(X7,X1)\|~m1_eqrel_1(X6,X1)\|~m1_eqrel_1(X5,X1)\|~m1_eqrel_1(X4,X1)\|~m1_eqrel_1(X3,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_18, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_19, negated_conjecture, (esk2_0=k2_xboole_0(k5_enumset1(esk3_0,esk4_0,esk5_0,esk6_0,esk7_0,esk8_0,esk9_0),k2_tarski(esk10_0,esk11_0))), inference(rw,[status(thm)],[c_0_15, c_0_10])). fof(c_0_20, plain, ![X45, X46, X47, X48, X49, X50, X51, X52, X53, X54, X55]:(~epred1_11(X55,X54,X53,X52,X51,X50,X49,X48,X47,X46,X45)\|(X47=X48\|(X47=X49\|(X47=X50\|(X47=X51\|(X47=X52\|(X47=X53\|(X47=X54\|(X47=X55\|(X48=X49\|(X48=X50\|(X48=X51\|(X48=X52\|(X48=X53\|(X48=X54\|(X48=X55\|(X49=X50\|(X49=X51\|(X49=X52\|(X49=X53\|(X49=X54\|(X49=X55\|(X50=X51\|(X50=X52\|(X50=X53\|(X50=X54\|(X50=X55\|(X51=X52\|(X51=X53\|(X51=X54\|(X51=X55\|(X52=X53\|(X52=X54\|(X52=X55\|(X53=X54\|(X53=X55\|(X54=X55\|k5_bvfunc_2(X45,X54,X46)=k2_partit1(X45,k2_partit1(X45,k2_partit1(X45,k2_partit1(X45,k2_partit1(X45,k2_partit1(X45,k2_partit1(X45,X47,X48),X49),X50),X51),X52),X53),X55)))))))))))))))))))))))))))))))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])). cnf(c_0_21, plain, (epred1_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11)\|v1_xboole_0(X11)\|X10!=k2_xboole_0(k5_enumset1(X9,X8,X7,X6,X5,X4,X3),k2_tarski(X1,X2))\|~m1_eqrel_1(X1,X11)\|~m1_eqrel_1(X2,X11)\|~m1_eqrel_1(X3,X11)\|~m1_eqrel_1(X4,X11)\|~m1_eqrel_1(X5,X11)\|~m1_eqrel_1(X6,X11)\|~m1_eqrel_1(X7,X11)\|~m1_eqrel_1(X8,X11)\|~m1_eqrel_1(X9,X11)\|~m1_subset_1(X10,k1_zfmisc_1(k1_bvfunc_2(X11)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_18])])). cnf(c_0_22, negated_conjecture, (k2_xboole_0(k5_enumset1(esk3_0,esk4_0,esk5_0,esk6_0,esk7_0,esk8_0,esk9_0),k2_tarski(esk10_0,esk11_0))=esk2_0), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_23, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k1_bvfunc_2(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_24, negated_conjecture, (m1_eqrel_1(esk10_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_25, negated_conjecture, (m1_eqrel_1(esk11_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_26, negated_conjecture, (m1_eqrel_1(esk9_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_27, negated_conjecture, (m1_eqrel_1(esk8_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_28, negated_conjecture, (m1_eqrel_1(esk7_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_29, negated_conjecture, (m1_eqrel_1(esk6_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_30, negated_conjecture, (m1_eqrel_1(esk5_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_31, negated_conjecture, (m1_eqrel_1(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_32, negated_conjecture, (m1_eqrel_1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_33, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_34, plain, (X9=X8\|X9=X7\|X9=X6\|X9=X5\|X9=X4\|X9=X3\|X9=X2\|X9=X1\|X8=X7\|X8=X6\|X8=X5\|X8=X4\|X8=X3\|X8=X2\|X8=X1\|X7=X6\|X7=X5\|X7=X4\|X7=X3\|X7=X2\|X7=X1\|X6=X5\|X6=X4\|X6=X3\|X6=X2\|X6=X1\|X5=X4\|X5=X3\|X5=X2\|X5=X1\|X4=X3\|X4=X2\|X4=X1\|X3=X2\|X3=X1\|X2=X1\|k5_bvfunc_2(X11,X2,X10)=k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,X9,X8),X7),X6),X5),X4),X3),X1)\|~epred1_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_35, negated_conjecture, (epred1_11(esk10_0,esk11_0,esk9_0,esk8_0,esk7_0,esk6_0,esk5_0,esk4_0,esk3_0,X1,X2)\|v1_xboole_0(X2)\|X1!=esk2_0\|~m1_eqrel_1(esk10_0,X2)\|~m1_eqrel_1(esk11_0,X2)\|~m1_eqrel_1(esk9_0,X2)\|~m1_eqrel_1(esk8_0,X2)\|~m1_eqrel_1(esk7_0,X2)\|~m1_eqrel_1(esk6_0,X2)\|~m1_eqrel_1(esk5_0,X2)\|~m1_eqrel_1(esk4_0,X2)\|~m1_eqrel_1(esk3_0,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k1_bvfunc_2(X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). cnf(c_0_36, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k1_bvfunc_2(esk1_0)))), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_37, negated_conjecture, (m1_eqrel_1(esk10_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_38, negated_conjecture, (m1_eqrel_1(esk11_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_39, negated_conjecture, (m1_eqrel_1(esk9_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_40, negated_conjecture, (m1_eqrel_1(esk8_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_41, negated_conjecture, (m1_eqrel_1(esk7_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_42, negated_conjecture, (m1_eqrel_1(esk6_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_43, negated_conjecture, (m1_eqrel_1(esk5_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_44, negated_conjecture, (m1_eqrel_1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_45, negated_conjecture, (m1_eqrel_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_46, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_47, negated_conjecture, (k5_bvfunc_2(esk1_0,esk11_0,esk2_0)!=k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,esk3_0,esk4_0),esk5_0),esk6_0),esk7_0),esk8_0),esk9_0),esk10_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_48, negated_conjecture, (esk10_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_49, negated_conjecture, (esk9_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_50, negated_conjecture, (esk8_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_51, negated_conjecture, (esk7_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_52, negated_conjecture, (esk6_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_53, negated_conjecture, (esk5_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_54, negated_conjecture, (esk4_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_55, negated_conjecture, (esk3_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_56, negated_conjecture, (esk9_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_57, negated_conjecture, (esk8_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_58, negated_conjecture, (esk7_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_59, negated_conjecture, (esk6_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_60, negated_conjecture, (esk5_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_61, negated_conjecture, (esk4_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_62, negated_conjecture, (esk3_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_63, negated_conjecture, (esk8_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_64, negated_conjecture, (esk7_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_65, negated_conjecture, (esk6_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_66, negated_conjecture, (esk5_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_67, negated_conjecture, (esk4_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_68, negated_conjecture, (esk3_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_69, negated_conjecture, (esk7_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_70, negated_conjecture, (esk6_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_71, negated_conjecture, (esk5_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_72, negated_conjecture, (esk4_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_73, negated_conjecture, (esk3_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_74, negated_conjecture, (esk6_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_75, negated_conjecture, (esk5_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_76, negated_conjecture, (esk4_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_77, negated_conjecture, (esk3_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_78, negated_conjecture, (esk5_0!=esk6_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_79, negated_conjecture, (esk4_0!=esk6_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_80, negated_conjecture, (esk3_0!=esk6_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_81, negated_conjecture, (esk4_0!=esk5_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_82, negated_conjecture, (esk3_0!=esk5_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_83, negated_conjecture, (esk3_0!=esk4_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_84, plain, (X8=X9\|X7=X9\|X7=X8\|X6=X9\|X6=X8\|X6=X7\|X5=X9\|X5=X8\|X5=X7\|X5=X6\|X4=X9\|X4=X8\|X4=X7\|X4=X6\|X4=X5\|X3=X9\|X3=X8\|X3=X7\|X3=X6\|X3=X5\|X3=X4\|X2=X9\|X2=X8\|X2=X7\|X2=X6\|X2=X5\|X2=X4\|X2=X3\|X1=X9\|X1=X8\|X1=X7\|X1=X6\|X1=X5\|X1=X4\|X1=X3\|X1=X2\|k5_bvfunc_2(X11,X2,X10)=k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,X9,X8),X7),X6),X5),X4),X3),X1)\|~epred1_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_85, negated_conjecture, (epred1_11(esk10_0,esk11_0,esk9_0,esk8_0,esk7_0,esk6_0,esk5_0,esk4_0,esk3_0,esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36]), c_0_37]), c_0_38]), c_0_39]), c_0_40]), c_0_41]), c_0_42]), c_0_43]), c_0_44]), c_0_45])]), c_0_46])])). cnf(c_0_86, negated_conjecture, (k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,esk3_0,esk4_0),esk5_0),esk6_0),esk7_0),esk8_0),esk9_0),esk10_0)!=k5_bvfunc_2(esk1_0,esk11_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_87, negated_conjecture, (esk11_0!=esk10_0), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_88, negated_conjecture, (esk10_0!=esk9_0), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_89, negated_conjecture, (esk10_0!=esk8_0), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_90, negated_conjecture, (esk10_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_91, negated_conjecture, (esk10_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_92, negated_conjecture, (esk10_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_93, negated_conjecture, (esk10_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_94, negated_conjecture, (esk10_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_95, negated_conjecture, (esk11_0!=esk9_0), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_96, negated_conjecture, (esk11_0!=esk8_0), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_97, negated_conjecture, (esk11_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_98, negated_conjecture, (esk11_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_99, negated_conjecture, (esk11_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_100, negated_conjecture, (esk11_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_101, negated_conjecture, (esk11_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_102, negated_conjecture, (esk9_0!=esk8_0), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_103, negated_conjecture, (esk9_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_104, negated_conjecture, (esk9_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_105, negated_conjecture, (esk9_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_106, negated_conjecture, (esk9_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_107, negated_conjecture, (esk9_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_108, negated_conjecture, (esk8_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_109, negated_conjecture, (esk8_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_110, negated_conjecture, (esk8_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_111, negated_conjecture, (esk8_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_112, negated_conjecture, (esk8_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_113, negated_conjecture, (esk7_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_114, negated_conjecture, (esk7_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_115, negated_conjecture, (esk7_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_116, negated_conjecture, (esk7_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_117, negated_conjecture, (esk6_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_118, negated_conjecture, (esk6_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_119, negated_conjecture, (esk6_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_120, negated_conjecture, (esk5_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_121, negated_conjecture, (esk5_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_122, negated_conjecture, (esk4_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_123, plain, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_86]), c_0_87]), c_0_88]), c_0_89]), c_0_90]), c_0_91]), c_0_92]), c_0_93]), c_0_94]), c_0_95]), c_0_96]), c_0_97]), c_0_98]), c_0_99]), c_0_100]), c_0_101]), c_0_102]), c_0_103]), c_0_104]), c_0_105]), c_0_106]), c_0_107]), c_0_108]), c_0_109]), c_0_110]), c_0_111]), c_0_112]), c_0_113]), c_0_114]), c_0_115]), c_0_116]), c_0_117]), c_0_118]), c_0_119]), c_0_120]), c_0_121]), c_0_122]), ['proof']). # SZS output end CNFRefutation	reserve Y for non empty set, G for Subset of PARTITIONS(Y), A,B,C,D,E,F for a_partition of Y; reserve Y for non empty set, G for Subset of PARTITIONS(Y), A, B, C, D, E, F, J, M for a_partition of Y, x,x1,x2,x3,x4,x5,x6,x7,x8,x9 for set; theorem for G being Subset of PARTITIONS(Y), A,B,C,D,E,F,J,M,N being a_partition of Y st G={A,B,C,D,E,F,J,M,N} & A<>B & A<>C & A<>D & A<>E & A<>F & A<>J & A<>M & A<>N & B<>C & B<>D & B<>E & B<>F & B<>J & B<>M & B<>N & C<>D & C <>E & C<>F & C<>J & C<>M & C<>N & D<>E & D<>F & D<>J & D<>M & D<>N & E<>F & E<> J & E<>M & E<>N & F<>J & F<>M & F<>N & J<>M & J<>N & M<>N holds CompF(N,G) = A '/\' B '/\' C '/\' D '/\' E '/\' F '/\' J '/\' M proof let G be Subset of PARTITIONS(Y); let A,B,C,D,E,F,J,M,N be a_partition of Y; {A,B,C,D,E,F,J,M,N} ={A,B,C,D,E,F,J} \/ {M,N} by ENUMSET1:83 .={A,B,C,D,E,F,J,N,M} by ENUMSET1:83; hence thesis by Th74; end;	Convert the following ATP output trace into a readable Mizar proof.
t62_pzfmisc1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d16_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,X1)&(v1_funct_1(X4)&v1_partfun1(X4,X1))))=>(X4=k6_pboole(X1,X2,X3)<=>![X5]:(r2_hidden(X5,X1)=>k1_funct_1(X4,X5)=k2_zfmisc_1(k1_funct_1(X2,X5),k1_funct_1(X3,X5))))))), file('/scratch/mptp/predsminms1/t62_pzfmisc1__0', d16_pboole)). fof(dt_k6_pboole, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>(v1_relat_1(k6_pboole(X1,X2,X3))&(v4_relat_1(k6_pboole(X1,X2,X3),X1)&(v1_funct_1(k6_pboole(X1,X2,X3))&v1_partfun1(k6_pboole(X1,X2,X3),X1))))), file('/scratch/mptp/predsminms1/t62_pzfmisc1__0', dt_k6_pboole)). fof(t96_zfmisc_1, axiom, ![X1, X2, X3, X4]:((r1_tarski(X1,X2)&r1_tarski(X3,X4))=>r1_tarski(k2_zfmisc_1(X1,X3),k2_zfmisc_1(X2,X4))), file('/scratch/mptp/predsminms1/t62_pzfmisc1__0', t96_zfmisc_1)). fof(d2_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>(r2_pboole(X1,X2,X3)<=>![X4]:(r2_hidden(X4,X1)=>r1_tarski(k1_funct_1(X2,X4),k1_funct_1(X3,X4)))))), file('/scratch/mptp/predsminms1/t62_pzfmisc1__0', d2_pboole)). fof(t62_pzfmisc1, conjecture, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,X1)&(v1_funct_1(X4)&v1_partfun1(X4,X1))))=>![X5]:((v1_relat_1(X5)&(v4_relat_1(X5,X1)&(v1_funct_1(X5)&v1_partfun1(X5,X1))))=>((r2_pboole(X1,X2,X3)&r2_pboole(X1,X4,X5))=>r2_pboole(X1,k6_pboole(X1,X2,X4),k6_pboole(X1,X3,X5))))))), file('/scratch/mptp/predsminms1/t62_pzfmisc1__0', t62_pzfmisc1)). fof(c_0_5, plain, ![X11, X12, X13, X14, X15]:((X14!=k6_pboole(X11,X12,X13)\|(~r2_hidden(X15,X11)\|k1_funct_1(X14,X15)=k2_zfmisc_1(k1_funct_1(X12,X15),k1_funct_1(X13,X15)))\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X11)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X11))))\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X11)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X11))))\|(~v1_relat_1(X12)\|(~v4_relat_1(X12,X11)\|(~v1_funct_1(X12)\|~v1_partfun1(X12,X11)))))&((r2_hidden(esk6_4(X11,X12,X13,X14),X11)\|X14=k6_pboole(X11,X12,X13)\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X11)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X11))))\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X11)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X11))))\|(~v1_relat_1(X12)\|(~v4_relat_1(X12,X11)\|(~v1_funct_1(X12)\|~v1_partfun1(X12,X11)))))&(k1_funct_1(X14,esk6_4(X11,X12,X13,X14))!=k2_zfmisc_1(k1_funct_1(X12,esk6_4(X11,X12,X13,X14)),k1_funct_1(X13,esk6_4(X11,X12,X13,X14)))\|X14=k6_pboole(X11,X12,X13)\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X11)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X11))))\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X11)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X11))))\|(~v1_relat_1(X12)\|(~v4_relat_1(X12,X11)\|(~v1_funct_1(X12)\|~v1_partfun1(X12,X11))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_pboole])])])])])). cnf(c_0_6, plain, (k1_funct_1(X1,X5)=k2_zfmisc_1(k1_funct_1(X3,X5),k1_funct_1(X4,X5))\|X1!=k6_pboole(X2,X3,X4)\|~r2_hidden(X5,X2)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v1_funct_1(X4)\|~v1_partfun1(X4,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_5])). fof(c_0_7, plain, ![X17, X18, X19]:((v1_relat_1(k6_pboole(X17,X18,X19))\|(~v1_relat_1(X18)\|(~v4_relat_1(X18,X17)\|(~v1_funct_1(X18)\|~v1_partfun1(X18,X17)))\|(~v1_relat_1(X19)\|(~v4_relat_1(X19,X17)\|(~v1_funct_1(X19)\|~v1_partfun1(X19,X17))))))&((v4_relat_1(k6_pboole(X17,X18,X19),X17)\|(~v1_relat_1(X18)\|(~v4_relat_1(X18,X17)\|(~v1_funct_1(X18)\|~v1_partfun1(X18,X17)))\|(~v1_relat_1(X19)\|(~v4_relat_1(X19,X17)\|(~v1_funct_1(X19)\|~v1_partfun1(X19,X17))))))&((v1_funct_1(k6_pboole(X17,X18,X19))\|(~v1_relat_1(X18)\|(~v4_relat_1(X18,X17)\|(~v1_funct_1(X18)\|~v1_partfun1(X18,X17)))\|(~v1_relat_1(X19)\|(~v4_relat_1(X19,X17)\|(~v1_funct_1(X19)\|~v1_partfun1(X19,X17))))))&(v1_partfun1(k6_pboole(X17,X18,X19),X17)\|(~v1_relat_1(X18)\|(~v4_relat_1(X18,X17)\|(~v1_funct_1(X18)\|~v1_partfun1(X18,X17)))\|(~v1_relat_1(X19)\|(~v4_relat_1(X19,X17)\|(~v1_funct_1(X19)\|~v1_partfun1(X19,X17))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_pboole])])])). fof(c_0_8, plain, ![X20, X21, X22, X23]:(~r1_tarski(X20,X21)\|~r1_tarski(X22,X23)\|r1_tarski(k2_zfmisc_1(X20,X22),k2_zfmisc_1(X21,X23))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t96_zfmisc_1])])). cnf(c_0_9, plain, (k1_funct_1(X1,X5)=k2_zfmisc_1(k1_funct_1(X3,X5),k1_funct_1(X4,X5))\|X1!=k6_pboole(X2,X3,X4)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~r2_hidden(X5,X2)), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_10, plain, (v1_relat_1(k6_pboole(X1,X2,X3))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_11, plain, (v4_relat_1(k6_pboole(X1,X2,X3),X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_12, plain, (v1_funct_1(k6_pboole(X1,X2,X3))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_13, plain, (v1_partfun1(k6_pboole(X1,X2,X3),X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_14, plain, (r1_tarski(k2_zfmisc_1(X1,X3),k2_zfmisc_1(X2,X4))\|~r1_tarski(X1,X2)\|~r1_tarski(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_15, plain, (k1_funct_1(k6_pboole(X1,X2,X3),X4)=k2_zfmisc_1(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~r2_hidden(X4,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_partfun1(k6_pboole(X1,X2,X3),X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(k6_pboole(X1,X2,X3))\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v4_relat_1(k6_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(k6_pboole(X1,X2,X3))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_9])])). cnf(c_0_16, plain, (v1_relat_1(k6_pboole(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_17, plain, (v4_relat_1(k6_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_18, plain, (v1_funct_1(k6_pboole(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_19, plain, (v1_partfun1(k6_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_13])). fof(c_0_20, plain, ![X24, X25, X26, X27]:((~r2_pboole(X24,X25,X26)\|(~r2_hidden(X27,X24)\|r1_tarski(k1_funct_1(X25,X27),k1_funct_1(X26,X27)))\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,X24)\|(~v1_funct_1(X26)\|~v1_partfun1(X26,X24))))\|(~v1_relat_1(X25)\|(~v4_relat_1(X25,X24)\|(~v1_funct_1(X25)\|~v1_partfun1(X25,X24)))))&((r2_hidden(esk7_3(X24,X25,X26),X24)\|r2_pboole(X24,X25,X26)\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,X24)\|(~v1_funct_1(X26)\|~v1_partfun1(X26,X24))))\|(~v1_relat_1(X25)\|(~v4_relat_1(X25,X24)\|(~v1_funct_1(X25)\|~v1_partfun1(X25,X24)))))&(~r1_tarski(k1_funct_1(X25,esk7_3(X24,X25,X26)),k1_funct_1(X26,esk7_3(X24,X25,X26)))\|r2_pboole(X24,X25,X26)\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,X24)\|(~v1_funct_1(X26)\|~v1_partfun1(X26,X24))))\|(~v1_relat_1(X25)\|(~v4_relat_1(X25,X24)\|(~v1_funct_1(X25)\|~v1_partfun1(X25,X24))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_pboole])])])])])). cnf(c_0_21, plain, (r1_tarski(k2_zfmisc_1(X1,X3),k2_zfmisc_1(X2,X4))\|~r1_tarski(X3,X4)\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_22, plain, (k1_funct_1(k6_pboole(X1,X2,X3),X4)=k2_zfmisc_1(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~r2_hidden(X4,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_15, c_0_16]), c_0_17]), c_0_18]), c_0_19])). fof(c_0_23, negated_conjecture, ~(![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,X1)&(v1_funct_1(X4)&v1_partfun1(X4,X1))))=>![X5]:((v1_relat_1(X5)&(v4_relat_1(X5,X1)&(v1_funct_1(X5)&v1_partfun1(X5,X1))))=>((r2_pboole(X1,X2,X3)&r2_pboole(X1,X4,X5))=>r2_pboole(X1,k6_pboole(X1,X2,X4),k6_pboole(X1,X3,X5)))))))), inference(assume_negation,[status(cth)],[t62_pzfmisc1])). cnf(c_0_24, plain, (r2_pboole(X2,X1,X3)\|~r1_tarski(k1_funct_1(X1,esk7_3(X2,X1,X3)),k1_funct_1(X3,esk7_3(X2,X1,X3)))\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_25, plain, (r1_tarski(k1_funct_1(k6_pboole(X6,X1,X3),X2),k2_zfmisc_1(X4,X5))\|~r1_tarski(k1_funct_1(X3,X2),X5)\|~r1_tarski(k1_funct_1(X1,X2),X4)\|~r2_hidden(X2,X6)\|~v1_partfun1(X3,X6)\|~v1_partfun1(X1,X6)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X6)\|~v4_relat_1(X1,X6)\|~v1_relat_1(X3)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). fof(c_0_26, negated_conjecture, ((v1_relat_1(esk2_0)&(v4_relat_1(esk2_0,esk1_0)&(v1_funct_1(esk2_0)&v1_partfun1(esk2_0,esk1_0))))&((v1_relat_1(esk3_0)&(v4_relat_1(esk3_0,esk1_0)&(v1_funct_1(esk3_0)&v1_partfun1(esk3_0,esk1_0))))&((v1_relat_1(esk4_0)&(v4_relat_1(esk4_0,esk1_0)&(v1_funct_1(esk4_0)&v1_partfun1(esk4_0,esk1_0))))&((v1_relat_1(esk5_0)&(v4_relat_1(esk5_0,esk1_0)&(v1_funct_1(esk5_0)&v1_partfun1(esk5_0,esk1_0))))&((r2_pboole(esk1_0,esk2_0,esk3_0)&r2_pboole(esk1_0,esk4_0,esk5_0))&~r2_pboole(esk1_0,k6_pboole(esk1_0,esk2_0,esk4_0),k6_pboole(esk1_0,esk3_0,esk5_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])). cnf(c_0_27, plain, (r2_pboole(X2,X1,X3)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~r1_tarski(k1_funct_1(X1,esk7_3(X2,X1,X3)),k1_funct_1(X3,esk7_3(X2,X1,X3)))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_28, plain, (r1_tarski(k1_funct_1(k6_pboole(X1,X2,X3),X4),k1_funct_1(k6_pboole(X8,X5,X7),X6))\|~r1_tarski(k1_funct_1(X3,X4),k1_funct_1(X7,X6))\|~r1_tarski(k1_funct_1(X2,X4),k1_funct_1(X5,X6))\|~r2_hidden(X4,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~r2_hidden(X6,X8)\|~v1_partfun1(X7,X8)\|~v1_partfun1(X5,X8)\|~v1_funct_1(X7)\|~v1_funct_1(X5)\|~v4_relat_1(X7,X8)\|~v4_relat_1(X5,X8)\|~v1_relat_1(X7)\|~v1_relat_1(X5)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_22])])). cnf(c_0_29, plain, (r1_tarski(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~r2_pboole(X1,X2,X3)\|~r2_hidden(X4,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_30, negated_conjecture, (r2_pboole(esk1_0,esk4_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_31, negated_conjecture, (v1_partfun1(esk5_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_32, negated_conjecture, (v1_partfun1(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_33, negated_conjecture, (v1_funct_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_34, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_35, negated_conjecture, (v4_relat_1(esk5_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_36, negated_conjecture, (v4_relat_1(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_37, negated_conjecture, (v1_relat_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_38, negated_conjecture, (v1_relat_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_39, plain, (r2_pboole(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))\|~v1_partfun1(k6_pboole(X5,X6,X7),X1)\|~v1_partfun1(k6_pboole(X2,X3,X4),X1)\|~v1_funct_1(k6_pboole(X5,X6,X7))\|~v1_funct_1(k6_pboole(X2,X3,X4))\|~v4_relat_1(k6_pboole(X5,X6,X7),X1)\|~v4_relat_1(k6_pboole(X2,X3,X4),X1)\|~v1_relat_1(k6_pboole(X5,X6,X7))\|~v1_relat_1(k6_pboole(X2,X3,X4))\|~r1_tarski(k1_funct_1(X4,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))),k1_funct_1(X7,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))))\|~r1_tarski(k1_funct_1(X3,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))),k1_funct_1(X6,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))))\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7)),X2)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7)),X5)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X7)\|~v1_relat_1(X6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28])])). cnf(c_0_40, plain, (r1_tarski(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~r2_hidden(X4,X1)\|~r2_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_41, negated_conjecture, (r2_pboole(esk1_0,esk4_0,esk5_0)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_42, negated_conjecture, (v1_partfun1(esk5_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_43, negated_conjecture, (v1_partfun1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_44, negated_conjecture, (v1_funct_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_45, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_46, negated_conjecture, (v4_relat_1(esk5_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_47, negated_conjecture, (v4_relat_1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_48, negated_conjecture, (v1_relat_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_49, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_50, negated_conjecture, (r2_pboole(esk1_0,esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_51, negated_conjecture, (v1_partfun1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_52, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_53, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_54, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_55, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_56, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_57, negated_conjecture, (v1_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_58, negated_conjecture, (v1_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_59, plain, (r2_pboole(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))\|~r1_tarski(k1_funct_1(X4,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))),k1_funct_1(X7,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))))\|~r1_tarski(k1_funct_1(X3,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))),k1_funct_1(X6,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))))\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7)),X2)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7)),X5)\|~v1_partfun1(k6_pboole(X5,X6,X7),X1)\|~v1_partfun1(k6_pboole(X2,X3,X4),X1)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(k6_pboole(X5,X6,X7),X1)\|~v4_relat_1(k6_pboole(X2,X3,X4),X1)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X7)\|~v1_relat_1(X6)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_39, c_0_16]), c_0_16]), c_0_18]), c_0_18])). cnf(c_0_60, negated_conjecture, (r1_tarski(k1_funct_1(esk4_0,X1),k1_funct_1(esk5_0,X1))\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42]), c_0_43]), c_0_44]), c_0_45]), c_0_46]), c_0_47]), c_0_48]), c_0_49])])])). cnf(c_0_61, negated_conjecture, (r2_pboole(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_62, negated_conjecture, (v1_partfun1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_63, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_64, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_65, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_66, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_67, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_68, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_69, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_70, negated_conjecture, (r2_pboole(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0))\|~r1_tarski(k1_funct_1(X3,esk7_3(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0))),k1_funct_1(X5,esk7_3(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0))))\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0)),X2)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0)),X4)\|~v1_partfun1(k6_pboole(X4,X5,esk5_0),X1)\|~v1_partfun1(k6_pboole(X2,X3,esk4_0),X1)\|~v1_partfun1(esk4_0,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(esk5_0,X4)\|~v1_partfun1(X5,X4)\|~v1_funct_1(X3)\|~v1_funct_1(X5)\|~v4_relat_1(k6_pboole(X4,X5,esk5_0),X1)\|~v4_relat_1(k6_pboole(X2,X3,esk4_0),X1)\|~v4_relat_1(esk4_0,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(esk5_0,X4)\|~v4_relat_1(X5,X4)\|~v1_relat_1(X3)\|~v1_relat_1(X5)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0)),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60]), c_0_45]), c_0_44]), c_0_49]), c_0_48])])])). cnf(c_0_71, negated_conjecture, (r1_tarski(k1_funct_1(esk2_0,X1),k1_funct_1(esk3_0,X1))\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), c_0_69])])])). cnf(c_0_72, plain, (r2_hidden(esk7_3(X1,X2,X3),X1)\|r2_pboole(X1,X2,X3)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_73, negated_conjecture, (r2_pboole(X1,k6_pboole(X2,esk2_0,esk4_0),k6_pboole(X3,esk3_0,esk5_0))\|~r2_hidden(esk7_3(X1,k6_pboole(X2,esk2_0,esk4_0),k6_pboole(X3,esk3_0,esk5_0)),esk1_0)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,esk2_0,esk4_0),k6_pboole(X3,esk3_0,esk5_0)),X2)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,esk2_0,esk4_0),k6_pboole(X3,esk3_0,esk5_0)),X3)\|~v1_partfun1(k6_pboole(X3,esk3_0,esk5_0),X1)\|~v1_partfun1(k6_pboole(X2,esk2_0,esk4_0),X1)\|~v1_partfun1(esk4_0,X2)\|~v1_partfun1(esk5_0,X3)\|~v1_partfun1(esk2_0,X2)\|~v1_partfun1(esk3_0,X3)\|~v4_relat_1(k6_pboole(X3,esk3_0,esk5_0),X1)\|~v4_relat_1(k6_pboole(X2,esk2_0,esk4_0),X1)\|~v4_relat_1(esk4_0,X2)\|~v4_relat_1(esk5_0,X3)\|~v4_relat_1(esk2_0,X2)\|~v4_relat_1(esk3_0,X3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_65]), c_0_64]), c_0_69]), c_0_68])])])). cnf(c_0_74, plain, (r2_pboole(X1,X2,X3)\|r2_hidden(esk7_3(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_75, negated_conjecture, (r2_pboole(esk1_0,k6_pboole(X1,esk2_0,esk4_0),k6_pboole(X2,esk3_0,esk5_0))\|~r2_hidden(esk7_3(esk1_0,k6_pboole(X1,esk2_0,esk4_0),k6_pboole(X2,esk3_0,esk5_0)),X1)\|~r2_hidden(esk7_3(esk1_0,k6_pboole(X1,esk2_0,esk4_0),k6_pboole(X2,esk3_0,esk5_0)),X2)\|~v1_partfun1(k6_pboole(X2,esk3_0,esk5_0),esk1_0)\|~v1_partfun1(k6_pboole(X1,esk2_0,esk4_0),esk1_0)\|~v1_partfun1(esk4_0,X1)\|~v1_partfun1(esk5_0,X2)\|~v1_partfun1(esk2_0,X1)\|~v1_partfun1(esk3_0,X2)\|~v4_relat_1(k6_pboole(X2,esk3_0,esk5_0),esk1_0)\|~v4_relat_1(k6_pboole(X1,esk2_0,esk4_0),esk1_0)\|~v4_relat_1(esk4_0,X1)\|~v4_relat_1(esk5_0,X2)\|~v4_relat_1(esk2_0,X1)\|~v4_relat_1(esk3_0,X2)\|~v1_funct_1(k6_pboole(X2,esk3_0,esk5_0))\|~v1_funct_1(k6_pboole(X1,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(X2,esk3_0,esk5_0))\|~v1_relat_1(k6_pboole(X1,esk2_0,esk4_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_74])])). cnf(c_0_76, negated_conjecture, (~r2_pboole(esk1_0,k6_pboole(esk1_0,esk2_0,esk4_0),k6_pboole(esk1_0,esk3_0,esk5_0))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_77, negated_conjecture, (r2_pboole(esk1_0,k6_pboole(esk1_0,esk2_0,esk4_0),k6_pboole(X1,esk3_0,esk5_0))\|~r2_hidden(esk7_3(esk1_0,k6_pboole(esk1_0,esk2_0,esk4_0),k6_pboole(X1,esk3_0,esk5_0)),X1)\|~v1_partfun1(k6_pboole(X1,esk3_0,esk5_0),esk1_0)\|~v1_partfun1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v1_partfun1(esk5_0,X1)\|~v1_partfun1(esk3_0,X1)\|~v1_funct_1(k6_pboole(X1,esk3_0,esk5_0))\|~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v4_relat_1(k6_pboole(X1,esk3_0,esk5_0),esk1_0)\|~v4_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v4_relat_1(esk5_0,X1)\|~v4_relat_1(esk3_0,X1)\|~v1_relat_1(k6_pboole(X1,esk3_0,esk5_0))\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_74]), c_0_43]), c_0_63]), c_0_47]), c_0_67])])])). cnf(c_0_78, negated_conjecture, (~r2_pboole(esk1_0,k6_pboole(esk1_0,esk2_0,esk4_0),k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_79, negated_conjecture, (~v1_partfun1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v1_partfun1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v4_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v4_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_74]), c_0_42]), c_0_62]), c_0_46]), c_0_66])]), c_0_78])])). cnf(c_0_80, negated_conjecture, (~v1_partfun1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v4_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v4_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_19]), c_0_43]), c_0_63]), c_0_45]), c_0_65]), c_0_47]), c_0_67]), c_0_49]), c_0_69])])])). cnf(c_0_81, negated_conjecture, (~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v4_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v4_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_19]), c_0_42]), c_0_62]), c_0_44]), c_0_64]), c_0_46]), c_0_66]), c_0_48]), c_0_68])])])). cnf(c_0_82, negated_conjecture, (~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v4_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_17]), c_0_43]), c_0_63]), c_0_45]), c_0_65]), c_0_47]), c_0_67]), c_0_49]), c_0_69])])])). cnf(c_0_83, negated_conjecture, (~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_17]), c_0_42]), c_0_62]), c_0_44]), c_0_64]), c_0_46]), c_0_66]), c_0_48]), c_0_68])])])). cnf(c_0_84, negated_conjecture, (~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_18]), c_0_43]), c_0_63]), c_0_45]), c_0_65]), c_0_47]), c_0_67]), c_0_49]), c_0_69])])])). cnf(c_0_85, negated_conjecture, (~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_18]), c_0_42]), c_0_62]), c_0_44]), c_0_64]), c_0_46]), c_0_66]), c_0_48]), c_0_68])])])). cnf(c_0_86, negated_conjecture, (~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_16]), c_0_43]), c_0_63]), c_0_45]), c_0_65]), c_0_47]), c_0_67]), c_0_49]), c_0_69])])])). cnf(c_0_87, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_16]), c_0_42]), c_0_62]), c_0_44]), c_0_64]), c_0_46]), c_0_66]), c_0_48]), c_0_68])]), ['proof']). # SZS output end CNFRefutation	reserve i, I for set, f for Function, x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I; theorem :: ZFMISC_1:119 x1 c= A & x2 c= B implies [\|x1,x2\|] c= [\|A,B\|] proof assume that A1: x1 c= A and A2: x2 c= B; let i; assume A3: i in I; then A4: x1.i c= A.i by A1,PBOOLE:def 2; x2.i c= B.i by A2,A3,PBOOLE:def 2; then [:x1.i,x2.i:] c= [:A.i,B.i:] by A4,ZFMISC_1:96; then [\|x1,x2\|].i c= [:A.i,B.i:] by A3,PBOOLE:def 16; hence thesis by A3,PBOOLE:def 16; end;	Convert the following ATP output trace into a readable Mizar proof.
t2_funct_4	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t2_funct_4, conjecture, ![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>![X2]:((v1_relat_1(X2)&v1_funct_1(X2))=>k3_relat_1(X2,X1)=k3_relat_1(X2,k5_relat_1(X1,k10_xtuple_0(X2))))), file('/scratch/mptp/predsminms1/t2_funct_4__0', t2_funct_4)). fof(t53_relat_1, axiom, ![X1, X2]:(v1_relat_1(X2)=>(r1_tarski(k10_xtuple_0(X2),X1)=>k3_relat_1(X2,k4_relat_1(X1))=X2)), file('/scratch/mptp/predsminms1/t2_funct_4__0', t53_relat_1)). fof(reflexivity_r1_tarski, axiom, ![X1, X2]:r1_tarski(X1,X1), file('/scratch/mptp/predsminms1/t2_funct_4__0', reflexivity_r1_tarski)). fof(t65_relat_1, axiom, ![X1, X2]:(v1_relat_1(X2)=>k5_relat_1(X2,X1)=k3_relat_1(k4_relat_1(X1),X2)), file('/scratch/mptp/predsminms1/t2_funct_4__0', t65_relat_1)). fof(t36_relat_1, axiom, ![X1]:(v1_relat_1(X1)=>![X2]:(v1_relat_1(X2)=>![X3]:(v1_relat_1(X3)=>k3_relat_1(k3_relat_1(X1,X2),X3)=k3_relat_1(X1,k3_relat_1(X2,X3))))), file('/scratch/mptp/predsminms1/t2_funct_4__0', t36_relat_1)). fof(dt_k4_relat_1, axiom, ![X1]:v1_relat_1(k4_relat_1(X1)), file('/scratch/mptp/predsminms1/t2_funct_4__0', dt_k4_relat_1)). fof(c_0_6, negated_conjecture, ~(![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>![X2]:((v1_relat_1(X2)&v1_funct_1(X2))=>k3_relat_1(X2,X1)=k3_relat_1(X2,k5_relat_1(X1,k10_xtuple_0(X2)))))), inference(assume_negation,[status(cth)],[t2_funct_4])). fof(c_0_7, plain, ![X6, X7]:(~v1_relat_1(X7)\|(~r1_tarski(k10_xtuple_0(X7),X6)\|k3_relat_1(X7,k4_relat_1(X6))=X7)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t53_relat_1])])). fof(c_0_8, plain, ![X8]:r1_tarski(X8,X8), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])])). fof(c_0_9, negated_conjecture, ((v1_relat_1(esk1_0)&v1_funct_1(esk1_0))&((v1_relat_1(esk2_0)&v1_funct_1(esk2_0))&k3_relat_1(esk2_0,esk1_0)!=k3_relat_1(esk2_0,k5_relat_1(esk1_0,k10_xtuple_0(esk2_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])). fof(c_0_10, plain, ![X9, X10]:(~v1_relat_1(X10)\|k5_relat_1(X10,X9)=k3_relat_1(k4_relat_1(X9),X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t65_relat_1])])). fof(c_0_11, plain, ![X11, X12, X13]:(~v1_relat_1(X11)\|(~v1_relat_1(X12)\|(~v1_relat_1(X13)\|k3_relat_1(k3_relat_1(X11,X12),X13)=k3_relat_1(X11,k3_relat_1(X12,X13))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t36_relat_1])])])). cnf(c_0_12, plain, (k3_relat_1(X1,k4_relat_1(X2))=X1\|~v1_relat_1(X1)\|~r1_tarski(k10_xtuple_0(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_13, plain, (r1_tarski(X1,X1)), inference(split_conjunct,[status(thm)],[c_0_8])). fof(c_0_14, plain, ![X14]:v1_relat_1(k4_relat_1(X14)), inference(variable_rename,[status(thm)],[dt_k4_relat_1])). cnf(c_0_15, negated_conjecture, (k3_relat_1(esk2_0,esk1_0)!=k3_relat_1(esk2_0,k5_relat_1(esk1_0,k10_xtuple_0(esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_16, plain, (k5_relat_1(X1,X2)=k3_relat_1(k4_relat_1(X2),X1)\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_17, negated_conjecture, (v1_relat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_18, plain, (k3_relat_1(k3_relat_1(X1,X2),X3)=k3_relat_1(X1,k3_relat_1(X2,X3))\|~v1_relat_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X3)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_19, plain, (k3_relat_1(X1,k4_relat_1(X2))=X1\|~v1_relat_1(X1)\|~r1_tarski(k10_xtuple_0(X1),X2)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_20, plain, (r1_tarski(X1,X1)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_21, plain, (v1_relat_1(k4_relat_1(X1))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_22, negated_conjecture, (k3_relat_1(esk2_0,k5_relat_1(esk1_0,k10_xtuple_0(esk2_0)))!=k3_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_23, plain, (k5_relat_1(X1,X2)=k3_relat_1(k4_relat_1(X2),X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_24, negated_conjecture, (v1_relat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_25, plain, (k3_relat_1(k3_relat_1(X1,X2),X3)=k3_relat_1(X1,k3_relat_1(X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_26, plain, (k3_relat_1(X1,k4_relat_1(k10_xtuple_0(X1)))=X1\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20])])). cnf(c_0_27, plain, (v1_relat_1(k4_relat_1(X1))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_28, negated_conjecture, (v1_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_29, negated_conjecture, (k3_relat_1(esk2_0,k3_relat_1(k4_relat_1(k10_xtuple_0(esk2_0)),esk1_0))!=k3_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23]), c_0_24])])])). cnf(c_0_30, plain, (k3_relat_1(X1,k3_relat_1(k4_relat_1(k10_xtuple_0(X1)),X2))=k3_relat_1(X1,X2)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_27])])])). cnf(c_0_31, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_32, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_24]), c_0_31])]), ['proof']). # SZS output end CNFRefutation	reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2,X,X9,Y,Y9,Z,Z9 for set; reserve A,D,D9 for non empty set; reserve f,g,h for Function; theorem gf = (g\|rng f)f proof x in dom(gf) iff x in dom((g\|rng f)f) proof A1: dom(g\|rng f) = dom g /\ rng f by RELAT_1:61; thus x in dom(gf) implies x in dom((g\|rng f)f) proof assume A2: x in dom(gf); then A3: x in dom f by FUNCT_1:11; x in dom f by A2,FUNCT_1:11; then A4: f.x in rng f by FUNCT_1:def 3; f.x in dom g by A2,FUNCT_1:11; then f.x in dom(g\|rng f) by A1,A4,XBOOLE_0:def 4; hence thesis by A3,FUNCT_1:11; end; assume A5: x in dom((g\|rng f)f); then f.x in dom(g\|rng f) by FUNCT_1:11; then A6: f.x in dom g by A1,XBOOLE_0:def 4; x in dom f by A5,FUNCT_1:11; hence thesis by A6,FUNCT_1:11; end; then A7: dom(gf) = dom((g\|rng f)f) by TARSKI:1; x in dom(gf) implies (gf).x = ((g\|rng f)f).x proof assume A8: x in dom(gf); then A9: x in dom f by FUNCT_1:11; then A10: f.x in rng f by FUNCT_1:def 3; thus (gf).x = g.(f.x) by A8,FUNCT_1:12 .= (g\|rng f).(f.x) by A10,FUNCT_1:49 .= ((g\|rng f)f).x by A9,FUNCT_1:13; end; hence thesis by A7,FUNCT_1:2; end;	Convert the following ATP output trace into a readable Mizar proof.
t18_borsuk_5	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t18_borsuk_5, conjecture, ![X1]:(v1_rat_1(X1)=>![X2]:((v1_xreal_0(X2)&~(v1_rat_1(X2)))=>~(v1_rat_1(k2_xcmplx_0(X1,X2))))), file('/scratch/mptp/predsminms1/t18_borsuk_5__0', t18_borsuk_5)). fof(fc4_borsuk_5, axiom, ![X1, X2]:((v1_rat_1(X1)&(v1_xreal_0(X2)&~(v1_rat_1(X2))))=>~(v1_rat_1(k2_xcmplx_0(X1,X2)))), file('/scratch/mptp/predsminms1/t18_borsuk_5__0', fc4_borsuk_5)). fof(c_0_2, negated_conjecture, ~(![X1]:(v1_rat_1(X1)=>![X2]:((v1_xreal_0(X2)&~(v1_rat_1(X2)))=>~(v1_rat_1(k2_xcmplx_0(X1,X2)))))), inference(assume_negation,[status(cth)],[t18_borsuk_5])). fof(c_0_3, plain, ![X5, X6]:(~v1_rat_1(X5)\|(~v1_xreal_0(X6)\|v1_rat_1(X6))\|~v1_rat_1(k2_xcmplx_0(X5,X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc4_borsuk_5])])])). fof(c_0_4, negated_conjecture, (v1_rat_1(esk1_0)&((v1_xreal_0(esk2_0)&~v1_rat_1(esk2_0))&v1_rat_1(k2_xcmplx_0(esk1_0,esk2_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2])])])])). cnf(c_0_5, plain, (v1_rat_1(X2)\|~v1_rat_1(X1)\|~v1_xreal_0(X2)\|~v1_rat_1(k2_xcmplx_0(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_6, negated_conjecture, (v1_rat_1(k2_xcmplx_0(esk1_0,esk2_0))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, negated_conjecture, (v1_xreal_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_8, negated_conjecture, (v1_rat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_9, negated_conjecture, (~v1_rat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_10, plain, (v1_rat_1(X2)\|~v1_rat_1(X1)\|~v1_xreal_0(X2)\|~v1_rat_1(k2_xcmplx_0(X1,X2))), inference(evalgc,[status(thm)],[c_0_5])). cnf(c_0_11, negated_conjecture, (v1_rat_1(k2_xcmplx_0(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_12, negated_conjecture, (v1_xreal_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_13, negated_conjecture, (v1_rat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_14, negated_conjecture, (~v1_rat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_15, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10, c_0_11]), c_0_12]), c_0_13])]), c_0_14]), ['proof']). # SZS output end CNFRefutation	reserve x1, x2, x3, x4, x5, x6, x7 for set; theorem for a being rational number, b being irrational real number holds a + b is irrational;	Convert the following ATP output trace into a readable Mizar proof.
t4_groupp_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t4_groupp_1, conjecture, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(v7_ordinal1(X3)=>(k5_group_1(X1,X3,k2_group_1(X1,X2))=k1_group_1(X1)=>k5_group_1(X1,X3,X2)=k1_group_1(X1))))), file('/scratch/mptp/predsminms1/t4_groupp_1__0', t4_groupp_1)). fof(involutiveness_k2_group_1, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))&m1_subset_1(X2,u1_struct_0(X1)))=>k2_group_1(X1,k2_group_1(X1,X2))=X2), file('/scratch/mptp/predsminms1/t4_groupp_1__0', involutiveness_k2_group_1)). fof(dt_k5_group_1, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))&(v1_int_1(X2)&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k5_group_1(X1,X2,X3),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t4_groupp_1__0', dt_k5_group_1)). fof(l46_group_1, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:((~(v2_struct_0(X2))&(v2_group_1(X2)&(v3_group_1(X2)&l3_algstr_0(X2))))=>![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>k5_group_1(X2,X1,k2_group_1(X2,X3))=k2_group_1(X2,k5_group_1(X2,X1,X3))))), file('/scratch/mptp/predsminms1/t4_groupp_1__0', l46_group_1)). fof(t8_group_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>k2_group_1(X1,k1_group_1(X1))=k1_group_1(X1)), file('/scratch/mptp/predsminms1/t4_groupp_1__0', t8_group_1)). fof(cc2_int_1, axiom, ![X1]:(v7_ordinal1(X1)=>v1_int_1(X1)), file('/scratch/mptp/predsminms1/t4_groupp_1__0', cc2_int_1)). fof(c_0_6, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(v7_ordinal1(X3)=>(k5_group_1(X1,X3,k2_group_1(X1,X2))=k1_group_1(X1)=>k5_group_1(X1,X3,X2)=k1_group_1(X1)))))), inference(assume_negation,[status(cth)],[t4_groupp_1])). fof(c_0_7, plain, ![X10, X11]:(v2_struct_0(X10)\|(~v2_group_1(X10)\|(~v3_group_1(X10)\|~l3_algstr_0(X10)))\|~m1_subset_1(X11,u1_struct_0(X10))\|k2_group_1(X10,k2_group_1(X10,X11))=X11), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[involutiveness_k2_group_1])])])). fof(c_0_8, plain, ![X12, X13, X14]:(v2_struct_0(X12)\|(~v2_group_1(X12)\|(~v3_group_1(X12)\|~l3_algstr_0(X12)))\|(~v1_int_1(X13)\|~m1_subset_1(X14,u1_struct_0(X12)))\|m1_subset_1(k5_group_1(X12,X13,X14),u1_struct_0(X12))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k5_group_1])])])). fof(c_0_9, negated_conjecture, ((~v2_struct_0(esk1_0)&(v2_group_1(esk1_0)&(v3_group_1(esk1_0)&l3_algstr_0(esk1_0))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(v7_ordinal1(esk3_0)&(k5_group_1(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0))=k1_group_1(esk1_0)&k5_group_1(esk1_0,esk3_0,esk2_0)!=k1_group_1(esk1_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6])])])])). fof(c_0_10, plain, ![X7, X8, X9]:(~v7_ordinal1(X7)\|(v2_struct_0(X8)\|(~v2_group_1(X8)\|(~v3_group_1(X8)\|~l3_algstr_0(X8)))\|(~m1_subset_1(X9,u1_struct_0(X8))\|k5_group_1(X8,X7,k2_group_1(X8,X9))=k2_group_1(X8,k5_group_1(X8,X7,X9))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[l46_group_1])])])])). cnf(c_0_11, plain, (v2_struct_0(X1)\|k2_group_1(X1,k2_group_1(X1,X2))=X2\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_12, plain, (v2_struct_0(X1)\|m1_subset_1(k5_group_1(X1,X2,X3),u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~v1_int_1(X2)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_13, negated_conjecture, (k5_group_1(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0))=k1_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_14, plain, (v2_struct_0(X2)\|k5_group_1(X2,X1,k2_group_1(X2,X3))=k2_group_1(X2,k5_group_1(X2,X1,X3))\|~v7_ordinal1(X1)\|~v2_group_1(X2)\|~v3_group_1(X2)\|~l3_algstr_0(X2)\|~m1_subset_1(X3,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_15, negated_conjecture, (v7_ordinal1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_16, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_17, negated_conjecture, (l3_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_18, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_19, negated_conjecture, (v2_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_20, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_21, plain, ![X16]:(v2_struct_0(X16)\|(~v2_group_1(X16)\|(~v3_group_1(X16)\|~l3_algstr_0(X16)))\|k2_group_1(X16,k1_group_1(X16))=k1_group_1(X16)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t8_group_1])])])). cnf(c_0_22, plain, (k2_group_1(X1,k2_group_1(X1,X2))=X2\|v2_struct_0(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_23, plain, (v2_struct_0(X1)\|m1_subset_1(k5_group_1(X1,X2,X3),u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~v1_int_1(X2)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_24, negated_conjecture, (k5_group_1(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0))=k1_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_25, plain, (k5_group_1(X2,X1,k2_group_1(X2,X3))=k2_group_1(X2,k5_group_1(X2,X1,X3))\|v2_struct_0(X2)\|~v2_group_1(X2)\|~v3_group_1(X2)\|~l3_algstr_0(X2)\|~v7_ordinal1(X1)\|~m1_subset_1(X3,u1_struct_0(X2))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_26, negated_conjecture, (v7_ordinal1(esk3_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_27, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_28, negated_conjecture, (l3_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_29, negated_conjecture, (v3_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_30, negated_conjecture, (v2_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_31, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_32, plain, (v2_struct_0(X1)\|k2_group_1(X1,k1_group_1(X1))=k1_group_1(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_33, plain, (k2_group_1(X1,k2_group_1(X1,k5_group_1(X1,X2,X3)))=k5_group_1(X1,X2,X3)\|v2_struct_0(X1)\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~v1_int_1(X2)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23])])). cnf(c_0_34, negated_conjecture, (k2_group_1(esk1_0,k5_group_1(esk1_0,esk3_0,esk2_0))=k1_group_1(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30])]), c_0_31])])). cnf(c_0_35, negated_conjecture, (k5_group_1(esk1_0,esk3_0,esk2_0)!=k1_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_36, plain, ![X15]:(~v7_ordinal1(X15)\|v1_int_1(X15)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_int_1])])). cnf(c_0_37, plain, (k2_group_1(X1,k1_group_1(X1))=k1_group_1(X1)\|v2_struct_0(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_38, negated_conjecture, (k2_group_1(esk1_0,k1_group_1(esk1_0))=k5_group_1(esk1_0,esk3_0,esk2_0)\|~v1_int_1(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_27]), c_0_28]), c_0_29]), c_0_30])]), c_0_31])])). cnf(c_0_39, negated_conjecture, (k5_group_1(esk1_0,esk3_0,esk2_0)!=k1_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_40, plain, (v1_int_1(X1)\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_41, negated_conjecture, (~v1_int_1(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38]), c_0_28]), c_0_29]), c_0_30])]), c_0_39]), c_0_31])])). cnf(c_0_42, plain, (v1_int_1(X1)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_43, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_26])]), ['proof']). # SZS output end CNFRefutation	reserve G for Group, a,b for Element of G, m, n for Nat, p for prime Nat; theorem Th4: a" \|^ n = 1_G implies a \|^ n = 1_G proof a"" = a; hence thesis by Th3; end;	Convert the following ATP output trace into a readable Mizar proof.
t34_cqc_the3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d5_cqc_the3, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X3]:(m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))=>(r5_cqc_the3(X1,X2,X3)<=>(r1_cqc_the3(X1,X2,X3)&r1_cqc_the3(X1,X3,X2)))))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', d5_cqc_the3)). fof(dt_k7_cqc_lang, axiom, ![X1, X2, X3]:((m1_qc_lang1(X1)&(m1_subset_1(X2,k3_cqc_lang(X1))&m1_subset_1(X3,k3_cqc_lang(X1))))=>m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', dt_k7_cqc_lang)). fof(redefinition_m2_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(X1))))=>![X3]:(m2_subset_1(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', redefinition_m2_subset_1)). fof(dt_k3_cqc_lang, axiom, ![X1]:(m1_qc_lang1(X1)=>m1_subset_1(k3_cqc_lang(X1),k1_zfmisc_1(k9_qc_lang1(X1)))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', dt_k3_cqc_lang)). fof(l42_cqc_the3, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X3]:(m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X4]:(m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X5]:(m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))=>((r5_cqc_the3(X1,X2,X3)&r5_cqc_the3(X1,X4,X5))=>r1_cqc_the3(X1,k7_cqc_lang(X1,X2,X4),k7_cqc_lang(X1,X3,X5)))))))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', l42_cqc_the3)). fof(dt_k9_qc_lang1, axiom, ![X1]:(m1_qc_lang1(X1)=>~(v1_xboole_0(k9_qc_lang1(X1)))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', dt_k9_qc_lang1)). fof(fc2_cqc_lang, axiom, ![X1]:(m1_qc_lang1(X1)=>~(v1_xboole_0(k3_cqc_lang(X1)))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', fc2_cqc_lang)). fof(t34_cqc_the3, conjecture, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X3]:(m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X4]:(m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X5]:(m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))=>((r5_cqc_the3(X1,X2,X3)&r5_cqc_the3(X1,X4,X5))=>r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X4),k7_cqc_lang(X1,X3,X5)))))))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', t34_cqc_the3)). fof(c_0_8, plain, ![X12, X13, X14]:(((r1_cqc_the3(X12,X13,X14)\|~r5_cqc_the3(X12,X13,X14)\|~m2_subset_1(X14,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m2_subset_1(X13,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m1_qc_lang1(X12))&(r1_cqc_the3(X12,X14,X13)\|~r5_cqc_the3(X12,X13,X14)\|~m2_subset_1(X14,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m2_subset_1(X13,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m1_qc_lang1(X12)))&(~r1_cqc_the3(X12,X13,X14)\|~r1_cqc_the3(X12,X14,X13)\|r5_cqc_the3(X12,X13,X14)\|~m2_subset_1(X14,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m2_subset_1(X13,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m1_qc_lang1(X12))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_cqc_the3])])])])). fof(c_0_9, plain, ![X23, X24, X25]:(~m1_qc_lang1(X23)\|(~m1_subset_1(X24,k3_cqc_lang(X23))\|~m1_subset_1(X25,k3_cqc_lang(X23)))\|m2_subset_1(k7_cqc_lang(X23,X24,X25),k9_qc_lang1(X23),k3_cqc_lang(X23))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_cqc_lang])])). fof(c_0_10, plain, ![X15, X16, X17]:((~m2_subset_1(X17,X15,X16)\|m1_subset_1(X17,X16)\|(v1_xboole_0(X15)\|(v1_xboole_0(X16)\|~m1_subset_1(X16,k1_zfmisc_1(X15)))))&(~m1_subset_1(X17,X16)\|m2_subset_1(X17,X15,X16)\|(v1_xboole_0(X15)\|(v1_xboole_0(X16)\|~m1_subset_1(X16,k1_zfmisc_1(X15)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_m2_subset_1])])])])])). fof(c_0_11, plain, ![X11]:(~m1_qc_lang1(X11)\|m1_subset_1(k3_cqc_lang(X11),k1_zfmisc_1(k9_qc_lang1(X11)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_cqc_lang])])). cnf(c_0_12, plain, (r5_cqc_the3(X1,X2,X3)\|~r1_cqc_the3(X1,X2,X3)\|~r1_cqc_the3(X1,X3,X2)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_13, plain, (m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)\|~m1_subset_1(X2,k3_cqc_lang(X1))\|~m1_subset_1(X3,k3_cqc_lang(X1))), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_14, plain, ![X18, X19, X20, X21, X22]:(~m1_qc_lang1(X18)\|(~m2_subset_1(X19,k9_qc_lang1(X18),k3_cqc_lang(X18))\|(~m2_subset_1(X20,k9_qc_lang1(X18),k3_cqc_lang(X18))\|(~m2_subset_1(X21,k9_qc_lang1(X18),k3_cqc_lang(X18))\|(~m2_subset_1(X22,k9_qc_lang1(X18),k3_cqc_lang(X18))\|(~r5_cqc_the3(X18,X19,X20)\|~r5_cqc_the3(X18,X21,X22)\|r1_cqc_the3(X18,k7_cqc_lang(X18,X19,X21),k7_cqc_lang(X18,X20,X22)))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l42_cqc_the3])])])). cnf(c_0_15, plain, (m2_subset_1(X1,X3,X2)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_16, plain, (m1_subset_1(k3_cqc_lang(X1),k1_zfmisc_1(k9_qc_lang1(X1)))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_17, plain, ![X26]:(~m1_qc_lang1(X26)\|~v1_xboole_0(k9_qc_lang1(X26))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k9_qc_lang1])])])). fof(c_0_18, plain, ![X27]:(~m1_qc_lang1(X27)\|~v1_xboole_0(k3_cqc_lang(X27))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_cqc_lang])])])). fof(c_0_19, negated_conjecture, ~(![X1]:(m1_qc_lang1(X1)=>![X2]:(m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X3]:(m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X4]:(m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X5]:(m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))=>((r5_cqc_the3(X1,X2,X3)&r5_cqc_the3(X1,X4,X5))=>r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X4),k7_cqc_lang(X1,X3,X5))))))))), inference(assume_negation,[status(cth)],[t34_cqc_the3])). cnf(c_0_20, plain, (r5_cqc_the3(X1,X2,X3)\|~m1_qc_lang1(X1)\|~r1_cqc_the3(X1,X3,X2)\|~r1_cqc_the3(X1,X2,X3)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_21, plain, (m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)\|~m1_subset_1(X3,k3_cqc_lang(X1))\|~m1_subset_1(X2,k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_22, plain, (r1_cqc_the3(X1,k7_cqc_lang(X1,X2,X4),k7_cqc_lang(X1,X3,X5))\|~m1_qc_lang1(X1)\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~r5_cqc_the3(X1,X2,X3)\|~r5_cqc_the3(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_23, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m2_subset_1(X1,X3,X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_24, plain, (m1_subset_1(k3_cqc_lang(X1),k1_zfmisc_1(k9_qc_lang1(X1)))\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_25, plain, (~m1_qc_lang1(X1)\|~v1_xboole_0(k9_qc_lang1(X1))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_26, plain, (~m1_qc_lang1(X1)\|~v1_xboole_0(k3_cqc_lang(X1))), inference(split_conjunct,[status(thm)],[c_0_18])). fof(c_0_27, negated_conjecture, (m1_qc_lang1(esk1_0)&(m2_subset_1(esk2_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))&(m2_subset_1(esk3_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))&(m2_subset_1(esk4_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))&(m2_subset_1(esk5_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))&((r5_cqc_the3(esk1_0,esk2_0,esk3_0)&r5_cqc_the3(esk1_0,esk4_0,esk5_0))&~r5_cqc_the3(esk1_0,k7_cqc_lang(esk1_0,esk2_0,esk4_0),k7_cqc_lang(esk1_0,esk3_0,esk5_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])). cnf(c_0_28, plain, (r5_cqc_the3(X1,X2,k7_cqc_lang(X1,X3,X4))\|~r1_cqc_the3(X1,k7_cqc_lang(X1,X3,X4),X2)\|~r1_cqc_the3(X1,X2,k7_cqc_lang(X1,X3,X4))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)\|~m1_subset_1(X4,k3_cqc_lang(X1))\|~m1_subset_1(X3,k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_21])])). cnf(c_0_29, plain, (r1_cqc_the3(X1,k7_cqc_lang(X1,X2,X4),k7_cqc_lang(X1,X3,X5))\|~m1_qc_lang1(X1)\|~r5_cqc_the3(X1,X4,X5)\|~r5_cqc_the3(X1,X2,X3)\|~m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_30, plain, (v1_xboole_0(k3_cqc_lang(X1))\|v1_xboole_0(k9_qc_lang1(X1))\|m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_subset_1(X2,k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24])])). cnf(c_0_31, plain, (~m1_qc_lang1(X1)\|~v1_xboole_0(k9_qc_lang1(X1))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_32, plain, (~m1_qc_lang1(X1)\|~v1_xboole_0(k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_33, plain, (m1_subset_1(X1,X3)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_34, negated_conjecture, (m2_subset_1(esk4_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_35, negated_conjecture, (m1_qc_lang1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_36, plain, (r1_cqc_the3(X1,X2,X3)\|~r5_cqc_the3(X1,X2,X3)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_37, negated_conjecture, (m2_subset_1(esk5_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_38, negated_conjecture, (m2_subset_1(esk2_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_39, negated_conjecture, (m2_subset_1(esk3_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_40, plain, (r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~r1_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~m1_subset_1(X5,k3_cqc_lang(X1))\|~m1_subset_1(X4,k3_cqc_lang(X1))\|~m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)\|~r5_cqc_the3(X1,X5,X3)\|~r5_cqc_the3(X1,X4,X2)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29])])). cnf(c_0_41, plain, (m2_subset_1(X1,k9_qc_lang1(X2),k3_cqc_lang(X2))\|~m1_subset_1(X1,k3_cqc_lang(X2))\|~m1_qc_lang1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_30, c_0_31]), c_0_32])). cnf(c_0_42, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m1_subset_1(X1,X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_43, negated_conjecture, (m2_subset_1(esk4_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_44, negated_conjecture, (m1_qc_lang1(esk1_0)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_45, plain, (r1_cqc_the3(X1,X2,X3)\|~m1_qc_lang1(X1)\|~r5_cqc_the3(X1,X2,X3)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_46, negated_conjecture, (m2_subset_1(esk5_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_47, negated_conjecture, (r5_cqc_the3(esk1_0,esk4_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_48, plain, (r1_cqc_the3(X1,X2,X3)\|~r5_cqc_the3(X1,X3,X2)\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_49, negated_conjecture, (m2_subset_1(esk2_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_50, negated_conjecture, (m2_subset_1(esk3_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_51, negated_conjecture, (r5_cqc_the3(esk1_0,esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_52, plain, (r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~r1_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~m1_subset_1(X5,k3_cqc_lang(X1))\|~m1_subset_1(X4,k3_cqc_lang(X1))\|~r5_cqc_the3(X1,X5,X3)\|~r5_cqc_the3(X1,X4,X2)\|~m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_40, c_0_41]), c_0_41])). cnf(c_0_53, plain, (v1_xboole_0(k9_qc_lang1(X1))\|v1_xboole_0(k3_cqc_lang(X1))\|m1_subset_1(X2,k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_24])])). cnf(c_0_54, negated_conjecture, (r5_cqc_the3(esk1_0,X1,esk4_0)\|~r1_cqc_the3(esk1_0,esk4_0,X1)\|~r1_cqc_the3(esk1_0,X1,esk4_0)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_43]), c_0_44])])])). cnf(c_0_55, negated_conjecture, (r1_cqc_the3(esk1_0,X1,esk5_0)\|~r5_cqc_the3(esk1_0,X1,esk5_0)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_44])])])). cnf(c_0_56, negated_conjecture, (r5_cqc_the3(esk1_0,esk4_0,esk5_0)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_57, plain, (r1_cqc_the3(X1,X2,X3)\|~m1_qc_lang1(X1)\|~r5_cqc_the3(X1,X3,X2)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_58, negated_conjecture, (r5_cqc_the3(esk1_0,X1,esk2_0)\|~r1_cqc_the3(esk1_0,esk2_0,X1)\|~r1_cqc_the3(esk1_0,X1,esk2_0)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_49]), c_0_44])])])). cnf(c_0_59, negated_conjecture, (r1_cqc_the3(esk1_0,X1,esk3_0)\|~r5_cqc_the3(esk1_0,X1,esk3_0)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_50]), c_0_44])])])). cnf(c_0_60, negated_conjecture, (r5_cqc_the3(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_61, negated_conjecture, (~r5_cqc_the3(esk1_0,k7_cqc_lang(esk1_0,esk2_0,esk4_0),k7_cqc_lang(esk1_0,esk3_0,esk5_0))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_62, plain, (r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~m1_subset_1(X5,k3_cqc_lang(X1))\|~m1_subset_1(X4,k3_cqc_lang(X1))\|~r5_cqc_the3(X1,X5,X3)\|~r5_cqc_the3(X1,X4,X2)\|~m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)\|~r5_cqc_the3(X1,X3,X5)\|~r5_cqc_the3(X1,X2,X4)\|~m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_29])])). cnf(c_0_63, plain, (m1_subset_1(X1,k3_cqc_lang(X2))\|~m2_subset_1(X1,k9_qc_lang1(X2),k3_cqc_lang(X2))\|~m1_qc_lang1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_53, c_0_32]), c_0_31])). cnf(c_0_64, negated_conjecture, (r5_cqc_the3(esk1_0,esk5_0,esk4_0)\|~r1_cqc_the3(esk1_0,esk5_0,esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_46]), c_0_56]), c_0_43])])])). cnf(c_0_65, negated_conjecture, (r1_cqc_the3(esk1_0,X1,esk4_0)\|~r5_cqc_the3(esk1_0,esk4_0,X1)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_43]), c_0_44])])])). cnf(c_0_66, negated_conjecture, (r5_cqc_the3(esk1_0,esk3_0,esk2_0)\|~r1_cqc_the3(esk1_0,esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_50]), c_0_60]), c_0_49])])])). cnf(c_0_67, negated_conjecture, (r1_cqc_the3(esk1_0,X1,esk2_0)\|~r5_cqc_the3(esk1_0,esk2_0,X1)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_49]), c_0_44])])])). cnf(c_0_68, negated_conjecture, (~r5_cqc_the3(esk1_0,k7_cqc_lang(esk1_0,esk2_0,esk4_0),k7_cqc_lang(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_69, plain, (r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~m1_subset_1(X5,k3_cqc_lang(X1))\|~m1_subset_1(X4,k3_cqc_lang(X1))\|~r5_cqc_the3(X1,X5,X3)\|~r5_cqc_the3(X1,X4,X2)\|~r5_cqc_the3(X1,X3,X5)\|~r5_cqc_the3(X1,X2,X4)\|~m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_62, c_0_41]), c_0_41])). cnf(c_0_70, negated_conjecture, (m1_subset_1(esk5_0,k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_46]), c_0_44])])])). cnf(c_0_71, negated_conjecture, (m1_subset_1(esk3_0,k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_50]), c_0_44])])])). cnf(c_0_72, negated_conjecture, (r5_cqc_the3(esk1_0,esk5_0,esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_56]), c_0_46])])])). cnf(c_0_73, negated_conjecture, (r5_cqc_the3(esk1_0,esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67]), c_0_60]), c_0_50])])])). cnf(c_0_74, negated_conjecture, (~m2_subset_1(k7_cqc_lang(esk1_0,esk2_0,esk4_0),k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_56]), c_0_60]), c_0_43]), c_0_49]), c_0_44])])])). cnf(c_0_75, negated_conjecture, (m1_subset_1(esk4_0,k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_43]), c_0_44])])])). cnf(c_0_76, negated_conjecture, (m1_subset_1(esk2_0,k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_49]), c_0_44])])])). cnf(c_0_77, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_21]), c_0_75]), c_0_76]), c_0_44])]), ['proof']). # SZS output end CNFRefutation	reserve A for QC-alphabet; reserve p, q, r, s, p1, q1 for Element of CQC-WFF(A), X, Y, Z, X1, X2 for Subset of CQC-WFF(A), h for QC-formula of A, x, y for bound_QC-variable of A, n for Element of NAT; theorem p \|-\| q & r \|-\| s implies p '&' r \|-\| q '&' s proof assume that A1: p \|-\| q and A2: r \|-\| s; A3: q '&' s \|- p '&' r by A1,A2,Lm4; p '&' r \|- q '&' s by A1,A2,Lm4; hence thesis by A3,Def5; end;	Convert the following ATP output trace into a readable Mizar proof.
t10_lfuzzy_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(redefinition_r2_relset_1, axiom, ![X1, X2, X3, X4]:((m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(r2_relset_1(X1,X2,X3,X4)<=>X3=X4)), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', redefinition_r2_relset_1)). fof(d4_lfuzzy_1, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),k1_numbers)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers))))))=>(v2_lfuzzy_1(X2,X1)<=>r2_relset_1(k2_zfmisc_1(X1,X1),k1_numbers,k2_fuzzy_4(X1,X1,X2),X2)))), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', d4_lfuzzy_1)). fof(dt_k2_fuzzy_4, axiom, ![X1, X2, X3]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&(v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X3)&(v1_funct_2(X3,k2_zfmisc_1(X2,X1),k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X1),k1_numbers))))))))=>(v5_relat_1(k2_fuzzy_4(X1,X2,X3),k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(k2_fuzzy_4(X1,X2,X3))&(v1_funct_2(k2_fuzzy_4(X1,X2,X3),k2_zfmisc_1(X1,X2),k1_numbers)&m1_subset_1(k2_fuzzy_4(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers))))))), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', dt_k2_fuzzy_4)). fof(t10_lfuzzy_1, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),k1_numbers)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers))))))=>![X3]:((v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X3)&(v1_funct_2(X3,k2_zfmisc_1(X1,X1),k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers))))))=>((v2_lfuzzy_1(X2,X1)&v2_lfuzzy_1(X3,X1))=>r2_relset_1(k2_zfmisc_1(X1,X1),k1_numbers,k2_fuzzy_4(X1,X1,k2_lfuzzy_1(k2_zfmisc_1(X1,X1),X2,X3)),k2_lfuzzy_1(k2_zfmisc_1(X1,X1),X2,X3)))))), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', t10_lfuzzy_1)). fof(t7_fuzzy_4, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(~(v1_xboole_0(X2))=>![X3]:((v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X3)&(v1_funct_2(X3,k2_zfmisc_1(X1,X2),k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers))))))=>![X4]:((v5_relat_1(X4,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X4)&(v1_funct_2(X4,k2_zfmisc_1(X1,X2),k1_numbers)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers))))))=>r2_relset_1(k2_zfmisc_1(X2,X1),k1_numbers,k2_fuzzy_4(X2,X1,k2_fuzzy_1(k2_zfmisc_1(X1,X2),X3,X4)),k2_fuzzy_1(k2_zfmisc_1(X2,X1),k2_fuzzy_4(X2,X1,X3),k2_fuzzy_4(X2,X1,X4))))))), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', t7_fuzzy_4)). fof(redefinition_k2_lfuzzy_1, axiom, ![X1, X2, X3]:((~(v1_xboole_0(X1))&((v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X2)&(v1_funct_2(X2,X1,k1_numbers)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))))&(v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X3)&(v1_funct_2(X3,X1,k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))))))=>k2_lfuzzy_1(X1,X2,X3)=k2_fuzzy_1(X1,X2,X3)), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', redefinition_k2_lfuzzy_1)). fof(fc10_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&~(v1_xboole_0(X2)))=>~(v1_xboole_0(k2_zfmisc_1(X1,X2)))), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', fc10_subset_1)). fof(c_0_7, plain, ![X8, X9, X10, X11]:((~r2_relset_1(X8,X9,X10,X11)\|X10=X11\|(~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(X8,X9)))\|~m1_subset_1(X11,k1_zfmisc_1(k2_zfmisc_1(X8,X9)))))&(X10!=X11\|r2_relset_1(X8,X9,X10,X11)\|(~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(X8,X9)))\|~m1_subset_1(X11,k1_zfmisc_1(k2_zfmisc_1(X8,X9)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r2_relset_1])])])). fof(c_0_8, plain, ![X12, X13]:((~v2_lfuzzy_1(X13,X12)\|r2_relset_1(k2_zfmisc_1(X12,X12),k1_numbers,k2_fuzzy_4(X12,X12,X13),X13)\|(~v5_relat_1(X13,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X13)\|(~v1_funct_2(X13,k2_zfmisc_1(X12,X12),k1_numbers)\|~m1_subset_1(X13,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X12,X12),k1_numbers))))))\|v1_xboole_0(X12))&(~r2_relset_1(k2_zfmisc_1(X12,X12),k1_numbers,k2_fuzzy_4(X12,X12,X13),X13)\|v2_lfuzzy_1(X13,X12)\|(~v5_relat_1(X13,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X13)\|(~v1_funct_2(X13,k2_zfmisc_1(X12,X12),k1_numbers)\|~m1_subset_1(X13,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X12,X12),k1_numbers))))))\|v1_xboole_0(X12))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_lfuzzy_1])])])])])). cnf(c_0_9, plain, (X3=X4\|~r2_relset_1(X1,X2,X3,X4)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_10, plain, (r2_relset_1(k2_zfmisc_1(X2,X2),k1_numbers,k2_fuzzy_4(X2,X2,X1),X1)\|v1_xboole_0(X2)\|~v2_lfuzzy_1(X1,X2)\|~v5_relat_1(X1,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X1)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_8])). fof(c_0_11, plain, ![X14, X15, X16]:((v5_relat_1(k2_fuzzy_4(X14,X15,X16),k1_rcomp_1(k6_numbers,np__1))\|(v1_xboole_0(X14)\|(v1_xboole_0(X15)\|(~v5_relat_1(X16,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,k2_zfmisc_1(X15,X14),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X15,X14),k1_numbers)))))))))&((v1_funct_1(k2_fuzzy_4(X14,X15,X16))\|(v1_xboole_0(X14)\|(v1_xboole_0(X15)\|(~v5_relat_1(X16,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,k2_zfmisc_1(X15,X14),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X15,X14),k1_numbers)))))))))&((v1_funct_2(k2_fuzzy_4(X14,X15,X16),k2_zfmisc_1(X14,X15),k1_numbers)\|(v1_xboole_0(X14)\|(v1_xboole_0(X15)\|(~v5_relat_1(X16,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,k2_zfmisc_1(X15,X14),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X15,X14),k1_numbers)))))))))&(m1_subset_1(k2_fuzzy_4(X14,X15,X16),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X14,X15),k1_numbers)))\|(v1_xboole_0(X14)\|(v1_xboole_0(X15)\|(~v5_relat_1(X16,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,k2_zfmisc_1(X15,X14),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X15,X14),k1_numbers)))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_fuzzy_4])])])])). fof(c_0_12, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:((v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),k1_numbers)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers))))))=>![X3]:((v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X3)&(v1_funct_2(X3,k2_zfmisc_1(X1,X1),k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers))))))=>((v2_lfuzzy_1(X2,X1)&v2_lfuzzy_1(X3,X1))=>r2_relset_1(k2_zfmisc_1(X1,X1),k1_numbers,k2_fuzzy_4(X1,X1,k2_lfuzzy_1(k2_zfmisc_1(X1,X1),X2,X3)),k2_lfuzzy_1(k2_zfmisc_1(X1,X1),X2,X3))))))), inference(assume_negation,[status(cth)],[t10_lfuzzy_1])). cnf(c_0_13, plain, (X3=X4\|~r2_relset_1(X1,X2,X3,X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_14, plain, (v1_xboole_0(X2)\|r2_relset_1(k2_zfmisc_1(X2,X2),k1_numbers,k2_fuzzy_4(X2,X2,X1),X1)\|~v1_funct_1(X1)\|~v2_lfuzzy_1(X1,X2)\|~v5_relat_1(X1,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_15, plain, (m1_subset_1(k2_fuzzy_4(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))\|v1_xboole_0(X1)\|v1_xboole_0(X2)\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X3)\|~v1_funct_2(X3,k2_zfmisc_1(X2,X1),k1_numbers)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X1),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_16, negated_conjecture, (~v1_xboole_0(esk1_0)&((v5_relat_1(esk2_0,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(esk2_0)&(v1_funct_2(esk2_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)&m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers))))))&((v5_relat_1(esk3_0,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(esk3_0)&(v1_funct_2(esk3_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)&m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers))))))&((v2_lfuzzy_1(esk2_0,esk1_0)&v2_lfuzzy_1(esk3_0,esk1_0))&~r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)),k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_12])])])])). fof(c_0_17, plain, ![X17, X18, X19, X20]:(v1_xboole_0(X17)\|(v1_xboole_0(X18)\|(~v5_relat_1(X19,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X19)\|(~v1_funct_2(X19,k2_zfmisc_1(X17,X18),k1_numbers)\|~m1_subset_1(X19,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X17,X18),k1_numbers)))))\|(~v5_relat_1(X20,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X20)\|(~v1_funct_2(X20,k2_zfmisc_1(X17,X18),k1_numbers)\|~m1_subset_1(X20,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X17,X18),k1_numbers)))))\|r2_relset_1(k2_zfmisc_1(X18,X17),k1_numbers,k2_fuzzy_4(X18,X17,k2_fuzzy_1(k2_zfmisc_1(X17,X18),X19,X20)),k2_fuzzy_1(k2_zfmisc_1(X18,X17),k2_fuzzy_4(X18,X17,X19),k2_fuzzy_4(X18,X17,X20))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t7_fuzzy_4])])])])). cnf(c_0_18, plain, (k2_fuzzy_4(X1,X1,X2)=X2\|v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers)))\|~m1_subset_1(k2_fuzzy_4(X1,X1,X2),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers)))\|~v2_lfuzzy_1(X2,X1)\|~v1_funct_2(X2,k2_zfmisc_1(X1,X1),k1_numbers)\|~v1_funct_1(X2)\|~v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_13, c_0_14])])). cnf(c_0_19, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|m1_subset_1(k2_fuzzy_4(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))\|~v1_funct_1(X3)\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_2(X3,k2_zfmisc_1(X2,X1),k1_numbers)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X1),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_20, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_21, negated_conjecture, (v2_lfuzzy_1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_22, negated_conjecture, (v1_funct_2(esk3_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_23, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_24, negated_conjecture, (v5_relat_1(esk3_0,k1_rcomp_1(k6_numbers,np__1))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_25, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_26, plain, ![X21, X22, X23]:(v1_xboole_0(X21)\|(~v5_relat_1(X22,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X22)\|(~v1_funct_2(X22,X21,k1_numbers)\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(X21,k1_numbers)))))\|(~v5_relat_1(X23,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X23)\|(~v1_funct_2(X23,X21,k1_numbers)\|~m1_subset_1(X23,k1_zfmisc_1(k2_zfmisc_1(X21,k1_numbers)))))))\|k2_lfuzzy_1(X21,X22,X23)=k2_fuzzy_1(X21,X22,X23)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k2_lfuzzy_1])])])). cnf(c_0_27, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|r2_relset_1(k2_zfmisc_1(X2,X1),k1_numbers,k2_fuzzy_4(X2,X1,k2_fuzzy_1(k2_zfmisc_1(X1,X2),X3,X4)),k2_fuzzy_1(k2_zfmisc_1(X2,X1),k2_fuzzy_4(X2,X1,X3),k2_fuzzy_4(X2,X1,X4)))\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X3)\|~v1_funct_2(X3,k2_zfmisc_1(X1,X2),k1_numbers)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))\|~v5_relat_1(X4,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X4)\|~v1_funct_2(X4,k2_zfmisc_1(X1,X2),k1_numbers)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_28, plain, (k2_fuzzy_4(X1,X1,X2)=X2\|v1_xboole_0(X1)\|~v2_lfuzzy_1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers)))\|~v1_funct_2(X2,k2_zfmisc_1(X1,X1),k1_numbers)\|~v1_funct_1(X2)\|~v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19])])). cnf(c_0_29, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_30, negated_conjecture, (v2_lfuzzy_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_31, negated_conjecture, (v1_funct_2(esk3_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_32, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_33, negated_conjecture, (v5_relat_1(esk3_0,k1_rcomp_1(k6_numbers,np__1))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_34, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_35, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_36, negated_conjecture, (v2_lfuzzy_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_37, negated_conjecture, (v1_funct_2(esk2_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_38, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_39, negated_conjecture, (v5_relat_1(esk2_0,k1_rcomp_1(k6_numbers,np__1))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_40, negated_conjecture, (~r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)),k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_41, plain, (v1_xboole_0(X1)\|k2_lfuzzy_1(X1,X2,X3)=k2_fuzzy_1(X1,X2,X3)\|~v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X2)\|~v1_funct_2(X2,X1,k1_numbers)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X3)\|~v1_funct_2(X3,X1,k1_numbers)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_42, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|r2_relset_1(k2_zfmisc_1(X2,X1),k1_numbers,k2_fuzzy_4(X2,X1,k2_fuzzy_1(k2_zfmisc_1(X1,X2),X3,X4)),k2_fuzzy_1(k2_zfmisc_1(X2,X1),k2_fuzzy_4(X2,X1,X3),k2_fuzzy_4(X2,X1,X4)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v5_relat_1(X4,k1_rcomp_1(k6_numbers,np__1))\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_2(X4,k2_zfmisc_1(X1,X2),k1_numbers)\|~v1_funct_2(X3,k2_zfmisc_1(X1,X2),k1_numbers)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_43, negated_conjecture, (k2_fuzzy_4(esk1_0,esk1_0,esk3_0)=esk3_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30]), c_0_31]), c_0_32]), c_0_33])]), c_0_34])])). cnf(c_0_44, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_45, negated_conjecture, (v2_lfuzzy_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_46, negated_conjecture, (v1_funct_2(esk2_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_47, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_48, negated_conjecture, (v5_relat_1(esk2_0,k1_rcomp_1(k6_numbers,np__1))), inference(evalgc,[status(thm)],[c_0_39])). fof(c_0_49, plain, ![X24, X25]:(v1_xboole_0(X24)\|v1_xboole_0(X25)\|~v1_xboole_0(k2_zfmisc_1(X24,X25))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc10_subset_1])])])). cnf(c_0_50, negated_conjecture, (~r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)),k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_51, plain, (k2_lfuzzy_1(X1,X2,X3)=k2_fuzzy_1(X1,X2,X3)\|v1_xboole_0(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_2(X3,X1,k1_numbers)\|~v1_funct_2(X2,X1,k1_numbers)\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_52, negated_conjecture, (r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),X1,esk3_0)),k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),k2_fuzzy_4(esk1_0,esk1_0,X1),esk3_0))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)))\|~v1_funct_2(X1,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)\|~v1_funct_1(X1)\|~v5_relat_1(X1,k1_rcomp_1(k6_numbers,np__1))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_29]), c_0_31]), c_0_32]), c_0_33])]), c_0_34])])). cnf(c_0_53, negated_conjecture, (k2_fuzzy_4(esk1_0,esk1_0,esk2_0)=esk2_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_44]), c_0_45]), c_0_46]), c_0_47]), c_0_48])]), c_0_34])])). cnf(c_0_54, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|~v1_xboole_0(k2_zfmisc_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_55, negated_conjecture, (v1_xboole_0(k2_zfmisc_1(esk1_0,esk1_0))\|~r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)),k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_29]), c_0_44]), c_0_31]), c_0_46]), c_0_32]), c_0_47]), c_0_33]), c_0_48])])])). cnf(c_0_56, negated_conjecture, (r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)),k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_44]), c_0_46]), c_0_47]), c_0_48])])])). cnf(c_0_57, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|~v1_xboole_0(k2_zfmisc_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_58, negated_conjecture, (v1_xboole_0(k2_zfmisc_1(esk1_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55, c_0_56])])])). cnf(c_0_59, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_58]), c_0_34]), ['proof']). # SZS output end CNFRefutation	reserve X, Y for non empty set; theorem Th10: for R,S being RMembership_Func of X,X holds R is symmetric & S is symmetric implies converse max(R,S) = max(R,S) proof let R,S be RMembership_Func of X,X; assume R is symmetric & S is symmetric; then converse R = R & converse S =S by Def4; hence thesis by FUZZY_4:7; end;	Convert the following ATP output trace into a readable Mizar proof.
t36_yellow_3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t36_yellow_3, conjecture, ![X1]:((~(v2_struct_0(X1))&(v5_orders_2(X1)&l1_orders_2(X1)))=>![X2]:((~(v2_struct_0(X2))&(v5_orders_2(X2)&l1_orders_2(X2)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))=>![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>((r2_yellow_0(X1,X3)&(r2_yellow_0(X2,X4)&![X7]:(m1_subset_1(X7,u1_struct_0(k3_yellow_3(X1,X2)))=>(r1_lattice3(k3_yellow_3(X1,X2),k6_yellow_3(X1,X2,X3,X4),X7)=>r1_orders_2(k3_yellow_3(X1,X2),X7,k7_yellow_3(X1,X2,X5,X6))))))=>(![X7]:(m1_subset_1(X7,u1_struct_0(X1))=>(r1_lattice3(X1,X3,X7)=>r1_orders_2(X1,X7,X5)))&![X7]:(m1_subset_1(X7,u1_struct_0(X2))=>(r1_lattice3(X2,X4,X7)=>r1_orders_2(X2,X7,X6))))))))))), file('/scratch/mptp/predsminms1/t36_yellow_3__0', t36_yellow_3)). fof(t33_yellow_3, axiom, ![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>![X2]:((~(v2_struct_0(X2))&l1_orders_2(X2))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))=>![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>((r1_lattice3(X1,X3,X5)&r1_lattice3(X2,X4,X6))=>r1_lattice3(k3_yellow_3(X1,X2),k6_yellow_3(X1,X2,X3,X4),k7_yellow_3(X1,X2,X5,X6))))))))), file('/scratch/mptp/predsminms1/t36_yellow_3__0', t33_yellow_3)). fof(t11_yellow_3, axiom, ![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>![X2]:((~(v2_struct_0(X2))&l1_orders_2(X2))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>![X5]:(m1_subset_1(X5,u1_struct_0(X2))=>![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>((r1_orders_2(X1,X3,X4)&r1_orders_2(X2,X5,X6))<=>r1_orders_2(k3_yellow_3(X1,X2),k7_yellow_3(X1,X2,X3,X5),k7_yellow_3(X1,X2,X4,X6))))))))), file('/scratch/mptp/predsminms1/t36_yellow_3__0', t11_yellow_3)). fof(dt_k7_yellow_3, axiom, ![X1, X2, X3, X4]:(((~(v2_struct_0(X1))&l1_orders_2(X1))&((~(v2_struct_0(X2))&l1_orders_2(X2))&(m1_subset_1(X3,u1_struct_0(X1))&m1_subset_1(X4,u1_struct_0(X2)))))=>m1_subset_1(k7_yellow_3(X1,X2,X3,X4),u1_struct_0(k3_yellow_3(X1,X2)))), file('/scratch/mptp/predsminms1/t36_yellow_3__0', dt_k7_yellow_3)). fof(d8_yellow_0, axiom, ![X1]:(l1_orders_2(X1)=>![X2]:(r2_yellow_0(X1,X2)<=>?[X3]:(m1_subset_1(X3,u1_struct_0(X1))&(r1_lattice3(X1,X2,X3)&(![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>(r1_lattice3(X1,X2,X4)=>r1_orders_2(X1,X4,X3)))&![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>((r1_lattice3(X1,X2,X4)&![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>(r1_lattice3(X1,X2,X5)=>r1_orders_2(X1,X5,X4))))=>X4=X3))))))), file('/scratch/mptp/predsminms1/t36_yellow_3__0', d8_yellow_0)). fof(c_0_5, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v5_orders_2(X1)&l1_orders_2(X1)))=>![X2]:((~(v2_struct_0(X2))&(v5_orders_2(X2)&l1_orders_2(X2)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))=>![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>((r2_yellow_0(X1,X3)&(r2_yellow_0(X2,X4)&![X7]:(m1_subset_1(X7,u1_struct_0(k3_yellow_3(X1,X2)))=>(r1_lattice3(k3_yellow_3(X1,X2),k6_yellow_3(X1,X2,X3,X4),X7)=>r1_orders_2(k3_yellow_3(X1,X2),X7,k7_yellow_3(X1,X2,X5,X6))))))=>(![X7]:(m1_subset_1(X7,u1_struct_0(X1))=>(r1_lattice3(X1,X3,X7)=>r1_orders_2(X1,X7,X5)))&![X7]:(m1_subset_1(X7,u1_struct_0(X2))=>(r1_lattice3(X2,X4,X7)=>r1_orders_2(X2,X7,X6)))))))))))), inference(assume_negation,[status(cth)],[t36_yellow_3])). fof(c_0_6, negated_conjecture, ![X14]:((~v2_struct_0(esk1_0)&(v5_orders_2(esk1_0)&l1_orders_2(esk1_0)))&((~v2_struct_0(esk2_0)&(v5_orders_2(esk2_0)&l1_orders_2(esk2_0)))&(m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&(m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0)))&(m1_subset_1(esk5_0,u1_struct_0(esk1_0))&(m1_subset_1(esk6_0,u1_struct_0(esk2_0))&((r2_yellow_0(esk1_0,esk3_0)&(r2_yellow_0(esk2_0,esk4_0)&(~m1_subset_1(X14,u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))\|(~r1_lattice3(k3_yellow_3(esk1_0,esk2_0),k6_yellow_3(esk1_0,esk2_0,esk3_0,esk4_0),X14)\|r1_orders_2(k3_yellow_3(esk1_0,esk2_0),X14,k7_yellow_3(esk1_0,esk2_0,esk5_0,esk6_0))))))&(((m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|m1_subset_1(esk7_0,u1_struct_0(esk1_0)))&((r1_lattice3(esk2_0,esk4_0,esk8_0)\|m1_subset_1(esk7_0,u1_struct_0(esk1_0)))&(~r1_orders_2(esk2_0,esk8_0,esk6_0)\|m1_subset_1(esk7_0,u1_struct_0(esk1_0)))))&(((m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|r1_lattice3(esk1_0,esk3_0,esk7_0))&((r1_lattice3(esk2_0,esk4_0,esk8_0)\|r1_lattice3(esk1_0,esk3_0,esk7_0))&(~r1_orders_2(esk2_0,esk8_0,esk6_0)\|r1_lattice3(esk1_0,esk3_0,esk7_0))))&((m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|~r1_orders_2(esk1_0,esk7_0,esk5_0))&((r1_lattice3(esk2_0,esk4_0,esk8_0)\|~r1_orders_2(esk1_0,esk7_0,esk5_0))&(~r1_orders_2(esk2_0,esk8_0,esk6_0)\|~r1_orders_2(esk1_0,esk7_0,esk5_0))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5])])])])])])). fof(c_0_7, plain, ![X17, X18, X19, X20, X21, X22]:(v2_struct_0(X17)\|~l1_orders_2(X17)\|(v2_struct_0(X18)\|~l1_orders_2(X18)\|(~m1_subset_1(X19,k1_zfmisc_1(u1_struct_0(X17)))\|(~m1_subset_1(X20,k1_zfmisc_1(u1_struct_0(X18)))\|(~m1_subset_1(X21,u1_struct_0(X17))\|(~m1_subset_1(X22,u1_struct_0(X18))\|(~r1_lattice3(X17,X19,X21)\|~r1_lattice3(X18,X20,X22)\|r1_lattice3(k3_yellow_3(X17,X18),k6_yellow_3(X17,X18,X19,X20),k7_yellow_3(X17,X18,X21,X22))))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t33_yellow_3])])])])). fof(c_0_8, plain, ![X23, X24, X25, X26, X27, X28]:((~r1_orders_2(X23,X25,X26)\|~r1_orders_2(X24,X27,X28)\|r1_orders_2(k3_yellow_3(X23,X24),k7_yellow_3(X23,X24,X25,X27),k7_yellow_3(X23,X24,X26,X28))\|~m1_subset_1(X28,u1_struct_0(X24))\|~m1_subset_1(X27,u1_struct_0(X24))\|~m1_subset_1(X26,u1_struct_0(X23))\|~m1_subset_1(X25,u1_struct_0(X23))\|(v2_struct_0(X24)\|~l1_orders_2(X24))\|(v2_struct_0(X23)\|~l1_orders_2(X23)))&((r1_orders_2(X23,X25,X26)\|~r1_orders_2(k3_yellow_3(X23,X24),k7_yellow_3(X23,X24,X25,X27),k7_yellow_3(X23,X24,X26,X28))\|~m1_subset_1(X28,u1_struct_0(X24))\|~m1_subset_1(X27,u1_struct_0(X24))\|~m1_subset_1(X26,u1_struct_0(X23))\|~m1_subset_1(X25,u1_struct_0(X23))\|(v2_struct_0(X24)\|~l1_orders_2(X24))\|(v2_struct_0(X23)\|~l1_orders_2(X23)))&(r1_orders_2(X24,X27,X28)\|~r1_orders_2(k3_yellow_3(X23,X24),k7_yellow_3(X23,X24,X25,X27),k7_yellow_3(X23,X24,X26,X28))\|~m1_subset_1(X28,u1_struct_0(X24))\|~m1_subset_1(X27,u1_struct_0(X24))\|~m1_subset_1(X26,u1_struct_0(X23))\|~m1_subset_1(X25,u1_struct_0(X23))\|(v2_struct_0(X24)\|~l1_orders_2(X24))\|(v2_struct_0(X23)\|~l1_orders_2(X23))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t11_yellow_3])])])])])). cnf(c_0_9, negated_conjecture, (r1_orders_2(k3_yellow_3(esk1_0,esk2_0),X1,k7_yellow_3(esk1_0,esk2_0,esk5_0,esk6_0))\|~m1_subset_1(X1,u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))\|~r1_lattice3(k3_yellow_3(esk1_0,esk2_0),k6_yellow_3(esk1_0,esk2_0,esk3_0,esk4_0),X1)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_10, plain, (v2_struct_0(X1)\|v2_struct_0(X2)\|r1_lattice3(k3_yellow_3(X1,X2),k6_yellow_3(X1,X2,X3,X4),k7_yellow_3(X1,X2,X5,X6))\|~l1_orders_2(X1)\|~l1_orders_2(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X6,u1_struct_0(X2))\|~r1_lattice3(X1,X3,X5)\|~r1_lattice3(X2,X4,X6)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_11, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_12, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_13, negated_conjecture, (l1_orders_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_14, negated_conjecture, (l1_orders_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_15, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_16, negated_conjecture, (~v2_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_17, plain, (r1_orders_2(X1,X2,X3)\|v2_struct_0(X1)\|v2_struct_0(X4)\|~r1_orders_2(k3_yellow_3(X4,X1),k7_yellow_3(X4,X1,X5,X2),k7_yellow_3(X4,X1,X6,X3))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X6,u1_struct_0(X4))\|~m1_subset_1(X5,u1_struct_0(X4))\|~l1_orders_2(X1)\|~l1_orders_2(X4)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_18, negated_conjecture, (r1_orders_2(k3_yellow_3(esk1_0,esk2_0),X1,k7_yellow_3(esk1_0,esk2_0,esk5_0,esk6_0))\|~m1_subset_1(X1,u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))\|~r1_lattice3(k3_yellow_3(esk1_0,esk2_0),k6_yellow_3(esk1_0,esk2_0,esk3_0,esk4_0),X1)), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_19, plain, (v2_struct_0(X2)\|v2_struct_0(X1)\|r1_lattice3(k3_yellow_3(X1,X2),k6_yellow_3(X1,X2,X3,X4),k7_yellow_3(X1,X2,X5,X6))\|~l1_orders_2(X2)\|~l1_orders_2(X1)\|~r1_lattice3(X2,X4,X6)\|~r1_lattice3(X1,X3,X5)\|~m1_subset_1(X6,u1_struct_0(X2))\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_20, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0)))), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_21, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_22, negated_conjecture, (l1_orders_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_23, negated_conjecture, (l1_orders_2(esk1_0)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_24, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_25, negated_conjecture, (~v2_struct_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_26, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_27, negated_conjecture, (m1_subset_1(esk6_0,u1_struct_0(esk2_0))), inference(split_conjunct,[status(thm)],[c_0_6])). fof(c_0_28, plain, ![X29, X30, X31, X32]:(v2_struct_0(X29)\|~l1_orders_2(X29)\|(v2_struct_0(X30)\|~l1_orders_2(X30)\|(~m1_subset_1(X31,u1_struct_0(X29))\|~m1_subset_1(X32,u1_struct_0(X30))))\|m1_subset_1(k7_yellow_3(X29,X30,X31,X32),u1_struct_0(k3_yellow_3(X29,X30)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k7_yellow_3])])])). cnf(c_0_29, plain, (r1_orders_2(X1,X2,X3)\|v2_struct_0(X4)\|v2_struct_0(X1)\|~r1_orders_2(k3_yellow_3(X1,X4),k7_yellow_3(X1,X4,X2,X5),k7_yellow_3(X1,X4,X3,X6))\|~m1_subset_1(X6,u1_struct_0(X4))\|~m1_subset_1(X5,u1_struct_0(X4))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_orders_2(X4)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_30, plain, (v2_struct_0(X4)\|v2_struct_0(X1)\|r1_orders_2(X1,X2,X3)\|~l1_orders_2(X4)\|~l1_orders_2(X1)\|~m1_subset_1(X6,u1_struct_0(X4))\|~m1_subset_1(X5,u1_struct_0(X4))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r1_orders_2(k3_yellow_3(X4,X1),k7_yellow_3(X4,X1,X5,X2),k7_yellow_3(X4,X1,X6,X3))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_31, negated_conjecture, (r1_orders_2(k3_yellow_3(esk1_0,esk2_0),k7_yellow_3(esk1_0,esk2_0,X1,X2),k7_yellow_3(esk1_0,esk2_0,esk5_0,esk6_0))\|~m1_subset_1(k7_yellow_3(esk1_0,esk2_0,X1,X2),u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))\|~r1_lattice3(esk2_0,esk4_0,X2)\|~r1_lattice3(esk1_0,esk3_0,X1)\|~m1_subset_1(X2,u1_struct_0(esk2_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19]), c_0_20]), c_0_21]), c_0_22]), c_0_23])]), c_0_24]), c_0_25])])). cnf(c_0_32, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_33, negated_conjecture, (m1_subset_1(esk6_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_34, plain, (v2_struct_0(X1)\|v2_struct_0(X2)\|m1_subset_1(k7_yellow_3(X1,X2,X3,X4),u1_struct_0(k3_yellow_3(X1,X2)))\|~l1_orders_2(X1)\|~l1_orders_2(X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_35, plain, ![X33, X34, X36, X37, X39, X40, X43]:(((m1_subset_1(esk9_2(X33,X34),u1_struct_0(X33))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33))&((r1_lattice3(X33,X34,esk9_2(X33,X34))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33))&((~m1_subset_1(X36,u1_struct_0(X33))\|(~r1_lattice3(X33,X34,X36)\|r1_orders_2(X33,X36,esk9_2(X33,X34)))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33))&((m1_subset_1(esk10_3(X33,X34,X37),u1_struct_0(X33))\|~r1_lattice3(X33,X34,X37)\|X37=esk9_2(X33,X34)\|~m1_subset_1(X37,u1_struct_0(X33))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33))&((r1_lattice3(X33,X34,esk10_3(X33,X34,X37))\|~r1_lattice3(X33,X34,X37)\|X37=esk9_2(X33,X34)\|~m1_subset_1(X37,u1_struct_0(X33))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33))&(~r1_orders_2(X33,esk10_3(X33,X34,X37),X37)\|~r1_lattice3(X33,X34,X37)\|X37=esk9_2(X33,X34)\|~m1_subset_1(X37,u1_struct_0(X33))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33)))))))&(((m1_subset_1(esk12_3(X33,X39,X40),u1_struct_0(X33))\|m1_subset_1(esk11_3(X33,X39,X40),u1_struct_0(X33))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(((r1_lattice3(X33,X39,esk12_3(X33,X39,X40))\|m1_subset_1(esk11_3(X33,X39,X40),u1_struct_0(X33))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(~m1_subset_1(X43,u1_struct_0(X33))\|(~r1_lattice3(X33,X39,X43)\|r1_orders_2(X33,X43,esk12_3(X33,X39,X40)))\|m1_subset_1(esk11_3(X33,X39,X40),u1_struct_0(X33))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33)))&(esk12_3(X33,X39,X40)!=X40\|m1_subset_1(esk11_3(X33,X39,X40),u1_struct_0(X33))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))))&(((m1_subset_1(esk12_3(X33,X39,X40),u1_struct_0(X33))\|r1_lattice3(X33,X39,esk11_3(X33,X39,X40))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(((r1_lattice3(X33,X39,esk12_3(X33,X39,X40))\|r1_lattice3(X33,X39,esk11_3(X33,X39,X40))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(~m1_subset_1(X43,u1_struct_0(X33))\|(~r1_lattice3(X33,X39,X43)\|r1_orders_2(X33,X43,esk12_3(X33,X39,X40)))\|r1_lattice3(X33,X39,esk11_3(X33,X39,X40))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33)))&(esk12_3(X33,X39,X40)!=X40\|r1_lattice3(X33,X39,esk11_3(X33,X39,X40))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))))&((m1_subset_1(esk12_3(X33,X39,X40),u1_struct_0(X33))\|~r1_orders_2(X33,esk11_3(X33,X39,X40),X40)\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(((r1_lattice3(X33,X39,esk12_3(X33,X39,X40))\|~r1_orders_2(X33,esk11_3(X33,X39,X40),X40)\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(~m1_subset_1(X43,u1_struct_0(X33))\|(~r1_lattice3(X33,X39,X43)\|r1_orders_2(X33,X43,esk12_3(X33,X39,X40)))\|~r1_orders_2(X33,esk11_3(X33,X39,X40),X40)\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33)))&(esk12_3(X33,X39,X40)!=X40\|~r1_orders_2(X33,esk11_3(X33,X39,X40),X40)\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_yellow_0])])])])])])). cnf(c_0_36, plain, (v2_struct_0(X4)\|v2_struct_0(X1)\|r1_orders_2(X1,X2,X3)\|~l1_orders_2(X4)\|~l1_orders_2(X1)\|~m1_subset_1(X6,u1_struct_0(X4))\|~m1_subset_1(X5,u1_struct_0(X4))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r1_orders_2(k3_yellow_3(X1,X4),k7_yellow_3(X1,X4,X2,X5),k7_yellow_3(X1,X4,X3,X6))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_37, negated_conjecture, (r1_orders_2(esk2_0,X1,esk6_0)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk2_0))\|~r1_lattice3(esk2_0,esk4_0,X1)\|~r1_lattice3(esk1_0,esk3_0,X2)\|~m1_subset_1(k7_yellow_3(esk1_0,esk2_0,X2,X1),u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32]), c_0_33]), c_0_23]), c_0_22])]), c_0_25]), c_0_24])])). cnf(c_0_38, plain, (v2_struct_0(X2)\|v2_struct_0(X1)\|m1_subset_1(k7_yellow_3(X1,X2,X3,X4),u1_struct_0(k3_yellow_3(X1,X2)))\|~l1_orders_2(X2)\|~l1_orders_2(X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_39, plain, (r1_lattice3(X1,X2,esk9_2(X1,X2))\|~r2_yellow_0(X1,X2)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_40, negated_conjecture, (r2_yellow_0(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_41, negated_conjecture, (r1_orders_2(esk1_0,X1,esk5_0)\|~m1_subset_1(X2,u1_struct_0(esk2_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~r1_lattice3(esk2_0,esk4_0,X2)\|~r1_lattice3(esk1_0,esk3_0,X1)\|~m1_subset_1(k7_yellow_3(esk1_0,esk2_0,X1,X2),u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_31]), c_0_33]), c_0_32]), c_0_22]), c_0_23])]), c_0_24]), c_0_25])])). cnf(c_0_42, negated_conjecture, (r2_yellow_0(esk2_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_43, negated_conjecture, (r1_orders_2(esk2_0,X1,esk6_0)\|~r1_lattice3(esk2_0,esk4_0,X1)\|~r1_lattice3(esk1_0,esk3_0,X2)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38]), c_0_22]), c_0_23])]), c_0_24]), c_0_25])])). cnf(c_0_44, plain, (r1_lattice3(X1,X2,esk9_2(X1,X2))\|~l1_orders_2(X1)\|~r2_yellow_0(X1,X2)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_45, negated_conjecture, (r2_yellow_0(esk1_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_46, plain, (m1_subset_1(esk9_2(X1,X2),u1_struct_0(X1))\|~r2_yellow_0(X1,X2)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_47, negated_conjecture, (r1_orders_2(esk1_0,X1,esk5_0)\|~r1_lattice3(esk2_0,esk4_0,X2)\|~r1_lattice3(esk1_0,esk3_0,X1)\|~m1_subset_1(X2,u1_struct_0(esk2_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_38]), c_0_22]), c_0_23])]), c_0_24]), c_0_25])])). cnf(c_0_48, negated_conjecture, (r2_yellow_0(esk2_0,esk4_0)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_49, negated_conjecture, (r1_lattice3(esk1_0,esk3_0,esk7_0)\|~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_50, negated_conjecture, (r1_orders_2(esk2_0,X1,esk6_0)\|~r1_lattice3(esk2_0,esk4_0,X1)\|~m1_subset_1(esk9_2(esk1_0,esk3_0),u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_45]), c_0_23])])])). cnf(c_0_51, plain, (m1_subset_1(esk9_2(X1,X2),u1_struct_0(X1))\|~l1_orders_2(X1)\|~r2_yellow_0(X1,X2)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_52, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)\|~r1_orders_2(esk1_0,esk7_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_53, negated_conjecture, (r1_orders_2(esk1_0,X1,esk5_0)\|~r1_lattice3(esk1_0,esk3_0,X1)\|~m1_subset_1(esk9_2(esk2_0,esk4_0),u1_struct_0(esk2_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_44]), c_0_48]), c_0_22])])])). cnf(c_0_54, negated_conjecture, (r1_lattice3(esk1_0,esk3_0,esk7_0)\|~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_55, negated_conjecture, (r1_orders_2(esk2_0,X1,esk6_0)\|~r1_lattice3(esk2_0,esk4_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_45]), c_0_23])])])). cnf(c_0_56, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|r1_lattice3(esk1_0,esk3_0,esk7_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_57, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)\|r1_lattice3(esk1_0,esk3_0,esk7_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_58, negated_conjecture, (~r1_orders_2(esk2_0,esk8_0,esk6_0)\|~r1_orders_2(esk1_0,esk7_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_59, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))\|~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_60, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)\|~r1_orders_2(esk1_0,esk7_0,esk5_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_61, negated_conjecture, (r1_orders_2(esk1_0,X1,esk5_0)\|~r1_lattice3(esk1_0,esk3_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_51]), c_0_48]), c_0_22])])])). cnf(c_0_62, negated_conjecture, (r1_lattice3(esk1_0,esk3_0,esk7_0)\|~r1_lattice3(esk2_0,esk4_0,esk8_0)\|~m1_subset_1(esk8_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55])])). cnf(c_0_63, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|r1_lattice3(esk1_0,esk3_0,esk7_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_64, negated_conjecture, (r1_lattice3(esk1_0,esk3_0,esk7_0)\|r1_lattice3(esk2_0,esk4_0,esk8_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_65, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)\|m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_66, negated_conjecture, (~r1_orders_2(esk1_0,esk7_0,esk5_0)\|~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_67, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|~r1_orders_2(esk1_0,esk7_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_68, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))\|~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_69, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)\|~r1_lattice3(esk1_0,esk3_0,esk7_0)\|~m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61])])). cnf(c_0_70, negated_conjecture, (r1_lattice3(esk1_0,esk3_0,esk7_0)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_62, c_0_63]), c_0_64])). cnf(c_0_71, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))\|r1_lattice3(esk2_0,esk4_0,esk8_0)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_72, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_73, negated_conjecture, (~r1_orders_2(esk2_0,esk8_0,esk6_0)\|~r1_lattice3(esk1_0,esk3_0,esk7_0)\|~m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_61])])). cnf(c_0_74, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|~r1_orders_2(esk1_0,esk7_0,esk5_0)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_75, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))\|~r1_lattice3(esk2_0,esk4_0,esk8_0)\|~m1_subset_1(esk8_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_55])])). cnf(c_0_76, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])]), c_0_71])). cnf(c_0_77, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))\|m1_subset_1(esk8_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_78, negated_conjecture, (~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_73, c_0_68]), c_0_54])). cnf(c_0_79, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|~r1_lattice3(esk1_0,esk3_0,esk7_0)\|~m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_61])])). cnf(c_0_80, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75, c_0_76])]), c_0_77])). cnf(c_0_81, negated_conjecture, (~r1_lattice3(esk2_0,esk4_0,esk8_0)\|~m1_subset_1(esk8_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_55])])). cnf(c_0_82, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79, c_0_70]), c_0_80])])). cnf(c_0_83, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81, c_0_76]), c_0_82])]), ['proof']). # SZS output end CNFRefutation	theorem Th36: for S1, S2 being antisymmetric non empty RelStr for D1 being Subset of S1, D2 being Subset of S2 for x being Element of S1, y being Element of S2 st ex_inf_of D1,S1 & ex_inf_of D2,S2 & for b being Element of [:S1,S2:] st b is_<=_than [:D1,D2:] holds [x,y] >= b holds (for c being Element of S1 st c is_<=_than D1 holds x >= c) & for d being Element of S2 st d is_<=_than D2 holds y >= d proof let S1, S2 be antisymmetric non empty RelStr, D1 be Subset of S1, D2 be Subset of S2, x be Element of S1, y be Element of S2 such that A1: ex_inf_of D1,S1 and A2: ex_inf_of D2,S2 and A3: for b being Element of [:S1,S2:] st b is_<=_than [:D1,D2:] holds [x, y] >= b; thus for c being Element of S1 st c is_<=_than D1 holds x >= c proof A4: inf D2 is_<=_than D2 by A2,YELLOW_0:31; let b be Element of S1; assume b is_<=_than D1; then [x,y] >= [b,inf D2] by A3,A4,Th33; hence thesis by Th11; end; A5: inf D1 is_<=_than D1 by A1,YELLOW_0:31; let b be Element of S2; assume b is_<=_than D2; then [x,y] >= [inf D1,b] by A3,A5,Th33; hence thesis by Th11; end;	Convert the following ATP output trace into a readable Mizar proof.
t23_graph_5	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t23_graph_5, conjecture, ![X1, X2, X3]:((~(v2_struct_0(X3))&l1_graph_1(X3))=>![X4]:(m2_finseq_1(X4,u4_struct_0(X3))=>![X5]:(m2_finseq_1(X5,u4_struct_0(X3))=>(r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,k8_finseq_1(u4_struct_0(X3),X4,X5)),X1),X2)=>(r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X4),X1),X2)&r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X5),X1),X2)))))), file('/scratch/mptp/predsminms1/t23_graph_5__0', t23_graph_5)). fof(redefinition_k8_finseq_1, axiom, ![X1, X2, X3]:((m1_finseq_1(X2,X1)&m1_finseq_1(X3,X1))=>k8_finseq_1(X1,X2,X3)=k7_finseq_1(X2,X3)), file('/scratch/mptp/predsminms1/t23_graph_5__0', redefinition_k8_finseq_1)). fof(redefinition_m2_finseq_1, axiom, ![X1, X2]:(m2_finseq_1(X2,X1)<=>m1_finseq_1(X2,X1)), file('/scratch/mptp/predsminms1/t23_graph_5__0', redefinition_m2_finseq_1)). fof(t22_graph_5, axiom, ![X1, X2, X3]:((~(v2_struct_0(X3))&l1_graph_1(X3))=>![X4]:(m2_finseq_1(X4,u4_struct_0(X3))=>![X5]:(m2_finseq_1(X5,u4_struct_0(X3))=>((r1_tarski(k10_xtuple_0(X4),k10_xtuple_0(X5))&r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X5),X1),X2))=>r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X4),X1),X2))))), file('/scratch/mptp/predsminms1/t23_graph_5__0', t22_graph_5)). fof(dt_m1_finseq_1, axiom, ![X1, X2]:(m1_finseq_1(X2,X1)=>(v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))), file('/scratch/mptp/predsminms1/t23_graph_5__0', dt_m1_finseq_1)). fof(t30_finseq_1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_finseq_1(X1)))=>![X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))=>r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X2,X1))))), file('/scratch/mptp/predsminms1/t23_graph_5__0', t30_finseq_1)). fof(t29_finseq_1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_finseq_1(X1)))=>![X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))=>r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X1,X2))))), file('/scratch/mptp/predsminms1/t23_graph_5__0', t29_finseq_1)). fof(dt_k8_finseq_1, axiom, ![X1, X2, X3]:((m1_finseq_1(X2,X1)&m1_finseq_1(X3,X1))=>m2_finseq_1(k8_finseq_1(X1,X2,X3),X1)), file('/scratch/mptp/predsminms1/t23_graph_5__0', dt_k8_finseq_1)). fof(c_0_8, negated_conjecture, ~(![X1, X2, X3]:((~(v2_struct_0(X3))&l1_graph_1(X3))=>![X4]:(m2_finseq_1(X4,u4_struct_0(X3))=>![X5]:(m2_finseq_1(X5,u4_struct_0(X3))=>(r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,k8_finseq_1(u4_struct_0(X3),X4,X5)),X1),X2)=>(r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X4),X1),X2)&r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X5),X1),X2))))))), inference(assume_negation,[status(cth)],[t23_graph_5])). fof(c_0_9, negated_conjecture, ((~v2_struct_0(esk3_0)&l1_graph_1(esk3_0))&(m2_finseq_1(esk4_0,u4_struct_0(esk3_0))&(m2_finseq_1(esk5_0,u4_struct_0(esk3_0))&(r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,k8_finseq_1(u4_struct_0(esk3_0),esk4_0,esk5_0)),esk1_0),esk2_0)&(~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk4_0),esk1_0),esk2_0)\|~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk5_0),esk1_0),esk2_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_8])])])])). fof(c_0_10, plain, ![X17, X18, X19]:(~m1_finseq_1(X18,X17)\|~m1_finseq_1(X19,X17)\|k8_finseq_1(X17,X18,X19)=k7_finseq_1(X18,X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k8_finseq_1])])). fof(c_0_11, plain, ![X13, X14]:((~m2_finseq_1(X14,X13)\|m1_finseq_1(X14,X13))&(~m1_finseq_1(X14,X13)\|m2_finseq_1(X14,X13))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_finseq_1])])). cnf(c_0_12, negated_conjecture, (r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,k8_finseq_1(u4_struct_0(esk3_0),esk4_0,esk5_0)),esk1_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_13, plain, (k8_finseq_1(X2,X1,X3)=k7_finseq_1(X1,X3)\|~m1_finseq_1(X1,X2)\|~m1_finseq_1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_14, plain, (m1_finseq_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_15, negated_conjecture, (m2_finseq_1(esk5_0,u4_struct_0(esk3_0))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_16, negated_conjecture, (m2_finseq_1(esk4_0,u4_struct_0(esk3_0))), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_17, plain, ![X25, X26, X27, X28, X29]:(v2_struct_0(X27)\|~l1_graph_1(X27)\|(~m2_finseq_1(X28,u4_struct_0(X27))\|(~m2_finseq_1(X29,u4_struct_0(X27))\|(~r1_tarski(k10_xtuple_0(X28),k10_xtuple_0(X29))\|~r1_tarski(k7_subset_1(u1_struct_0(X27),k2_graph_5(X27,X29),X25),X26)\|r1_tarski(k7_subset_1(u1_struct_0(X27),k2_graph_5(X27,X28),X25),X26))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t22_graph_5])])])])). cnf(c_0_18, negated_conjecture, (r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,k8_finseq_1(u4_struct_0(esk3_0),esk4_0,esk5_0)),esk1_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_19, plain, (k8_finseq_1(X2,X1,X3)=k7_finseq_1(X1,X3)\|~m1_finseq_1(X3,X2)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_20, plain, (m1_finseq_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_21, negated_conjecture, (m2_finseq_1(esk5_0,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_22, negated_conjecture, (m2_finseq_1(esk4_0,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_23, plain, (v2_struct_0(X1)\|r1_tarski(k7_subset_1(u1_struct_0(X1),k2_graph_5(X1,X2),X4),X5)\|~l1_graph_1(X1)\|~m2_finseq_1(X2,u4_struct_0(X1))\|~m2_finseq_1(X3,u4_struct_0(X1))\|~r1_tarski(k10_xtuple_0(X2),k10_xtuple_0(X3))\|~r1_tarski(k7_subset_1(u1_struct_0(X1),k2_graph_5(X1,X3),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_24, negated_conjecture, (r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,k7_finseq_1(esk4_0,esk5_0)),esk1_0),esk2_0)\|~m1_finseq_1(esk5_0,u4_struct_0(esk3_0))\|~m1_finseq_1(esk4_0,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19])])). cnf(c_0_25, negated_conjecture, (m1_finseq_1(esk5_0,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_21])])). cnf(c_0_26, negated_conjecture, (m1_finseq_1(esk4_0,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_22])])). cnf(c_0_27, negated_conjecture, (l1_graph_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_28, negated_conjecture, (~v2_struct_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_29, negated_conjecture, (~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk4_0),esk1_0),esk2_0)\|~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk5_0),esk1_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_30, plain, (v2_struct_0(X1)\|r1_tarski(k7_subset_1(u1_struct_0(X1),k2_graph_5(X1,X2),X4),X5)\|~l1_graph_1(X1)\|~m2_finseq_1(X3,u4_struct_0(X1))\|~m2_finseq_1(X2,u4_struct_0(X1))\|~r1_tarski(k10_xtuple_0(X2),k10_xtuple_0(X3))\|~r1_tarski(k7_subset_1(u1_struct_0(X1),k2_graph_5(X1,X3),X4),X5)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_31, negated_conjecture, (r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,k7_finseq_1(esk4_0,esk5_0)),esk1_0),esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25]), c_0_26])])). cnf(c_0_32, negated_conjecture, (l1_graph_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_33, negated_conjecture, (~v2_struct_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_28])). fof(c_0_34, plain, ![X11, X12]:((v1_relat_1(X12)\|~m1_finseq_1(X12,X11))&((v1_funct_1(X12)\|~m1_finseq_1(X12,X11))&(v1_finseq_1(X12)\|~m1_finseq_1(X12,X11)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_finseq_1])])])). cnf(c_0_35, negated_conjecture, (~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk4_0),esk1_0),esk2_0)\|~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk5_0),esk1_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_36, negated_conjecture, (r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,X1),esk1_0),esk2_0)\|~r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(esk4_0,esk5_0)))\|~m2_finseq_1(k7_finseq_1(esk4_0,esk5_0),u4_struct_0(esk3_0))\|~m2_finseq_1(X1,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32])]), c_0_33])])). fof(c_0_37, plain, ![X15, X16]:(~v1_relat_1(X15)\|(~v1_funct_1(X15)\|~v1_finseq_1(X15))\|(~v1_relat_1(X16)\|(~v1_funct_1(X16)\|~v1_finseq_1(X16))\|r1_tarski(k10_xtuple_0(X15),k10_xtuple_0(k7_finseq_1(X16,X15))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_finseq_1])])])). cnf(c_0_38, plain, (v1_finseq_1(X1)\|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_39, plain, (v1_funct_1(X1)\|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_40, plain, (v1_relat_1(X1)\|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_41, negated_conjecture, (~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk4_0),esk1_0),esk2_0)\|~r1_tarski(k10_xtuple_0(esk5_0),k10_xtuple_0(k7_finseq_1(esk4_0,esk5_0)))\|~m2_finseq_1(k7_finseq_1(esk4_0,esk5_0),u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36]), c_0_21])])])). cnf(c_0_42, plain, (r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X2,X1)))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_finseq_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_43, plain, (v1_finseq_1(X1)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_44, plain, (v1_funct_1(X1)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_45, plain, (v1_relat_1(X1)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_40])). fof(c_0_46, plain, ![X20, X21]:(~v1_relat_1(X20)\|(~v1_funct_1(X20)\|~v1_finseq_1(X20))\|(~v1_relat_1(X21)\|(~v1_funct_1(X21)\|~v1_finseq_1(X21))\|r1_tarski(k10_xtuple_0(X20),k10_xtuple_0(k7_finseq_1(X20,X21))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t29_finseq_1])])])). fof(c_0_47, plain, ![X22, X23, X24]:(~m1_finseq_1(X23,X22)\|~m1_finseq_1(X24,X22)\|m2_finseq_1(k8_finseq_1(X22,X23,X24),X22)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_finseq_1])])). cnf(c_0_48, negated_conjecture, (~r1_tarski(k10_xtuple_0(esk5_0),k10_xtuple_0(k7_finseq_1(esk4_0,esk5_0)))\|~m2_finseq_1(k7_finseq_1(esk4_0,esk5_0),u4_struct_0(esk3_0))\|~r1_tarski(k10_xtuple_0(esk4_0),k10_xtuple_0(k7_finseq_1(esk4_0,esk5_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_36]), c_0_22])])])). cnf(c_0_49, plain, (r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X2,X1)))\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_finseq_1(X2)\|~v1_finseq_1(X1)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_50, negated_conjecture, (v1_finseq_1(esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_26])])). cnf(c_0_51, negated_conjecture, (v1_finseq_1(esk5_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_25])])). cnf(c_0_52, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_26])])). cnf(c_0_53, negated_conjecture, (v1_funct_1(esk5_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_25])])). cnf(c_0_54, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_26])])). cnf(c_0_55, negated_conjecture, (v1_relat_1(esk5_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_25])])). cnf(c_0_56, plain, (r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X1,X2)))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_finseq_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_57, plain, (m2_finseq_1(k8_finseq_1(X2,X1,X3),X2)\|~m1_finseq_1(X1,X2)\|~m1_finseq_1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_58, negated_conjecture, (~r1_tarski(k10_xtuple_0(esk4_0),k10_xtuple_0(k7_finseq_1(esk4_0,esk5_0)))\|~m2_finseq_1(k7_finseq_1(esk4_0,esk5_0),u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55])])])). cnf(c_0_59, plain, (r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X1,X2)))\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_finseq_1(X2)\|~v1_finseq_1(X1)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_60, plain, (m2_finseq_1(k8_finseq_1(X2,X1,X3),X2)\|~m1_finseq_1(X3,X2)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_61, negated_conjecture, (~m2_finseq_1(k7_finseq_1(esk4_0,esk5_0),u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_51]), c_0_50]), c_0_53]), c_0_52]), c_0_55]), c_0_54])])])). cnf(c_0_62, plain, (m2_finseq_1(k7_finseq_1(X2,X3),X1)\|~m1_finseq_1(X3,X1)\|~m1_finseq_1(X2,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_19])])). cnf(c_0_63, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_25]), c_0_26])]), ['proof']). # SZS output end CNFRefutation	reserve n,m,i,j,k for Element of NAT, x,y,e,X,V,U for set, W,f,g for Function; reserve p,q for FinSequence; reserve G for Graph, pe,qe for FinSequence of the carrier' of G; theorem Th23: vertices(pe^qe) \ X c= V implies vertices(pe) \ X c= V & vertices(qe) \ X c= V proof A1: rng pe c= rng(pe^qe) & rng qe c= rng(pe^qe) by FINSEQ_1:29,30; assume vertices(pe^qe) \ X c= V; hence thesis by A1,Th22; end;	Convert the following ATP output trace into a readable Mizar proof.
t75_exchsort	"Proof found!\n# SZS status Theorem\n# SZS output start CNFRefutation\nfof(t12_funct_5, axiom, ![X1,(...TRUNCATED)	"reserve a,a1,a2,b,c,d for ordinal number,\n n,m,k for Nat,\n x,y,z,t,X,Y,Z for set;\nreserve f,g (...TRUNCATED)	Convert the following ATP output trace into a readable Mizar proof.

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