TSTP Solution File: SCT163+1 by E-SAT---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SCT163+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:17:37 EDT 2023
% Result : ContradictoryAxioms 7.21s 1.39s
% Output : CNFRefutation 7.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 61 ( 30 unt; 0 def)
% Number of atoms : 137 ( 43 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 127 ( 51 ~; 52 |; 9 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-5 aty)
% Number of variables : 144 ( 14 sgn; 76 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_range__ex1__eq,axiom,
! [X18,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X18),c_Set_Oimage(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))))
<=> ? [X3] :
( X18 = hAPP(X2,X3)
& ! [X84] :
( X18 = hAPP(X2,X84)
=> X84 = X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_range__ex1__eq) ).
fof(fact_range__eqI,axiom,
! [X13,X9,X7,X2,X18] :
( X18 = hAPP(X2,X7)
=> hBOOL(hAPP(hAPP(c_member(X9),X18),c_Set_Oimage(X13,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_range__eqI) ).
fof(fact_inj__Suc,axiom,
! [X62] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X62),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_inj__Suc) ).
fof(fact_rev__finite__subset,axiom,
! [X11,X10,X9] :
( c_Finite__Set_Ofinite(X9,X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> c_Finite__Set_Ofinite(X9,X11) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_rev__finite__subset) ).
fof(fact_subset__UNIV,axiom,
! [X11,X9] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_subset__UNIV) ).
fof(fact_gr0__conv__Suc,axiom,
! [X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))
<=> ? [X53] : X20 = hAPP(c_Nat_OSuc,X53) ),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_gr0__conv__Suc) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [X2,X9] :
( c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(X9,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> c_Set_Oimage(X9,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_finite__UNIV__inj__surj) ).
fof(fact_zero__less__Suc,axiom,
! [X17] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X17))),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_zero__less__Suc) ).
fof(fact_UNIV__I,axiom,
! [X7,X9] : hBOOL(hAPP(hAPP(c_member(X9),X7),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_UNIV__I) ).
fof(fact_finite__imageD,axiom,
! [X11,X2,X13,X9] :
( c_Finite__Set_Ofinite(X9,c_Set_Oimage(X13,X9,X2,X11))
=> ( c_Fun_Oinj__on(X13,X9,X2,X11)
=> c_Finite__Set_Ofinite(X13,X11) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_finite__imageD) ).
fof(fact_finite__indi,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_finite__indi) ).
fof(fact_inj__on__def,axiom,
! [X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X11)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X9),X3),X11))
=> ! [X43] :
( hBOOL(hAPP(hAPP(c_member(X9),X43),X11))
=> ( hAPP(X2,X3) = hAPP(X2,X43)
=> X3 = X43 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_inj__on__def) ).
fof(fact_less__zeroE,axiom,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_less__zeroE) ).
fof(fact_lessI,axiom,
! [X17] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X17))),
file('/export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p',fact_lessI) ).
fof(c_0_14,plain,
! [X591,X592,X593,X594,X596,X597] :
( ( X591 = hAPP(X592,esk14_4(X591,X592,X593,X594))
| ~ hBOOL(hAPP(hAPP(c_member(X593),X591),c_Set_Oimage(X594,X593,X592,c_Orderings_Otop__class_Otop(tc_fun(X594,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X594,X593,X592,c_Orderings_Otop__class_Otop(tc_fun(X594,tc_HOL_Obool))) )
& ( X591 != hAPP(X592,X596)
| X596 = esk14_4(X591,X592,X593,X594)
| ~ hBOOL(hAPP(hAPP(c_member(X593),X591),c_Set_Oimage(X594,X593,X592,c_Orderings_Otop__class_Otop(tc_fun(X594,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X594,X593,X592,c_Orderings_Otop__class_Otop(tc_fun(X594,tc_HOL_Obool))) )
& ( X591 = hAPP(X592,esk15_5(X591,X592,X593,X594,X597))
| X591 != hAPP(X592,X597)
| hBOOL(hAPP(hAPP(c_member(X593),X591),c_Set_Oimage(X594,X593,X592,c_Orderings_Otop__class_Otop(tc_fun(X594,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X594,X593,X592,c_Orderings_Otop__class_Otop(tc_fun(X594,tc_HOL_Obool))) )
& ( esk15_5(X591,X592,X593,X594,X597) != X597
| X591 != hAPP(X592,X597)
| hBOOL(hAPP(hAPP(c_member(X593),X591),c_Set_Oimage(X594,X593,X592,c_Orderings_Otop__class_Otop(tc_fun(X594,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X594,X593,X592,c_Orderings_Otop__class_Otop(tc_fun(X594,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__ex1__eq])])])])]) ).
fof(c_0_15,plain,
! [X568,X569,X570,X571,X572] :
( X572 != hAPP(X571,X570)
| hBOOL(hAPP(hAPP(c_member(X569),X572),c_Set_Oimage(X568,X569,X571,c_Orderings_Otop__class_Otop(tc_fun(X568,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
cnf(c_0_16,plain,
( X3 = esk14_4(X1,X2,X4,X5)
| X1 != hAPP(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
| X1 != hAPP(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X734] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X734),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(c_0_19,plain,
! [X610,X611,X612] :
( ~ c_Finite__Set_Ofinite(X612,X611)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X612,tc_HOL_Obool),X610),X611))
| c_Finite__Set_Ofinite(X612,X610) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).
fof(c_0_20,plain,
! [X559,X560] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X560,tc_HOL_Obool),X559),c_Orderings_Otop__class_Otop(tc_fun(X560,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
cnf(c_0_21,plain,
( X1 = esk14_4(X2,X3,X4,X5)
| X2 != hAPP(X3,X1)
| ~ c_Fun_Oinj__on(X5,X4,X3,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
inference(csr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X935,X937,X938] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X935))
| X935 = hAPP(c_Nat_OSuc,esk26_1(X935)) )
& ( X937 != hAPP(c_Nat_OSuc,X938)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X937)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])]) ).
fof(c_0_24,plain,
! [X584,X585] :
( ~ c_Finite__Set_Ofinite(X585,c_Orderings_Otop__class_Otop(tc_fun(X585,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X585,X585,X584,c_Orderings_Otop__class_Otop(tc_fun(X585,tc_HOL_Obool)))
| c_Set_Oimage(X585,X585,X584,c_Orderings_Otop__class_Otop(tc_fun(X585,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X585,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
cnf(c_0_25,plain,
( c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( X1 = esk14_4(X2,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)
| X2 != hAPP(c_Nat_OSuc,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( X1 = hAPP(c_Nat_OSuc,esk26_1(X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,plain,
! [X921] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X921))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
cnf(c_0_30,plain,
( c_Set_Oimage(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X543,X544] : hBOOL(hAPP(hAPP(c_member(X544),X543),c_Orderings_Otop__class_Otop(tc_fun(X544,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(c_0_32,plain,
! [X622,X623,X624,X625] :
( ~ c_Finite__Set_Ofinite(X625,c_Set_Oimage(X624,X625,X623,X622))
| ~ c_Fun_Oinj__on(X624,X625,X623,X622)
| c_Finite__Set_Ofinite(X624,X622) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
cnf(c_0_33,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[fact_finite__indi]) ).
fof(c_0_35,plain,
! [X717,X718,X719,X720,X721,X722,X723,X724,X725,X726] :
( ( ~ c_Fun_Oinj__on(X720,X719,X718,X717)
| ~ hBOOL(hAPP(hAPP(c_member(X720),X721),X717))
| ~ hBOOL(hAPP(hAPP(c_member(X720),X722),X717))
| hAPP(X718,X721) != hAPP(X718,X722)
| X721 = X722 )
& ( hBOOL(hAPP(hAPP(c_member(X726),esk19_4(X723,X724,X725,X726)),X723))
| c_Fun_Oinj__on(X726,X725,X724,X723) )
& ( hBOOL(hAPP(hAPP(c_member(X726),esk20_4(X723,X724,X725,X726)),X723))
| c_Fun_Oinj__on(X726,X725,X724,X723) )
& ( hAPP(X724,esk19_4(X723,X724,X725,X726)) = hAPP(X724,esk20_4(X723,X724,X725,X726))
| c_Fun_Oinj__on(X726,X725,X724,X723) )
& ( esk19_4(X723,X724,X725,X726) != esk20_4(X723,X724,X725,X726)
| c_Fun_Oinj__on(X726,X725,X724,X723) ) ),
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)],[fact_inj__on__def])])])])])]) ).
cnf(c_0_36,plain,
esk14_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = X1,
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
( esk14_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = esk26_1(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_38,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( X1 = hAPP(X2,esk14_4(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_40,plain,
( c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_41,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,plain,
( c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,X4))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,plain,
( hAPP(X1,esk19_4(X2,X1,X3,X4)) = hAPP(X1,esk20_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk19_4(X1,X2,X3,X4) != esk20_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,plain,
esk26_1(hAPP(c_Nat_OSuc,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_47,plain,
( hAPP(c_Nat_OSuc,esk14_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)) = X1
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_22]),c_0_41])]) ).
cnf(c_0_48,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X1,tc_Arrow__Order__Mirabelle_Oindi,X3,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
c_Fun_Oinj__on(X1,X2,c_Nat_OSuc,X3),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_44]),c_0_36]),c_0_45]) ).
cnf(c_0_50,plain,
( esk14_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = esk26_1(X1)
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
c_Finite__Set_Ofinite(X1,X2),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_52,plain,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(c_0_53,plain,
! [X945] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X945),hAPP(c_Nat_OSuc,X945))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
cnf(c_0_54,plain,
esk14_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = esk26_1(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).
fof(c_0_55,plain,
! [X911] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X911),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[c_0_52]) ).
cnf(c_0_56,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,plain,
hAPP(c_Nat_OSuc,esk26_1(X1)) = X1,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_51])]),c_0_54]) ).
cnf(c_0_58,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_59,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk26_1(X1)),X1)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
$false,
inference(spm,[status(thm)],[c_0_58,c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SCT163+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.10 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n010.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 2400
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Oct 2 11:32:35 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.47 Running first-order model finding
% 0.16/0.47 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.JIbCNfpLIs/E---3.1_14854.p
% 7.21/1.39 # Version: 3.1pre001
% 7.21/1.39 # Preprocessing class: FSLMSMSMSSSNFFN.
% 7.21/1.39 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.21/1.39 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 7.21/1.39 # Starting new_bool_3 with 600s (2) cores
% 7.21/1.39 # Starting new_bool_1 with 300s (1) cores
% 7.21/1.39 # Starting sh5l with 300s (1) cores
% 7.21/1.39 # new_bool_3 with pid 14933 completed with status 0
% 7.21/1.39 # Result found by new_bool_3
% 7.21/1.39 # Preprocessing class: FSLMSMSMSSSNFFN.
% 7.21/1.39 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.21/1.39 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 7.21/1.39 # Starting new_bool_3 with 600s (2) cores
% 7.21/1.39 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 7.21/1.39 # Search class: FGHSM-FSLM32-DFFFFFNN
% 7.21/1.39 # Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 7.21/1.39 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 45s (1) cores
% 7.21/1.39 # Starting new_bool_3 with 61s (1) cores
% 7.21/1.39 # G-E--_301_C18_F1_URBAN_S5PRR_S0Y with pid 14936 completed with status 0
% 7.21/1.39 # Result found by G-E--_301_C18_F1_URBAN_S5PRR_S0Y
% 7.21/1.39 # Preprocessing class: FSLMSMSMSSSNFFN.
% 7.21/1.39 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.21/1.39 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 7.21/1.39 # Starting new_bool_3 with 600s (2) cores
% 7.21/1.39 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 7.21/1.39 # Search class: FGHSM-FSLM32-DFFFFFNN
% 7.21/1.39 # Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 7.21/1.39 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 45s (1) cores
% 7.21/1.39 # Preprocessing time : 0.520 s
% 7.21/1.39
% 7.21/1.39 # Proof found!
% 7.21/1.39 # SZS status ContradictoryAxioms
% 7.21/1.39 # SZS output start CNFRefutation
% See solution above
% 7.21/1.39 # Parsed axioms : 533
% 7.21/1.39 # Removed by relevancy pruning/SinE : 228
% 7.21/1.39 # Initial clauses : 475
% 7.21/1.39 # Removed in clause preprocessing : 34
% 7.21/1.39 # Initial clauses in saturation : 441
% 7.21/1.39 # Processed clauses : 998
% 7.21/1.39 # ...of these trivial : 37
% 7.21/1.39 # ...subsumed : 357
% 7.21/1.39 # ...remaining for further processing : 604
% 7.21/1.39 # Other redundant clauses eliminated : 118
% 7.21/1.39 # Clauses deleted for lack of memory : 0
% 7.21/1.39 # Backward-subsumed : 33
% 7.21/1.39 # Backward-rewritten : 53
% 7.21/1.39 # Generated clauses : 7936
% 7.21/1.39 # ...of the previous two non-redundant : 7229
% 7.21/1.39 # ...aggressively subsumed : 0
% 7.21/1.39 # Contextual simplify-reflections : 7
% 7.21/1.39 # Paramodulations : 7780
% 7.21/1.39 # Factorizations : 10
% 7.21/1.39 # NegExts : 0
% 7.21/1.39 # Equation resolutions : 150
% 7.21/1.39 # Total rewrite steps : 1351
% 7.21/1.39 # Propositional unsat checks : 0
% 7.21/1.39 # Propositional check models : 0
% 7.21/1.39 # Propositional check unsatisfiable : 0
% 7.21/1.39 # Propositional clauses : 0
% 7.21/1.39 # Propositional clauses after purity: 0
% 7.21/1.39 # Propositional unsat core size : 0
% 7.21/1.39 # Propositional preprocessing time : 0.000
% 7.21/1.39 # Propositional encoding time : 0.000
% 7.21/1.39 # Propositional solver time : 0.000
% 7.21/1.39 # Success case prop preproc time : 0.000
% 7.21/1.39 # Success case prop encoding time : 0.000
% 7.21/1.39 # Success case prop solver time : 0.000
% 7.21/1.39 # Current number of processed clauses : 478
% 7.21/1.39 # Positive orientable unit clauses : 96
% 7.21/1.39 # Positive unorientable unit clauses: 7
% 7.21/1.39 # Negative unit clauses : 42
% 7.21/1.39 # Non-unit-clauses : 333
% 7.21/1.39 # Current number of unprocessed clauses: 6633
% 7.21/1.39 # ...number of literals in the above : 30267
% 7.21/1.39 # Current number of archived formulas : 0
% 7.21/1.39 # Current number of archived clauses : 86
% 7.21/1.39 # Clause-clause subsumption calls (NU) : 35439
% 7.21/1.39 # Rec. Clause-clause subsumption calls : 8773
% 7.21/1.39 # Non-unit clause-clause subsumptions : 281
% 7.21/1.39 # Unit Clause-clause subsumption calls : 2916
% 7.21/1.39 # Rewrite failures with RHS unbound : 39
% 7.21/1.39 # BW rewrite match attempts : 1716
% 7.21/1.39 # BW rewrite match successes : 57
% 7.21/1.39 # Condensation attempts : 0
% 7.21/1.39 # Condensation successes : 0
% 7.21/1.39 # Termbank termtop insertions : 307629
% 7.21/1.39
% 7.21/1.39 # -------------------------------------------------
% 7.21/1.39 # User time : 0.851 s
% 7.21/1.39 # System time : 0.026 s
% 7.21/1.39 # Total time : 0.878 s
% 7.21/1.39 # Maximum resident set size: 4104 pages
% 7.21/1.39
% 7.21/1.39 # -------------------------------------------------
% 7.21/1.39 # User time : 1.725 s
% 7.21/1.39 # System time : 0.030 s
% 7.21/1.39 # Total time : 1.755 s
% 7.21/1.39 # Maximum resident set size: 2440 pages
% 7.21/1.39 % E---3.1 exiting
%------------------------------------------------------------------------------