%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT163+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:07:59 PM UTC 2026
% Result : ContradictoryAxioms 4.58s 1.03s
% Output : CNFRefutation 4.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 29 unt; 0 def)
% Number of atoms : 133 ( 45 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 110 ( 42 ~; 43 |; 10 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-5 aty)
% Number of variables : 180 ( 39 sgn 93 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_nat_Oinject,axiom,
! [X74,X75] :
( hAPP(c_Nat_OSuc,X75) = hAPP(c_Nat_OSuc,X74)
<=> X75 = X74 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
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/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
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/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_finite,axiom,
! [X11,X9] :
( class_Finite__Set_Ofinite(X9)
=> c_Finite__Set_Ofinite(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).
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/benchmark/theBenchmark.p',fact_inj__on__def) ).
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/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(fact_top__apply,axiom,
! [X7,X13,X9] :
( class_Orderings_Otop(X9)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X13,X9)),X7) = c_Orderings_Otop__class_Otop(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
fof(arity_fun__Orderings_Otop,axiom,
! [X85,X86] :
( class_Orderings_Otop(X86)
=> class_Orderings_Otop(tc_fun(X85,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(fact_mem__def,axiom,
! [X11,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
<=> hBOOL(hAPP(X11,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(help_c__COMBS__1,axiom,
! [X12,X70,X15,X9,X42,X13] : hAPP(c_COMBS(X13,X42,X9,X15,X70),X12) = hAPP(hAPP(X15,X12),hAPP(X70,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_top1I,axiom,
! [X7,X9] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).
fof(arity_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
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/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_Zero__neq__Suc,axiom,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_image__iff,axiom,
! [X11,X2,X13,X4,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X4),c_Set_Oimage(X13,X9,X2,X11)))
<=> ? [X3] :
( X4 = hAPP(X2,X3)
& hBOOL(hAPP(hAPP(c_member(X13),X3),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
fof(c_0_16,plain,
! [X1276,X1277] :
( ( hAPP(c_Nat_OSuc,X1277) = hAPP(c_Nat_OSuc,X1276)
| X1277 != X1276 )
& ( X1277 = X1276
| hAPP(c_Nat_OSuc,X1277) != hAPP(c_Nat_OSuc,X1276) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])])]) ).
fof(c_0_17,plain,
! [X1288,X1290,X1291] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1290))
| X1290 != hAPP(c_Nat_OSuc,X1291) )
& ( X1288 = hAPP(c_Nat_OSuc,esk34_1(X1288))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1288)) ) ),
inference(fof_nnf,[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_gr0__conv__Suc])])])])])]) ).
fof(c_0_18,plain,
! [X1225] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1225))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(c_0_19,plain,
! [X988,X989] :
( c_Finite__Set_Ofinite(X989,X988)
| ~ class_Finite__Set_Ofinite(X989) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])])]) ).
cnf(c_0_20,plain,
( hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 = hAPP(c_Nat_OSuc,esk34_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,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_18]) ).
fof(c_0_23,plain,
! [X346,X347,X348,X349,X350,X351,X352,X353,X354,X355] :
( ( c_Fun_Oinj__on(X355,X354,X353,X352)
| esk5_4(X352,X353,X354,X355) != esk6_4(X352,X353,X354,X355) )
& ( c_Fun_Oinj__on(X355,X354,X353,X352)
| hAPP(X353,esk5_4(X352,X353,X354,X355)) = hAPP(X353,esk6_4(X352,X353,X354,X355)) )
& ( c_Fun_Oinj__on(X355,X354,X353,X352)
| hBOOL(hAPP(hAPP(c_member(X355),esk6_4(X352,X353,X354,X355)),X352)) )
& ( c_Fun_Oinj__on(X355,X354,X353,X352)
| hBOOL(hAPP(hAPP(c_member(X355),esk5_4(X352,X353,X354,X355)),X352)) )
& ( X350 = X351
| hAPP(X347,X350) != hAPP(X347,X351)
| ~ hBOOL(hAPP(hAPP(c_member(X349),X351),X346))
| ~ hBOOL(hAPP(hAPP(c_member(X349),X350),X346))
| ~ c_Fun_Oinj__on(X349,X348,X347,X346) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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])])])])])])]) ).
fof(c_0_24,plain,
! [X1448,X1449,X1450,X1451] :
( c_Finite__Set_Ofinite(X1450,X1448)
| ~ c_Fun_Oinj__on(X1450,X1451,X1449,X1448)
| ~ c_Finite__Set_Ofinite(X1451,c_Set_Oimage(X1450,X1451,X1449,X1448)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])])]) ).
cnf(c_0_25,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).
cnf(c_0_27,plain,
esk34_1(hAPP(c_Nat_OSuc,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]),c_0_22])]) ).
cnf(c_0_28,plain,
( c_Fun_Oinj__on(X4,X3,X1,X2)
| hAPP(X1,esk5_4(X2,X1,X3,X4)) = hAPP(X1,esk6_4(X2,X1,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_29,plain,
! [X183,X184,X185] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X184,X185)),X183) = c_Orderings_Otop__class_Otop(X185)
| ~ class_Orderings_Otop(X185) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])])]) ).
fof(c_0_30,plain,
! [X1639,X1640] :
( class_Orderings_Otop(tc_fun(X1639,X1640))
| ~ class_Orderings_Otop(X1640) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])])]) ).
cnf(c_0_31,plain,
( ~ c_Fun_Oinj__on(X2,X1,X3,X4)
| ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,X4))
| c_Finite__Set_Ofinite(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
( esk5_4(X1,X2,X3,X4) != esk6_4(X1,X2,X3,X4)
| c_Fun_Oinj__on(X4,X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
( c_Fun_Oinj__on(X3,X2,c_Nat_OSuc,X1)
| esk5_4(X1,c_Nat_OSuc,X2,X3) = esk6_4(X1,c_Nat_OSuc,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_27]) ).
fof(c_0_35,plain,
! [X146,X147,X148] :
( ( hBOOL(hAPP(hAPP(c_member(X148),X147),X146))
| ~ hBOOL(hAPP(X146,X147)) )
& ( hBOOL(hAPP(X146,X147))
| ~ hBOOL(hAPP(hAPP(c_member(X148),X147),X146)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])]) ).
fof(c_0_36,plain,
! [X1666,X1667,X1668,X1669,X1670,X1671] : hAPP(c_COMBS(X1671,X1670,X1669,X1668,X1667),X1666) = hAPP(hAPP(X1668,X1666),hAPP(X1667,X1666)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
cnf(c_0_37,plain,
( ~ class_Orderings_Otop(X1)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2,X1)),X3) = c_Orderings_Otop__class_Otop(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(tc_fun(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_39,plain,
! [X170,X171] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X171,tc_HOL_Obool)),X170)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
cnf(c_0_40,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]) ).
fof(c_0_41,plain,
! [X1608,X1609] :
( c_Set_Oimage(X1609,X1609,X1608,c_Orderings_Otop__class_Otop(tc_fun(X1609,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1609,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(X1609,X1609,X1608,c_Orderings_Otop__class_Otop(tc_fun(X1609,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X1609,c_Orderings_Otop__class_Otop(tc_fun(X1609,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])])]) ).
cnf(c_0_42,plain,
( ~ c_Fun_Oinj__on(X1,tc_Product__Type_Ounit,X3,X2)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_43,plain,
c_Fun_Oinj__on(X1,X2,c_Nat_OSuc,X3),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,plain,
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(hAPP(c_member(X3),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
( ~ class_Orderings_Otop(X3)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_fun(X2,X3))),X4) = c_Orderings_Otop__class_Otop(tc_fun(X2,X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_Orderings_Otop__class_Otop(tc_HOL_Obool),
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_49,plain,
( ~ c_Fun_Oinj__on(X1,X1,X2,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_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)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
c_Finite__Set_Ofinite(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,plain,
( ~ hBOOL(hAPP(hAPP(X5,X6),X6))
| hBOOL(hAPP(c_COMBS(X1,X2,X3,c_member(X4),X5),X6)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_46,c_0_40]) ).
cnf(c_0_53,plain,
hBOOL(c_Orderings_Otop__class_Otop(tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_54,plain,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X24),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_55,plain,
! [X1541,X1542,X1543,X1544,X1545,X1547,X1548,X1549,X1550,X1551,X1552] :
( ( hBOOL(hAPP(hAPP(c_member(X1552),X1550),c_Set_Oimage(X1549,X1552,X1548,X1547)))
| X1550 != hAPP(X1548,X1551)
| ~ hBOOL(hAPP(hAPP(c_member(X1549),X1551),X1547)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X1545),X1544),c_Set_Oimage(X1543,X1545,X1542,X1541)))
| X1544 = hAPP(X1542,esk42_4(X1541,X1542,X1543,X1544)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X1545),X1544),c_Set_Oimage(X1543,X1545,X1542,X1541)))
| hBOOL(hAPP(hAPP(c_member(X1543),esk42_4(X1541,X1542,X1543,X1544)),X1541)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_image__iff])])])])])])]) ).
cnf(c_0_56,plain,
( ~ c_Fun_Oinj__on(X1,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| 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)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_57,plain,
hBOOL(hAPP(c_COMBS(X1,X2,X3,c_member(X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_fun(X6,tc_HOL_Obool)))),X7)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_48]),c_0_53])]) ).
fof(c_0_58,plain,
! [X1227] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1227),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_54])]) ).
cnf(c_0_59,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X5),X1),c_Set_Oimage(X4,X5,X2,X3)))
| X1 = hAPP(X2,esk42_4(X3,X2,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,plain,
c_Set_Oimage(X1,X1,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_56,c_0_43]) ).
cnf(c_0_61,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_45]),c_0_52]) ).
cnf(c_0_62,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,plain,
hAPP(c_Nat_OSuc,esk42_4(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Nat_OSuc,X1,X2)) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_64,plain,
$false,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SCT163+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 04:35:07 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.33 Running first-order theorem proving
% 0.04/0.33 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.58/1.03 % Version: 3.5.1
% 4.58/1.03 % Preprocessing class: FSLMSMSMSSSNFFN.
% 4.58/1.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.58/1.03 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 4.58/1.03 % Starting new_bool_3 with 600s (2) cores
% 4.58/1.03 % Starting new_bool_1 with 300s (1) cores
% 4.58/1.03 % Starting sh5l with 300s (1) cores
% 4.58/1.03 % G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with pid 1565362 completed with status 0
% 4.58/1.03 % Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S
% 4.58/1.03 % Preprocessing class: FSLMSMSMSSSNFFN.
% 4.58/1.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.58/1.03 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 4.58/1.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.58/1.03 % No SInE strategy applied
% 4.58/1.03 % Search class: FGHSM-FSLM32-DFFFFFNN
% 4.58/1.03 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 4.58/1.03 % Starting SubtermCWHack with 109s (1) cores
% 4.58/1.03 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 4.58/1.03 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 4.58/1.03 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 4.58/1.03 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 1565373 completed with status 0
% 4.58/1.03 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 4.58/1.03 % Preprocessing class: FSLMSMSMSSSNFFN.
% 4.58/1.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.58/1.03 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 4.58/1.03 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.58/1.03 % No SInE strategy applied
% 4.58/1.03 % Search class: FGHSM-FSLM32-DFFFFFNN
% 4.58/1.03 % Scheduled 13 strats onto 4 cores with 1200 seconds (1200 total)
% 4.58/1.03 % Starting SubtermCWHack with 109s (1) cores
% 4.58/1.03 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 121s (1) cores
% 4.58/1.03 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 90s (1) cores
% 4.58/1.03 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 90s (1) cores
% 4.58/1.03 % Preprocessing time : 0.010 s
% 4.58/1.03 % Presaturation interreduction done
% 4.58/1.03
% 4.58/1.03 % Proof found!
% 4.58/1.03 % SZS status ContradictoryAxioms
% 4.58/1.03 % SZS output start CNFRefutation
% See solution above
% 4.58/1.03 % Parsed axioms : 533
% 4.58/1.03 % Removed by relevancy pruning/SinE : 0
% 4.58/1.03 % Initial clauses : 804
% 4.58/1.03 % Removed in clause preprocessing : 53
% 4.58/1.03 % Initial clauses in saturation : 751
% 4.58/1.03 % Processed clauses : 3847
% 4.58/1.03 % ...of these trivial : 234
% 4.58/1.03 % ...subsumed : 1607
% 4.58/1.03 % ...remaining for further processing : 2006
% 4.58/1.03 % Other redundant clauses eliminated : 134
% 4.58/1.03 % Clauses deleted for lack of memory : 0
% 4.58/1.03 % Backward-subsumed : 31
% 4.58/1.03 % Backward-rewritten : 244
% 4.58/1.03 % Generated clauses : 42034
% 4.58/1.03 % ...of the previous two non-redundant : 38360
% 4.58/1.03 % ...aggressively subsumed : 0
% 4.58/1.03 % Contextual simplify-reflections : 3
% 4.58/1.03 % Paramodulations : 41896
% 4.58/1.03 % Factorizations : 8
% 4.58/1.03 % NegExts : 0
% 4.58/1.03 % Equation resolutions : 142
% 4.58/1.03 % Disequality decompositions : 0
% 4.58/1.03 % Total rewrite steps : 10435
% 4.58/1.03 % ...of those cached : 7983
% 4.58/1.03 % Propositional unsat checks : 0
% 4.58/1.03 % Propositional check models : 0
% 4.58/1.03 % Propositional check unsatisfiable : 0
% 4.58/1.03 % Propositional clauses : 0
% 4.58/1.03 % Propositional clauses after purity: 0
% 4.58/1.03 % Propositional unsat core size : 0
% 4.58/1.03 % Propositional preprocessing time : 0.000
% 4.58/1.03 % Propositional encoding time : 0.000
% 4.58/1.03 % Propositional solver time : 0.000
% 4.58/1.03 % Success case prop preproc time : 0.000
% 4.58/1.03 % Success case prop encoding time : 0.000
% 4.58/1.03 % Success case prop solver time : 0.000
% 4.58/1.03 % Current number of processed clauses : 1087
% 4.58/1.03 % Positive orientable unit clauses : 374
% 4.58/1.03 % Positive unorientable unit clauses: 17
% 4.58/1.03 % Negative unit clauses : 130
% 4.58/1.03 % Non-unit-clauses : 566
% 4.58/1.03 % Current number of unprocessed clauses: 34971
% 4.58/1.03 % ...number of literals in the above : 80178
% 4.58/1.03 % Current number of archived formulas : 0
% 4.58/1.03 % Current number of archived clauses : 824
% 4.58/1.03 % Clause-clause subsumption calls (NU) : 134546
% 4.58/1.03 % Rec. Clause-clause subsumption calls : 57914
% 4.58/1.03 % Non-unit clause-clause subsumptions : 898
% 4.58/1.03 % Unit Clause-clause subsumption calls : 6503
% 4.58/1.03 % Rewrite failures with RHS unbound : 521
% 4.58/1.03 % BW rewrite match attempts : 8835
% 4.58/1.03 % BW rewrite match successes : 352
% 4.58/1.03 % Condensation attempts : 0
% 4.58/1.03 % Condensation successes : 0
% 4.58/1.03 % Termbank termtop insertions : 1030507
% 4.58/1.03 % Search garbage collected termcells : 11632
% 4.58/1.03
% 4.58/1.03 % -------------------------------------------------
% 4.58/1.03 % User time : 0.632 s
% 4.58/1.03 % System time : 0.034 s
% 4.58/1.03 % Total time : 0.666 s
% 4.58/1.03 % Maximum resident set size: 7200 pages
% 4.58/1.03
% 4.58/1.03 % -------------------------------------------------
% 4.58/1.03 % User time : 2.512 s
% 4.58/1.03 % System time : 0.101 s
% 4.58/1.03 % Total time : 2.613 s
% 4.58/1.03 % Maximum resident set size: 5632 pages
% 4.58/1.03 % E exiting
%------------------------------------------------------------------------------