%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW296+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 : n014.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 03:10:14 PM UTC 2026
% Result : ContradictoryAxioms 98.44s 15.58s
% Output : CNFRefutation 98.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 93 ( 76 unt; 0 def)
% Number of atoms : 112 ( 95 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 29 ~; 15 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-5 aty)
% Number of variables : 169 ( 18 sgn 94 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X23,X6] :
( hAPP(c_Set_OCollect(X6),X23) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X23,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X6] : c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6),hAPP(c_COMBK(tc_HOL_Obool,X6),c_fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X23,X6] : hAPP(c_Set_OCollect(X6),X23) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X23,X6] : hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6),c_fNot),X23)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Set_OCollect(X6),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_vimage__Collect__eq,axiom,
! [X23,X2,X19,X6] : hAPP(c_Set_Ovimage(X6,X19,X2),hAPP(c_Set_OCollect(X19),X23)) = hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBB(X19,tc_HOL_Obool,X6),X23),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
fof(help_c__COMBK__1,axiom,
! [X331,X102,X6,X115] : hAPP(hAPP(c_COMBK(X115,X6),X102),X331) = X102,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_double__complement,axiom,
! [X129,X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),X129)) = X129,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_vimage__ident,axiom,
! [X229,X6] : hAPP(c_Set_Ovimage(X6,X6,c_COMBI(X6)),X229) = X229,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__ident) ).
fof(fact_UNIV__def,axiom,
! [X6] : c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6),hAPP(c_COMBK(tc_HOL_Obool,X6),c_fTrue)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Zero__not__Suc,axiom,
! [X56] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X56),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(help_c__fNot__1,axiom,
! [X23] :
( ~ hBOOL(X23)
| ~ hBOOL(hAPP(c_fNot,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_sum__case__KK,axiom,
! [X38,X31,X27,X6,X19] : hAPP(c_Sum__Type_Osum_Osum__case(X19,X6,X27,hAPP(c_COMBK(X6,X19),X31),hAPP(c_COMBK(X6,X27),X31)),X38) = X31,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__case__KK) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_add__eq__self__zero,axiom,
! [X8,X56] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X56),X8) = X56
=> X8 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(help_c__COMBI__1,axiom,
! [X102,X115] : hAPP(c_COMBI(X115),X102) = X102,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(help_c__COMBB__1,axiom,
! [X89,X39,X23,X27,X6,X19] : hAPP(hAPP(hAPP(c_COMBB(X19,X6,X27),X23),X39),X89) = hAPP(X23,hAPP(X39,X89)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X8,X56] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X56),hAPP(c_Nat_OSuc,X8)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X56),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X56] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X56),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X56,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X8] : X8 != hAPP(c_Nat_OSuc,X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_21,plain,
! [X23,X6] :
( hAPP(c_Set_OCollect(X6),X23) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X23,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_22,plain,
! [X13198] : c_Orderings_Obot__class_Obot(tc_fun(X13198,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X13198),hAPP(c_COMBK(tc_HOL_Obool,X13198),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_23,plain,
! [X7916,X7917] : hAPP(c_Set_OCollect(X7917),X7916) = X7916,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_24,plain,
! [X7918,X7919] : hAPP(c_Set_OCollect(X7919),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7919),c_fNot),X7918)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7919,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7919),X7918)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_25,plain,
! [X15654,X15655,X15656,X15657] : hAPP(c_Set_Ovimage(X15657,X15656,X15655),hAPP(c_Set_OCollect(X15656),X15654)) = hAPP(c_Set_OCollect(X15657),hAPP(hAPP(c_COMBB(X15656,tc_HOL_Obool,X15657),X15654),X15655)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_26,plain,
! [X13199,X13200,X13201,X13202,X13204] :
( ( hAPP(c_Set_OCollect(X13204),X13202) = c_Orderings_Obot__class_Obot(tc_fun(X13204,tc_HOL_Obool))
| hBOOL(hAPP(X13202,esk365_1(X13202))) )
& ( ~ hBOOL(hAPP(X13199,X13201))
| hAPP(c_Set_OCollect(X13200),X13199) != c_Orderings_Obot__class_Obot(tc_fun(X13200,tc_HOL_Obool)) ) ),
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)],[c_0_21])])])])])]) ).
fof(c_0_27,plain,
! [X17682,X17683,X17684,X17685] : hAPP(hAPP(c_COMBK(X17685,X17684),X17683),X17682) = X17683,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_28,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_30,plain,
! [X4011,X4012] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4012,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4012,tc_HOL_Obool)),X4011)) = X4011,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_31,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_32,plain,
! [X15701,X15702] : hAPP(c_Set_Ovimage(X15702,X15702,c_COMBI(X15702)),X15701) = X15701,
inference(variable_rename,[status(thm)],[fact_vimage__ident]) ).
cnf(c_0_33,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_34,plain,
! [X7904] : c_Orderings_Otop__class_Otop(tc_fun(X7904,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7904),hAPP(c_COMBK(tc_HOL_Obool,X7904),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_35,plain,
! [X56] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X56),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_36,plain,
! [X23] :
( ~ hBOOL(X23)
| ~ hBOOL(hAPP(c_fNot,X23)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(c_0_37,plain,
! [X2084,X2085,X2086,X2087,X2088] : hAPP(c_Sum__Type_Osum_Osum__case(X2088,X2087,X2086,hAPP(c_COMBK(X2087,X2088),X2085),hAPP(c_COMBK(X2087,X2086),X2085)),X2084) = X2085,
inference(variable_rename,[status(thm)],[fact_sum__case__KK]) ).
cnf(c_0_38,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk365_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_39,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_41,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_29]),c_0_29]) ).
cnf(c_0_43,plain,
hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_29]),c_0_29]) ).
fof(c_0_45,plain,
! [X13216] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X13216,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X13216,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X13216,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
cnf(c_0_46,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_47,plain,
! [X867,X868] :
( X867 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X868),X867) != X868 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_48,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_49,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_50,plain,
! [X505] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X505),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_35])]) ).
fof(c_0_51,plain,
! [X17708] :
( ~ hBOOL(X17708)
| ~ hBOOL(hAPP(c_fNot,X17708)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_36])]) ).
cnf(c_0_52,plain,
hAPP(c_Sum__Type_Osum_Osum__case(X1,X2,X3,hAPP(c_COMBK(X2,X1),X4),hAPP(c_COMBK(X2,X3),X4)),X5) = X4,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_53,plain,
( hBOOL(hAPP(X1,esk365_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_54,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_55,plain,
! [X17680,X17681] : hAPP(c_COMBI(X17681),X17680) = X17680,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
cnf(c_0_56,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42]) ).
cnf(c_0_57,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_COMBI(X1)) = X2,
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_58,plain,
! [X17686,X17687,X17688,X17689,X17690,X17691] : hAPP(hAPP(hAPP(c_COMBB(X17691,X17690,X17689),X17688),X17687),X17686) = hAPP(X17688,hAPP(X17687,X17686)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_59,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_60,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_46,c_0_29]) ).
cnf(c_0_61,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_62,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_63,plain,
! [X877,X878] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X878),hAPP(c_Nat_OSuc,X877)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X878),X877)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_64,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_65,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_66,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_52]) ).
cnf(c_0_67,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_68,plain,
c_COMBI(tc_HOL_Obool) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_69,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_59,c_0_42]) ).
cnf(c_0_71,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_39,c_0_60]) ).
cnf(c_0_72,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2
| X1 = hAPP(c_Int_Onat,c_Int_OPls) ),
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_73,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_74,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_64,c_0_62]) ).
fof(c_0_75,plain,
! [X871] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X871),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X871,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_76,plain,
! [X8] : X8 != hAPP(c_Nat_OSuc,X8),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_77,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_78,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).
cnf(c_0_79,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_54]),c_0_71]) ).
cnf(c_0_80,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_81,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_75]) ).
fof(c_0_82,plain,
! [X342] : X342 != hAPP(c_Nat_OSuc,X342),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_76])]) ).
cnf(c_0_83,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_77,c_0_66]) ).
cnf(c_0_84,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != X1,
inference(spm,[status(thm)],[c_0_80,c_0_73]) ).
cnf(c_0_86,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onat,c_Int_OPls)) = X1,
inference(rw,[status(thm)],[c_0_81,c_0_62]) ).
cnf(c_0_87,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_88,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_83]),c_0_84]) ).
cnf(c_0_89,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88])]) ).
cnf(c_0_91,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_92,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_88]),c_0_87]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW296+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 09:45:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 98.44/15.58 % Version: 3.5.1
% 98.44/15.58 % Preprocessing class: FMLMSMSMSSSNFFN.
% 98.44/15.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 98.44/15.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 98.44/15.58 % Starting new_bool_3 with 300s (1) cores
% 98.44/15.58 % Starting new_bool_1 with 300s (1) cores
% 98.44/15.58 % Starting sh5l with 300s (1) cores
% 98.44/15.58 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3765448 completed with status 0
% 98.44/15.58 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 98.44/15.58 % Preprocessing class: FMLMSMSMSSSNFFN.
% 98.44/15.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 98.44/15.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 98.44/15.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 98.44/15.58 % No SInE strategy applied
% 98.44/15.58 % Search class: FGHSM-SMLM33-DFFFFFNN
% 98.44/15.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 98.44/15.58 % Starting SubtermCWHack with 136s (1) cores
% 98.44/15.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 98.44/15.58 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 98.44/15.58 % Starting SAT001_CA_MinMin_p005000_rr with 136s (1) cores
% 98.44/15.58 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 98.44/15.58 % SAT001_CA_MinMin_p005000_rr with pid 3765587 completed with status 0
% 98.44/15.58 % Result found by SAT001_CA_MinMin_p005000_rr
% 98.44/15.58 % Preprocessing class: FMLMSMSMSSSNFFN.
% 98.44/15.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 98.44/15.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 98.44/15.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 98.44/15.58 % No SInE strategy applied
% 98.44/15.58 % Search class: FGHSM-SMLM33-DFFFFFNN
% 98.44/15.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 98.44/15.58 % Starting SubtermCWHack with 136s (1) cores
% 98.44/15.58 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 98.44/15.58 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 98.44/15.58 % Starting SAT001_CA_MinMin_p005000_rr with 136s (1) cores
% 98.44/15.58 % Preprocessing time : 0.218 s
% 98.44/15.58 % Presaturation interreduction done
% 98.44/15.58
% 98.44/15.58 % Proof found!
% 98.44/15.58 % SZS status ContradictoryAxioms
% 98.44/15.58 % SZS output start CNFRefutation
% See solution above
% 98.44/15.58 % Parsed axioms : 5222
% 98.44/15.58 % Removed by relevancy pruning/SinE : 0
% 98.44/15.58 % Initial clauses : 7592
% 98.44/15.58 % Removed in clause preprocessing : 261
% 98.44/15.58 % Initial clauses in saturation : 7331
% 98.44/15.58 % Processed clauses : 22487
% 98.44/15.58 % ...of these trivial : 527
% 98.44/15.58 % ...subsumed : 9432
% 98.44/15.58 % ...remaining for further processing : 12528
% 98.44/15.58 % Other redundant clauses eliminated : 3647
% 98.44/15.58 % Clauses deleted for lack of memory : 0
% 98.44/15.58 % Backward-subsumed : 112
% 98.44/15.58 % Backward-rewritten : 522
% 98.44/15.58 % Generated clauses : 290704
% 98.44/15.58 % ...of the previous two non-redundant : 278841
% 98.44/15.58 % ...aggressively subsumed : 0
% 98.44/15.58 % Contextual simplify-reflections : 27
% 98.44/15.58 % Paramodulations : 287051
% 98.44/15.58 % Factorizations : 4
% 98.44/15.58 % NegExts : 0
% 98.44/15.58 % Equation resolutions : 3707
% 98.44/15.58 % Disequality decompositions : 0
% 98.44/15.58 % Total rewrite steps : 70500
% 98.44/15.58 % ...of those cached : 52573
% 98.44/15.58 % Propositional unsat checks : 3
% 98.44/15.58 % Propositional check models : 2
% 98.44/15.58 % Propositional check unsatisfiable : 0
% 98.44/15.58 % Propositional clauses : 0
% 98.44/15.58 % Propositional clauses after purity: 0
% 98.44/15.58 % Propositional unsat core size : 0
% 98.44/15.58 % Propositional preprocessing time : 0.000
% 98.44/15.58 % Propositional encoding time : 0.249
% 98.44/15.58 % Propositional solver time : 0.129
% 98.44/15.58 % Success case prop preproc time : 0.000
% 98.44/15.58 % Success case prop encoding time : 0.000
% 98.44/15.58 % Success case prop solver time : 0.000
% 98.44/15.58 % Current number of processed clauses : 5525
% 98.44/15.58 % Positive orientable unit clauses : 1697
% 98.44/15.58 % Positive unorientable unit clauses: 121
% 98.44/15.58 % Negative unit clauses : 1542
% 98.44/15.58 % Non-unit-clauses : 2165
% 98.44/15.58 % Current number of unprocessed clauses: 243286
% 98.44/15.58 % ...number of literals in the above : 448685
% 98.44/15.58 % Current number of archived formulas : 0
% 98.44/15.58 % Current number of archived clauses : 6550
% 98.44/15.58 % Clause-clause subsumption calls (NU) : 6038616
% 98.44/15.58 % Rec. Clause-clause subsumption calls : 2451422
% 98.44/15.58 % Non-unit clause-clause subsumptions : 5265
% 98.44/15.58 % Unit Clause-clause subsumption calls : 350373
% 98.44/15.58 % Rewrite failures with RHS unbound : 400
% 98.44/15.58 % BW rewrite match attempts : 46476
% 98.44/15.58 % BW rewrite match successes : 1472
% 98.44/15.58 % Condensation attempts : 314237
% 98.44/15.58 % Condensation successes : 1589
% 98.44/15.58 % Termbank termtop insertions : 9392325
% 98.44/15.58 % Search garbage collected termcells : 101869
% 98.44/15.58
% 98.44/15.58 % -------------------------------------------------
% 98.44/15.58 % User time : 13.703 s
% 98.44/15.58 % System time : 0.420 s
% 98.44/15.58 % Total time : 14.123 s
% 98.44/15.58 % Maximum resident set size: 42744 pages
% 98.44/15.58
% 98.44/15.58 % -------------------------------------------------
% 98.44/15.58 % User time : 66.565 s
% 98.44/15.58 % System time : 1.943 s
% 98.44/15.58 % Total time : 68.509 s
% 98.44/15.58 % Maximum resident set size: 12800 pages
% 98.44/15.58 % E exiting
%------------------------------------------------------------------------------