%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW354+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 03:10:22 PM UTC 2026
% Result : ContradictoryAxioms 194.76s 31.48s
% Output : CNFRefutation 194.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 91 ( 75 unt; 0 def)
% Number of atoms : 115 ( 92 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 56 ( 32 ~; 18 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 155 ( 17 sgn 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X17,X5] :
( hAPP(c_Set_OCollect(X5),X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X17,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X17,X5] : hAPP(c_Set_OCollect(X5),X17) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X17,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X17)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_vimage__Collect__eq,axiom,
! [X17,X2,X11,X5] : hAPP(c_Set_Ovimage(X5,X11,X2),hAPP(c_Set_OCollect(X11),X17)) = hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(X11,tc_HOL_Obool,X5),X17),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
fof(help_c__COMBK__1,axiom,
! [X327,X49,X11,X5] : hAPP(hAPP(c_COMBK(X5,X11),X49),X327) = X49,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_double__complement,axiom,
! [X13,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X13)) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_vimage__id,axiom,
! [X13,X5] : hAPP(c_Set_Ovimage(X5,X5,c_Fun_Oid(X5)),X13) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__id) ).
fof(fact_UNIV__def,axiom,
! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Zero__not__Suc,axiom,
! [X111] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X111),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(help_c__fNot__1,axiom,
! [X17] :
( ~ hBOOL(X17)
| ~ hBOOL(hAPP(c_fNot,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(fact_id__apply,axiom,
! [X86,X5] : hAPP(c_Fun_Oid(X5),X86) = X86,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__apply) ).
fof(help_c__COMBB__1,axiom,
! [X36,X20,X17,X82,X5,X11] : hAPP(hAPP(hAPP(c_COMBB(X11,X5,X82),X17),X20),X36) = hAPP(X17,hAPP(X20,X36)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__0__iff,axiom,
! [X6,X16,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X16 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X16),X6)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_add__Suc__right,axiom,
! [X81,X111] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X111),hAPP(c_Nat_OSuc,X81)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X111),X81)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X111] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X111),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X111,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X81] : X81 != hAPP(c_Nat_OSuc,X81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_21,plain,
! [X17,X5] :
( hAPP(c_Set_OCollect(X5),X17) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X17,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_22,plain,
! [X6699] : c_Orderings_Obot__class_Obot(tc_fun(X6699,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6699),hAPP(c_COMBK(tc_HOL_Obool,X6699),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_23,plain,
! [X6686,X6687] : hAPP(c_Set_OCollect(X6687),X6686) = X6686,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_24,plain,
! [X8000,X8001] : hAPP(c_Set_OCollect(X8001),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8001),c_fNot),X8000)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8001,tc_HOL_Obool)),hAPP(c_Set_OCollect(X8001),X8000)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_25,plain,
! [X10532,X10533,X10534,X10535] : hAPP(c_Set_Ovimage(X10535,X10534,X10533),hAPP(c_Set_OCollect(X10534),X10532)) = hAPP(c_Set_OCollect(X10535),hAPP(hAPP(c_COMBB(X10534,tc_HOL_Obool,X10535),X10532),X10533)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_26,plain,
! [X6674,X6675,X6676,X6677,X6679] :
( ( hAPP(c_Set_OCollect(X6679),X6677) = c_Orderings_Obot__class_Obot(tc_fun(X6679,tc_HOL_Obool))
| hBOOL(hAPP(X6677,esk181_1(X6677))) )
& ( ~ hBOOL(hAPP(X6674,X6676))
| hAPP(c_Set_OCollect(X6675),X6674) != c_Orderings_Obot__class_Obot(tc_fun(X6675,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,
! [X17673,X17674,X17675,X17676] : hAPP(hAPP(c_COMBK(X17676,X17675),X17674),X17673) = X17674,
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,
! [X7970,X7971] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7971,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7971,tc_HOL_Obool)),X7970)) = X7970,
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,
! [X11165,X11166] : hAPP(c_Set_Ovimage(X11166,X11166,c_Fun_Oid(X11166)),X11165) = X11165,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
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,
! [X6944] : c_Orderings_Otop__class_Otop(tc_fun(X6944,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6944),hAPP(c_COMBK(tc_HOL_Obool,X6944),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_35,plain,
! [X111] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X111),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_36,plain,
! [X17] :
( ~ hBOOL(X17)
| ~ hBOOL(hAPP(c_fNot,X17)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_37,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk181_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,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_40,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_41,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_42,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,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_44,plain,
! [X8089] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8089,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8089,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X8089,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
cnf(c_0_45,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_46,plain,
! [X3890] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3890),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_35])]) ).
cnf(c_0_47,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_48,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_49,plain,
! [X17699] :
( ~ hBOOL(X17699)
| ~ hBOOL(hAPP(c_fNot,X17699)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_36])]) ).
cnf(c_0_50,plain,
( hBOOL(hAPP(X1,esk181_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_51,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_52,plain,
! [X11167,X11168] : hAPP(c_Fun_Oid(X11168),X11167) = X11167,
inference(variable_rename,[status(thm)],[fact_id__apply]) ).
cnf(c_0_53,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_40,c_0_41]),c_0_41]) ).
cnf(c_0_54,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_55,plain,
! [X17677,X17678,X17679,X17680,X17681,X17682] : hAPP(hAPP(hAPP(c_COMBB(X17682,X17681,X17680),X17679),X17678),X17677) = hAPP(X17679,hAPP(X17678,X17677)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_56,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_44]) ).
cnf(c_0_57,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_45,c_0_29]) ).
fof(c_0_58,plain,
! [X3858,X3859,X3860] :
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3860)
| X3859 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3860),X3859),X3858)
| X3858 != c_Groups_Ozero__class_Ozero(X3860) )
& ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3860)
| X3858 = c_Groups_Ozero__class_Ozero(X3860)
| X3859 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3860),X3859),X3858) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])])]) ).
fof(c_0_59,plain,
! [X2301,X2302] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2302),hAPP(c_Nat_OSuc,X2301)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2302),X2301)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_60,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_61,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_62,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_63,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_50]),c_0_51]),c_0_38]) ).
cnf(c_0_64,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_65,plain,
c_Fun_Oid(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_53,c_0_54]) ).
cnf(c_0_66,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_67,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_56,c_0_41]) ).
cnf(c_0_68,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_38,c_0_57]) ).
cnf(c_0_69,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,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_59]) ).
cnf(c_0_71,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(c_0_72,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_73,plain,
! [X3903] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3903),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3903,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_74,plain,
! [X81] : X81 != hAPP(c_Nat_OSuc,X81),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_75,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_76,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_77,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_51]),c_0_68]) ).
cnf(c_0_78,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_61]),c_0_71])]),c_0_72]) ).
cnf(c_0_79,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_73]) ).
fof(c_0_80,plain,
! [X2405] : X2405 != hAPP(c_Nat_OSuc,X2405),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_74])]) ).
cnf(c_0_81,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_75,c_0_63]) ).
cnf(c_0_82,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,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_78,c_0_70]) ).
cnf(c_0_84,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_79,c_0_61]) ).
cnf(c_0_85,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_86,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_81]),c_0_82]) ).
cnf(c_0_87,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_88,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86])]) ).
cnf(c_0_89,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_90,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_86]),c_0_85]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW354+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 % Computer : n007.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Mon Sep 21 09:46:36 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.44 Running first-order theorem proving
% 0.09/0.44 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 194.76/31.47 % Version: 3.5.1
% 194.76/31.47 % Preprocessing class: FMLMSMSMSSSNFFN.
% 194.76/31.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 194.76/31.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 194.76/31.47 % Starting new_bool_3 with 300s (1) cores
% 194.76/31.47 % Starting new_bool_1 with 300s (1) cores
% 194.76/31.47 % Starting sh5l with 300s (1) cores
% 194.76/31.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 778905 completed with status 0
% 194.76/31.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 194.76/31.47 % Preprocessing class: FMLMSMSMSSSNFFN.
% 194.76/31.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 194.76/31.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 194.76/31.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 194.76/31.47 % No SInE strategy applied
% 194.76/31.47 % Search class: FGHSM-SMLM33-DFFFFFNN
% 194.76/31.47 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 194.76/31.47 % Starting SubtermCWHack with 135s (1) cores
% 194.76/31.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 194.76/31.47 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 194.76/31.48 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 194.76/31.48 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 194.76/31.48 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 779108 completed with status 0
% 194.76/31.48 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 194.76/31.48 % Preprocessing class: FMLMSMSMSSSNFFN.
% 194.76/31.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 194.76/31.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 194.76/31.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 194.76/31.48 % No SInE strategy applied
% 194.76/31.48 % Search class: FGHSM-SMLM33-DFFFFFNN
% 194.76/31.48 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 194.76/31.48 % Starting SubtermCWHack with 135s (1) cores
% 194.76/31.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 194.76/31.48 % Preprocessing time : 0.230 s
% 194.76/31.48 % Presaturation interreduction done
% 194.76/31.48
% 194.76/31.48 % Proof found!
% 194.76/31.48 % SZS status ContradictoryAxioms
% 194.76/31.48 % SZS output start CNFRefutation
% See solution above
% 194.76/31.48 % Parsed axioms : 5245
% 194.76/31.48 % Removed by relevancy pruning/SinE : 0
% 194.76/31.48 % Initial clauses : 7571
% 194.76/31.48 % Removed in clause preprocessing : 235
% 194.76/31.48 % Initial clauses in saturation : 7336
% 194.76/31.48 % Processed clauses : 17790
% 194.76/31.48 % ...of these trivial : 409
% 194.76/31.48 % ...subsumed : 4341
% 194.76/31.48 % ...remaining for further processing : 13040
% 194.76/31.48 % Other redundant clauses eliminated : 4721
% 194.76/31.48 % Clauses deleted for lack of memory : 0
% 194.76/31.48 % Backward-subsumed : 92
% 194.76/31.48 % Backward-rewritten : 813
% 194.76/31.48 % Generated clauses : 605552
% 194.76/31.48 % ...of the previous two non-redundant : 581133
% 194.76/31.48 % ...aggressively subsumed : 0
% 194.76/31.48 % Contextual simplify-reflections : 28
% 194.76/31.48 % Paramodulations : 600788
% 194.76/31.48 % Factorizations : 10
% 194.76/31.48 % NegExts : 0
% 194.76/31.48 % Equation resolutions : 4821
% 194.76/31.48 % Disequality decompositions : 0
% 194.76/31.48 % Total rewrite steps : 187589
% 194.76/31.48 % ...of those cached : 151043
% 194.76/31.48 % Propositional unsat checks : 3
% 194.76/31.48 % Propositional check models : 2
% 194.76/31.48 % Propositional check unsatisfiable : 0
% 194.76/31.48 % Propositional clauses : 0
% 194.76/31.48 % Propositional clauses after purity: 0
% 194.76/31.48 % Propositional unsat core size : 0
% 194.76/31.48 % Propositional preprocessing time : 0.000
% 194.76/31.48 % Propositional encoding time : 0.656
% 194.76/31.48 % Propositional solver time : 0.362
% 194.76/31.48 % Success case prop preproc time : 0.000
% 194.76/31.48 % Success case prop encoding time : 0.000
% 194.76/31.48 % Success case prop solver time : 0.000
% 194.76/31.48 % Current number of processed clauses : 5723
% 194.76/31.48 % Positive orientable unit clauses : 1540
% 194.76/31.48 % Positive unorientable unit clauses: 130
% 194.76/31.48 % Negative unit clauses : 208
% 194.76/31.48 % Non-unit-clauses : 3845
% 194.76/31.48 % Current number of unprocessed clauses: 573338
% 194.76/31.48 % ...number of literals in the above : 1776869
% 194.76/31.48 % Current number of archived formulas : 0
% 194.76/31.48 % Current number of archived clauses : 6863
% 194.76/31.48 % Clause-clause subsumption calls (NU) : 5150583
% 194.76/31.48 % Rec. Clause-clause subsumption calls : 2486201
% 194.76/31.48 % Non-unit clause-clause subsumptions : 2962
% 194.76/31.48 % Unit Clause-clause subsumption calls : 90817
% 194.76/31.48 % Rewrite failures with RHS unbound : 0
% 194.76/31.48 % BW rewrite match attempts : 53003
% 194.76/31.48 % BW rewrite match successes : 1275
% 194.76/31.48 % Condensation attempts : 0
% 194.76/31.48 % Condensation successes : 0
% 194.76/31.48 % Termbank termtop insertions : 24853807
% 194.76/31.48 % Search garbage collected termcells : 100214
% 194.76/31.48
% 194.76/31.48 % -------------------------------------------------
% 194.76/31.48 % User time : 29.248 s
% 194.76/31.48 % System time : 0.887 s
% 194.76/31.48 % Total time : 30.135 s
% 194.76/31.48 % Maximum resident set size: 42944 pages
% 194.76/31.48
% 194.76/31.48 % -------------------------------------------------
% 194.76/31.48 % User time : 130.402 s
% 194.76/31.48 % System time : 3.415 s
% 194.76/31.48 % Total time : 133.817 s
% 194.76/31.48 % Maximum resident set size: 12288 pages
% 194.76/31.48 % E exiting
%------------------------------------------------------------------------------