%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW369+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 : n001.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 03:10:24 PM UTC 2026
% Result : ContradictoryAxioms 93.39s 20.33s
% Output : CNFRefutation 93.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 82 ( 66 unt; 0 def)
% Number of atoms : 106 ( 83 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 : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 133 ( 16 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X48,X7] :
( hAPP(c_Set_OCollect(X7),X48) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X48,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X7] : c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7),hAPP(c_COMBK(tc_HOL_Obool,X7),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X48,X7] : hAPP(c_Set_OCollect(X7),X48) = X48,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X48,X7] : hAPP(c_Set_OCollect(X7),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7),c_fNot),X48)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7),X48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X280,X279,X7,X30] : hAPP(hAPP(c_COMBK(X30,X7),X279),X280) = X279,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Zero__not__Suc,axiom,
! [X13] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X9,X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),X9)) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X48] :
( ~ hBOOL(X48)
| ~ hBOOL(hAPP(c_fNot,X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_UNIV__def,axiom,
! [X7] : c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7),hAPP(c_COMBK(tc_HOL_Obool,X7),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
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(help_c__COMBB__1,axiom,
! [X34,X47,X48,X24,X7,X5] : hAPP(hAPP(hAPP(c_COMBB(X5,X7,X24),X48),X47),X34) = hAPP(X48,hAPP(X47,X34)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_Compl__empty__eq,axiom,
! [X7] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_add__0__iff,axiom,
! [X10,X11,X7] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
=> ( X11 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X11),X10)
<=> X10 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_add__Suc__right,axiom,
! [X14,X13] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),hAPP(c_Nat_OSuc,X14)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X199,X30] : hAPP(c_List_Orev(X30),hAPP(c_List_Orev(X30),X199)) = X199,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
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,
! [X13] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X14] : X14 != hAPP(c_Nat_OSuc,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,plain,
! [X48,X7] :
( hAPP(c_Set_OCollect(X7),X48) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X48,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_20,plain,
! [X5970] : c_Orderings_Obot__class_Obot(tc_fun(X5970,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5970),hAPP(c_COMBK(tc_HOL_Obool,X5970),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X5945,X5946] : hAPP(c_Set_OCollect(X5946),X5945) = X5945,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X7232,X7233] : hAPP(c_Set_OCollect(X7233),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7233),c_fNot),X7232)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7233,tc_HOL_Obool)),hAPP(c_Set_OCollect(X7233),X7232)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_23,plain,
! [X5953,X5954,X5955,X5956,X5958] :
( ( hAPP(c_Set_OCollect(X5958),X5956) = c_Orderings_Obot__class_Obot(tc_fun(X5958,tc_HOL_Obool))
| hBOOL(hAPP(X5956,esk161_1(X5956))) )
& ( ~ hBOOL(hAPP(X5953,X5955))
| hAPP(c_Set_OCollect(X5954),X5953) != c_Orderings_Obot__class_Obot(tc_fun(X5954,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_19])])])])])]) ).
fof(c_0_24,plain,
! [X17474,X17475,X17476,X17477] : hAPP(hAPP(c_COMBK(X17477,X17476),X17475),X17474) = X17475,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_25,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_20]) ).
cnf(c_0_26,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X13] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X13),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_28,plain,
! [X7203,X7204] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7204,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7204,tc_HOL_Obool)),X7203)) = X7203,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_29,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_22]) ).
fof(c_0_30,plain,
! [X48] :
( ~ hBOOL(X48)
| ~ hBOOL(hAPP(c_fNot,X48)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_31,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk161_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,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_25,c_0_26]) ).
fof(c_0_34,plain,
! [X6481] : c_Orderings_Otop__class_Otop(tc_fun(X6481,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6481),hAPP(c_COMBK(tc_HOL_Obool,X6481),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_35,plain,
! [X2314] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2314),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
cnf(c_0_36,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_37,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_38,plain,
! [X17478,X17479,X17480,X17481,X17482,X17483] : hAPP(hAPP(hAPP(c_COMBB(X17483,X17482,X17481),X17480),X17479),X17478) = hAPP(X17480,hAPP(X17479,X17478)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_39,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_28]) ).
cnf(c_0_40,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_29,c_0_26]),c_0_26]) ).
fof(c_0_41,plain,
! [X17500] :
( ~ hBOOL(X17500)
| ~ hBOOL(hAPP(c_fNot,X17500)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
cnf(c_0_42,plain,
( hBOOL(hAPP(X1,esk161_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_43,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_44,plain,
! [X7322] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7322,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X7322,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X7322,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__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,
! [X2651,X2652,X2653] :
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2653)
| X2652 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2653),X2652),X2651)
| X2651 != c_Groups_Ozero__class_Ozero(X2653) )
& ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2653)
| X2651 = c_Groups_Ozero__class_Ozero(X2653)
| X2652 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2653),X2652),X2651) ) ),
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_47,plain,
! [X1658,X1659] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1659),hAPP(c_Nat_OSuc,X1658)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1659),X1658)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_48,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_49,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_50,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,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_39,c_0_40]),c_0_40]) ).
fof(c_0_52,plain,
! [X15282,X15283] : hAPP(c_List_Orev(X15283),hAPP(c_List_Orev(X15283),X15282)) = X15282,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_53,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_42]),c_0_43]),c_0_32]) ).
cnf(c_0_55,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,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_26]) ).
cnf(c_0_57,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_46]) ).
cnf(c_0_58,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_47]) ).
cnf(c_0_59,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_60,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_61,plain,
! [X2327] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2327),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2327,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_62,plain,
! [X14] : X14 != hAPP(c_Nat_OSuc,X14),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_63,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_50]) ).
cnf(c_0_64,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_65,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_66,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_55,c_0_40]) ).
cnf(c_0_67,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_32,c_0_56]) ).
cnf(c_0_68,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_57,c_0_58]),c_0_49]),c_0_59])]),c_0_60]) ).
cnf(c_0_69,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_61]) ).
fof(c_0_70,plain,
! [X364] : X364 != hAPP(c_Nat_OSuc,X364),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_62])]) ).
cnf(c_0_71,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_65,c_0_54]) ).
cnf(c_0_73,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_66]),c_0_67]),c_0_43]) ).
cnf(c_0_74,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_68,c_0_58]) ).
cnf(c_0_75,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_69,c_0_49]) ).
cnf(c_0_76,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_78,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_80,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_81,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_77]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW369+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/5.45 % Computer : n001.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Mon Sep 21 09:55:19 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/5.50 Running first-order theorem proving
% 0.22/5.50 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
% 93.39/20.33 % Version: 3.5.1
% 93.39/20.33 % Preprocessing class: FMLMSMSMSSSNFFN.
% 93.39/20.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 93.39/20.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 93.39/20.33 % Starting new_bool_3 with 300s (1) cores
% 93.39/20.33 % Starting new_bool_1 with 300s (1) cores
% 93.39/20.33 % Starting sh5l with 300s (1) cores
% 93.39/20.33 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2829093 completed with status 0
% 93.39/20.33 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 93.39/20.33 % Preprocessing class: FMLMSMSMSSSNFFN.
% 93.39/20.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 93.39/20.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 93.39/20.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 93.39/20.33 % No SInE strategy applied
% 93.39/20.33 % Search class: FGHSM-SMLM33-DFFFFFNN
% 93.39/20.33 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 93.39/20.33 % Starting SubtermCWHack with 135s (1) cores
% 93.39/20.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 93.39/20.33 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 93.39/20.33 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 93.39/20.33 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 93.39/20.33 % SAT001_CA_MinMin_p005000_rr with pid 2829103 completed with status 0
% 93.39/20.33 % Result found by SAT001_CA_MinMin_p005000_rr
% 93.39/20.33 % Preprocessing class: FMLMSMSMSSSNFFN.
% 93.39/20.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 93.39/20.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 93.39/20.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 93.39/20.33 % No SInE strategy applied
% 93.39/20.33 % Search class: FGHSM-SMLM33-DFFFFFNN
% 93.39/20.33 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 93.39/20.33 % Starting SubtermCWHack with 135s (1) cores
% 93.39/20.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 93.39/20.33 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 93.39/20.33 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 93.39/20.33 % Preprocessing time : 0.215 s
% 93.39/20.33 % Presaturation interreduction done
% 93.39/20.33
% 93.39/20.33 % Proof found!
% 93.39/20.33 % SZS status ContradictoryAxioms
% 93.39/20.33 % SZS output start CNFRefutation
% See solution above
% 93.39/20.33 % Parsed axioms : 5230
% 93.39/20.33 % Removed by relevancy pruning/SinE : 0
% 93.39/20.33 % Initial clauses : 7605
% 93.39/20.33 % Removed in clause preprocessing : 245
% 93.39/20.33 % Initial clauses in saturation : 7360
% 93.39/20.33 % Processed clauses : 20948
% 93.39/20.33 % ...of these trivial : 442
% 93.39/20.33 % ...subsumed : 8440
% 93.39/20.33 % ...remaining for further processing : 12066
% 93.39/20.33 % Other redundant clauses eliminated : 2548
% 93.39/20.33 % Clauses deleted for lack of memory : 0
% 93.39/20.33 % Backward-subsumed : 211
% 93.39/20.33 % Backward-rewritten : 341
% 93.39/20.33 % Generated clauses : 203301
% 93.39/20.33 % ...of the previous two non-redundant : 193522
% 93.39/20.33 % ...aggressively subsumed : 0
% 93.39/20.33 % Contextual simplify-reflections : 34
% 93.39/20.33 % Paramodulations : 200776
% 93.39/20.33 % Factorizations : 2
% 93.39/20.33 % NegExts : 0
% 93.39/20.33 % Equation resolutions : 2589
% 93.39/20.33 % Disequality decompositions : 0
% 93.39/20.33 % Total rewrite steps : 63750
% 93.39/20.33 % ...of those cached : 47495
% 93.39/20.33 % Propositional unsat checks : 3
% 93.39/20.33 % Propositional check models : 2
% 93.39/20.33 % Propositional check unsatisfiable : 0
% 93.39/20.33 % Propositional clauses : 0
% 93.39/20.33 % Propositional clauses after purity: 0
% 93.39/20.33 % Propositional unsat core size : 0
% 93.39/20.33 % Propositional preprocessing time : 0.000
% 93.39/20.33 % Propositional encoding time : 0.262
% 93.39/20.33 % Propositional solver time : 0.135
% 93.39/20.33 % Success case prop preproc time : 0.000
% 93.39/20.33 % Success case prop encoding time : 0.000
% 93.39/20.33 % Success case prop solver time : 0.000
% 93.39/20.33 % Current number of processed clauses : 5087
% 93.39/20.33 % Positive orientable unit clauses : 1624
% 93.39/20.33 % Positive unorientable unit clauses: 128
% 93.39/20.33 % Negative unit clauses : 1237
% 93.39/20.33 % Non-unit-clauses : 2098
% 93.39/20.33 % Current number of unprocessed clauses: 179583
% 93.39/20.33 % ...number of literals in the above : 325768
% 93.39/20.33 % Current number of archived formulas : 0
% 93.39/20.33 % Current number of archived clauses : 6519
% 93.39/20.33 % Clause-clause subsumption calls (NU) : 4452193
% 93.39/20.33 % Rec. Clause-clause subsumption calls : 1912281
% 93.39/20.33 % Non-unit clause-clause subsumptions : 3803
% 93.39/20.33 % Unit Clause-clause subsumption calls : 330501
% 93.39/20.33 % Rewrite failures with RHS unbound : 307
% 93.39/20.33 % BW rewrite match attempts : 42892
% 93.39/20.33 % BW rewrite match successes : 1030
% 93.39/20.33 % Condensation attempts : 224935
% 93.39/20.33 % Condensation successes : 849
% 93.39/20.33 % Termbank termtop insertions : 7420004
% 93.39/20.33 % Search garbage collected termcells : 102497
% 93.39/20.33
% 93.39/20.33 % -------------------------------------------------
% 93.39/20.33 % User time : 13.178 s
% 93.39/20.33 % System time : 0.428 s
% 93.39/20.33 % Total time : 13.605 s
% 93.39/20.33 % Maximum resident set size: 42588 pages
% 93.39/20.33
% 93.39/20.33 % -------------------------------------------------
% 93.39/20.33 % User time : 61.732 s
% 93.39/20.33 % System time : 1.758 s
% 93.39/20.33 % Total time : 63.490 s
% 93.39/20.33 % Maximum resident set size: 12288 pages
% 93.39/20.33 % E exiting
%------------------------------------------------------------------------------