%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW352+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 : n006.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 115.19s 21.74s
% Output : CNFRefutation 115.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 83 ( 67 unt; 0 def)
% Number of atoms : 107 ( 84 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,
! [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(help_c__COMBK__1,axiom,
! [X325,X47,X15,X5] : hAPP(hAPP(c_COMBK(X5,X15),X47),X325) = X47,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
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,
! [X109] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X109),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X10,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)),X10)) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
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(help_c__COMBB__1,axiom,
! [X35,X16,X17,X79,X5,X15] : hAPP(hAPP(hAPP(c_COMBB(X15,X5,X79),X17),X16),X35) = hAPP(X17,hAPP(X16,X35)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__0__iff,axiom,
! [X6,X13,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X13 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X13),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,
! [X87,X109] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),hAPP(c_Nat_OSuc,X87)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),X87)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X272,X5] : hAPP(c_List_Orev(X5),hAPP(c_List_Orev(X5),X272)) = X272,
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,
! [X109] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X109,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X87] : X87 != hAPP(c_Nat_OSuc,X87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,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_20,plain,
! [X6920] : c_Orderings_Obot__class_Obot(tc_fun(X6920,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6920),hAPP(c_COMBK(tc_HOL_Obool,X6920),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X6896,X6897] : hAPP(c_Set_OCollect(X6897),X6896) = X6896,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X6938,X6939] : hAPP(c_Set_OCollect(X6939),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6939),c_fNot),X6938)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6939,tc_HOL_Obool)),hAPP(c_Set_OCollect(X6939),X6938)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_23,plain,
! [X6882,X6883,X6884,X6885,X6887] :
( ( hAPP(c_Set_OCollect(X6887),X6885) = c_Orderings_Obot__class_Obot(tc_fun(X6887,tc_HOL_Obool))
| hBOOL(hAPP(X6885,esk194_1(X6885))) )
& ( ~ hBOOL(hAPP(X6882,X6884))
| hAPP(c_Set_OCollect(X6883),X6882) != c_Orderings_Obot__class_Obot(tc_fun(X6883,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,
! [X17643,X17644,X17645,X17646] : hAPP(hAPP(c_COMBK(X17646,X17645),X17644),X17643) = X17644,
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,
! [X6931] : c_Orderings_Otop__class_Otop(tc_fun(X6931,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6931),hAPP(c_COMBK(tc_HOL_Obool,X6931),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_28,plain,
! [X109] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X109),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_29,plain,
! [X3238,X3239] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3239,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3239,tc_HOL_Obool)),X3238)) = X3238,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_30,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_31,plain,
! [X17] :
( ~ hBOOL(X17)
| ~ hBOOL(hAPP(c_fNot,X17)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_32,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk194_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,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_35,plain,
! [X4732] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4732,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4732,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X4732,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
cnf(c_0_36,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_27]) ).
fof(c_0_37,plain,
! [X4508] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X4508),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
cnf(c_0_38,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_39,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_40,plain,
! [X17647,X17648,X17649,X17650,X17651,X17652] : hAPP(hAPP(hAPP(c_COMBB(X17652,X17651,X17650),X17649),X17648),X17647) = hAPP(X17649,hAPP(X17648,X17647)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
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_29]) ).
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_30,c_0_26]),c_0_26]) ).
fof(c_0_43,plain,
! [X17669] :
( ~ hBOOL(X17669)
| ~ hBOOL(hAPP(c_fNot,X17669)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
cnf(c_0_44,plain,
( hBOOL(hAPP(X1,esk194_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_45,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_46,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_35]) ).
cnf(c_0_47,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_36,c_0_26]) ).
fof(c_0_48,plain,
! [X4460,X4461,X4462] :
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4462)
| X4461 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4462),X4461),X4460)
| X4460 != c_Groups_Ozero__class_Ozero(X4462) )
& ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4462)
| X4460 = c_Groups_Ozero__class_Ozero(X4462)
| X4461 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4462),X4461),X4460) ) ),
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_49,plain,
! [X2998,X2999] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2999),hAPP(c_Nat_OSuc,X2998)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2999),X2998)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_50,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_51,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_52,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
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_41,c_0_42]),c_0_42]) ).
fof(c_0_54,plain,
! [X16320,X16321] : hAPP(c_List_Orev(X16321),hAPP(c_List_Orev(X16321),X16320)) = X16320,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_55,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_56,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_44]),c_0_45]),c_0_33]) ).
cnf(c_0_57,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_46,c_0_42]) ).
cnf(c_0_58,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_33,c_0_47]) ).
cnf(c_0_59,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_48]) ).
cnf(c_0_60,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_49]) ).
cnf(c_0_61,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_62,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_63,plain,
! [X4524] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4524),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X4524,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_64,plain,
! [X87] : X87 != hAPP(c_Nat_OSuc,X87),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_65,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_52]) ).
cnf(c_0_66,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_57]),c_0_45]),c_0_58]) ).
cnf(c_0_69,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_59,c_0_60]),c_0_51]),c_0_61])]),c_0_62]) ).
cnf(c_0_70,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_63]) ).
fof(c_0_71,plain,
! [X2665] : X2665 != hAPP(c_Nat_OSuc,X2665),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_64])]) ).
cnf(c_0_72,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_67,c_0_56]) ).
cnf(c_0_74,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_58]),c_0_68]) ).
cnf(c_0_75,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_69,c_0_60]) ).
cnf(c_0_76,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_70,c_0_51]) ).
cnf(c_0_77,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_79,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_81,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_82,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_78]),c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW352+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.56 % Computer : n006.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Mon Sep 21 09:48:42 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.61 Running first-order theorem proving
% 0.10/0.61 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
% 115.19/21.74 % Version: 3.5.1
% 115.19/21.74 % Preprocessing class: FMLMSLSMSSSNFFN.
% 115.19/21.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 115.19/21.74 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 115.19/21.74 % Starting new_bool_3 with 300s (1) cores
% 115.19/21.74 % Starting new_bool_1 with 300s (1) cores
% 115.19/21.74 % Starting sh5l with 300s (1) cores
% 115.19/21.74 % SAT001_MinMin_p005000_rr_RG with pid 2554422 completed with status 0
% 115.19/21.74 % Result found by SAT001_MinMin_p005000_rr_RG
% 115.19/21.74 % Preprocessing class: FMLMSLSMSSSNFFN.
% 115.19/21.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 115.19/21.74 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 115.19/21.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 115.19/21.74 % No SInE strategy applied
% 115.19/21.74 % Search class: FGHSM-SMLM33-DFFFFFNN
% 115.19/21.74 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 115.19/21.74 % Starting SubtermCWHack with 135s (1) cores
% 115.19/21.74 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 115.19/21.74 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 115.19/21.74 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 115.19/21.74 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 115.19/21.74 % SAT001_MinMin_p005000_rr_RG with pid 2554463 completed with status 0
% 115.19/21.74 % Result found by SAT001_MinMin_p005000_rr_RG
% 115.19/21.74 % Preprocessing class: FMLMSLSMSSSNFFN.
% 115.19/21.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 115.19/21.74 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 115.19/21.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 115.19/21.74 % No SInE strategy applied
% 115.19/21.74 % Search class: FGHSM-SMLM33-DFFFFFNN
% 115.19/21.74 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 115.19/21.74 % Starting SubtermCWHack with 135s (1) cores
% 115.19/21.74 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 115.19/21.74 % Preprocessing time : 0.339 s
% 115.19/21.74 % Presaturation interreduction done
% 115.19/21.74
% 115.19/21.74 % Proof found!
% 115.19/21.74 % SZS status ContradictoryAxioms
% 115.19/21.74 % SZS output start CNFRefutation
% See solution above
% 115.19/21.74 % Parsed axioms : 5242
% 115.19/21.74 % Removed by relevancy pruning/SinE : 0
% 115.19/21.74 % Initial clauses : 7568
% 115.19/21.74 % Removed in clause preprocessing : 234
% 115.19/21.74 % Initial clauses in saturation : 7334
% 115.19/21.74 % Processed clauses : 21701
% 115.19/21.74 % ...of these trivial : 412
% 115.19/21.74 % ...subsumed : 8404
% 115.19/21.74 % ...remaining for further processing : 12885
% 115.19/21.74 % Other redundant clauses eliminated : 1475
% 115.19/21.74 % Clauses deleted for lack of memory : 0
% 115.19/21.74 % Backward-subsumed : 297
% 115.19/21.74 % Backward-rewritten : 528
% 115.19/21.74 % Generated clauses : 203610
% 115.19/21.74 % ...of the previous two non-redundant : 193057
% 115.19/21.74 % ...aggressively subsumed : 0
% 115.19/21.74 % Contextual simplify-reflections : 57
% 115.19/21.74 % Paramodulations : 202138
% 115.19/21.74 % Factorizations : 12
% 115.19/21.74 % NegExts : 0
% 115.19/21.74 % Equation resolutions : 1526
% 115.19/21.74 % Disequality decompositions : 0
% 115.19/21.74 % Total rewrite steps : 64151
% 115.19/21.74 % ...of those cached : 46074
% 115.19/21.74 % Propositional unsat checks : 3
% 115.19/21.74 % Propositional check models : 2
% 115.19/21.74 % Propositional check unsatisfiable : 0
% 115.19/21.74 % Propositional clauses : 0
% 115.19/21.74 % Propositional clauses after purity: 0
% 115.19/21.74 % Propositional unsat core size : 0
% 115.19/21.74 % Propositional preprocessing time : 0.000
% 115.19/21.74 % Propositional encoding time : 0.358
% 115.19/21.74 % Propositional solver time : 0.198
% 115.19/21.74 % Success case prop preproc time : 0.000
% 115.19/21.74 % Success case prop encoding time : 0.000
% 115.19/21.74 % Success case prop solver time : 0.000
% 115.19/21.74 % Current number of processed clauses : 5654
% 115.19/21.74 % Positive orientable unit clauses : 1617
% 115.19/21.74 % Positive unorientable unit clauses: 130
% 115.19/21.74 % Negative unit clauses : 749
% 115.19/21.74 % Non-unit-clauses : 3158
% 115.19/21.74 % Current number of unprocessed clauses: 167732
% 115.19/21.74 % ...number of literals in the above : 321222
% 115.19/21.74 % Current number of archived formulas : 0
% 115.19/21.74 % Current number of archived clauses : 6781
% 115.19/21.74 % Clause-clause subsumption calls (NU) : 6092051
% 115.19/21.74 % Rec. Clause-clause subsumption calls : 2686408
% 115.19/21.74 % Non-unit clause-clause subsumptions : 6388
% 115.19/21.74 % Unit Clause-clause subsumption calls : 170944
% 115.19/21.74 % Rewrite failures with RHS unbound : 0
% 115.19/21.74 % BW rewrite match attempts : 40571
% 115.19/21.74 % BW rewrite match successes : 1448
% 115.19/21.74 % Condensation attempts : 0
% 115.19/21.74 % Condensation successes : 0
% 115.19/21.74 % Termbank termtop insertions : 6916843
% 115.19/21.74 % Search garbage collected termcells : 100406
% 115.19/21.74
% 115.19/21.74 % -------------------------------------------------
% 115.19/21.74 % User time : 18.917 s
% 115.19/21.74 % System time : 0.494 s
% 115.19/21.74 % Total time : 19.411 s
% 115.19/21.74 % Maximum resident set size: 42876 pages
% 115.19/21.74
% 115.19/21.74 % -------------------------------------------------
% 115.19/21.74 % User time : 75.403 s
% 115.19/21.74 % System time : 1.917 s
% 115.19/21.74 % Total time : 77.321 s
% 115.19/21.74 % Maximum resident set size: 12544 pages
% 115.19/21.74 % E exiting
%------------------------------------------------------------------------------