%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW301+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 : n003.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 03:10:15 PM UTC 2026
% Result : ContradictoryAxioms 133.20s 21.70s
% Output : CNFRefutation 133.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 81 ( 64 unt; 0 def)
% Number of atoms : 100 ( 83 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 : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 132 ( 16 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X23,X5] :
( hAPP(c_Set_OCollect(X5),X23) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X23,X3)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X23,X5] : hAPP(c_Set_OCollect(X5),X23) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X23,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X23)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X304,X303,X5,X44] : hAPP(hAPP(c_COMBK(X44,X5),X303),X304) = X303,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Zero__neq__Suc,axiom,
! [X73] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X73),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X18,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)),X18)) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
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_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/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_add__eq__self__zero,axiom,
! [X74,X73] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),X74) = X73
=> X74 = 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__COMBB__1,axiom,
! [X30,X26,X23,X132,X5,X17] : hAPP(hAPP(hAPP(c_COMBB(X17,X5,X132),X23),X26),X30) = hAPP(X23,hAPP(X26,X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_Compl__empty__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_add__Suc__right,axiom,
! [X74,X73] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),hAPP(c_Nat_OSuc,X74)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),X74)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X225,X44] : hAPP(c_List_Orev(X44),hAPP(c_List_Orev(X44),X225)) = X225,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X73] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X73),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X73,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X74] : X74 != hAPP(c_Nat_OSuc,X74),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_18,plain,
! [X23,X5] :
( hAPP(c_Set_OCollect(X5),X23) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X23,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_19,plain,
! [X10933] : c_Orderings_Obot__class_Obot(tc_fun(X10933,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10933),hAPP(c_COMBK(tc_HOL_Obool,X10933),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_20,plain,
! [X10949,X10950] : hAPP(c_Set_OCollect(X10950),X10949) = X10949,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X10956,X10957] : hAPP(c_Set_OCollect(X10957),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10957),c_fNot),X10956)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10957,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10957),X10956)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_22,plain,
! [X10934,X10935,X10936,X10937,X10939] :
( ( hAPP(c_Set_OCollect(X10939),X10937) = c_Orderings_Obot__class_Obot(tc_fun(X10939,tc_HOL_Obool))
| hBOOL(hAPP(X10937,esk294_1(X10937))) )
& ( ~ hBOOL(hAPP(X10934,X10936))
| hAPP(c_Set_OCollect(X10935),X10934) != c_Orderings_Obot__class_Obot(tc_fun(X10935,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_18])])])])])]) ).
fof(c_0_23,plain,
! [X17523,X17524,X17525,X17526] : hAPP(hAPP(c_COMBK(X17526,X17525),X17524),X17523) = X17524,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_24,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_19]) ).
cnf(c_0_25,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X73] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X73),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_27,plain,
! [X5760,X5761] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5761,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5761,tc_HOL_Obool)),X5760)) = X5760,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_28,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_21]) ).
fof(c_0_29,plain,
! [X23] :
( ~ hBOOL(X23)
| ~ hBOOL(hAPP(c_fNot,X23)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_30,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk294_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,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_24,c_0_25]) ).
fof(c_0_33,plain,
! [X10951] : c_Orderings_Otop__class_Otop(tc_fun(X10951,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10951),hAPP(c_COMBK(tc_HOL_Obool,X10951),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_34,plain,
! [X3150,X3151] :
( X3150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3151),X3150) != X3151 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_35,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_36,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_37,plain,
! [X3139] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3139),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).
fof(c_0_38,plain,
! [X17527,X17528,X17529,X17530,X17531,X17532] : hAPP(hAPP(hAPP(c_COMBB(X17532,X17531,X17530),X17529),X17528),X17527) = hAPP(X17529,hAPP(X17528,X17527)),
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_27]) ).
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_28,c_0_25]),c_0_25]) ).
fof(c_0_41,plain,
! [X17549] :
( ~ hBOOL(X17549)
| ~ hBOOL(hAPP(c_fNot,X17549)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
cnf(c_0_42,plain,
( hBOOL(hAPP(X1,esk294_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_30,c_0_25]) ).
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_31,c_0_32]) ).
fof(c_0_44,plain,
! [X6564] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6564,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X6564,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X6564,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_33]) ).
cnf(c_0_46,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_34]) ).
cnf(c_0_47,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_48,plain,
! [X2844,X2845] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2845),hAPP(c_Nat_OSuc,X2844)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2845),X2844)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_49,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_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,
! [X15527,X15528] : hAPP(c_List_Orev(X15528),hAPP(c_List_Orev(X15528),X15527)) = X15527,
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_31,c_0_42]),c_0_43]),c_0_31]) ).
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_25]) ).
cnf(c_0_57,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_46,c_0_47]) ).
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_48]) ).
cnf(c_0_59,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_49,c_0_47]) ).
fof(c_0_60,plain,
! [X3154] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3154),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3154,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_61,plain,
! [X74] : X74 != hAPP(c_Nat_OSuc,X74),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_62,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_63,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_64,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_65,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_66,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_31,c_0_56]) ).
cnf(c_0_67,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_57,c_0_58]),c_0_59]) ).
cnf(c_0_68,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_60]) ).
fof(c_0_69,plain,
! [X2804] : X2804 != hAPP(c_Nat_OSuc,X2804),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_61])]) ).
cnf(c_0_70,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_64,c_0_54]) ).
cnf(c_0_72,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_65]),c_0_66]),c_0_43]) ).
cnf(c_0_73,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_67,c_0_58]) ).
cnf(c_0_74,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_68,c_0_47]) ).
cnf(c_0_75,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_77,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76])]) ).
cnf(c_0_79,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_80,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_76]),c_0_75]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW301+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n003.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 09:48:01 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.51 Running first-order theorem proving
% 0.27/0.51 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
% 133.20/21.70 % Version: 3.5.1
% 133.20/21.70 % Preprocessing class: FMLMSMSMSSSNFFN.
% 133.20/21.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 133.20/21.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 133.20/21.70 % Starting new_bool_3 with 300s (1) cores
% 133.20/21.70 % Starting new_bool_1 with 300s (1) cores
% 133.20/21.70 % Starting sh5l with 300s (1) cores
% 133.20/21.70 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3990302 completed with status 0
% 133.20/21.70 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 133.20/21.70 % Preprocessing class: FMLMSMSMSSSNFFN.
% 133.20/21.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 133.20/21.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 133.20/21.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 133.20/21.70 % No SInE strategy applied
% 133.20/21.70 % Search class: FGHSM-SMLM33-DFFFFFNN
% 133.20/21.70 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 133.20/21.70 % Starting SubtermCWHack with 135s (1) cores
% 133.20/21.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 133.20/21.70 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 133.20/21.70 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 133.20/21.70 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 133.20/21.70 % SAT001_CA_MinMin_p005000_rr with pid 3990314 completed with status 0
% 133.20/21.70 % Result found by SAT001_CA_MinMin_p005000_rr
% 133.20/21.70 % Preprocessing class: FMLMSMSMSSSNFFN.
% 133.20/21.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 133.20/21.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 133.20/21.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 133.20/21.70 % No SInE strategy applied
% 133.20/21.70 % Search class: FGHSM-SMLM33-DFFFFFNN
% 133.20/21.70 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 133.20/21.70 % Starting SubtermCWHack with 135s (1) cores
% 133.20/21.70 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 133.20/21.70 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 133.20/21.70 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 133.20/21.70 % Preprocessing time : 0.305 s
% 133.20/21.70 % Presaturation interreduction done
% 133.20/21.70
% 133.20/21.70 % Proof found!
% 133.20/21.70 % SZS status ContradictoryAxioms
% 133.20/21.70 % SZS output start CNFRefutation
% See solution above
% 133.20/21.70 % Parsed axioms : 5224
% 133.20/21.70 % Removed by relevancy pruning/SinE : 0
% 133.20/21.70 % Initial clauses : 7581
% 133.20/21.70 % Removed in clause preprocessing : 250
% 133.20/21.70 % Initial clauses in saturation : 7331
% 133.20/21.70 % Processed clauses : 21002
% 133.20/21.70 % ...of these trivial : 414
% 133.20/21.70 % ...subsumed : 7451
% 133.20/21.70 % ...remaining for further processing : 13137
% 133.20/21.70 % Other redundant clauses eliminated : 1471
% 133.20/21.70 % Clauses deleted for lack of memory : 0
% 133.20/21.70 % Backward-subsumed : 135
% 133.20/21.70 % Backward-rewritten : 402
% 133.20/21.70 % Generated clauses : 191944
% 133.20/21.70 % ...of the previous two non-redundant : 182738
% 133.20/21.70 % ...aggressively subsumed : 0
% 133.20/21.70 % Contextual simplify-reflections : 32
% 133.20/21.70 % Paramodulations : 190490
% 133.20/21.70 % Factorizations : 2
% 133.20/21.70 % NegExts : 0
% 133.20/21.70 % Equation resolutions : 1518
% 133.20/21.70 % Disequality decompositions : 0
% 133.20/21.70 % Total rewrite steps : 62088
% 133.20/21.70 % ...of those cached : 44102
% 133.20/21.70 % Propositional unsat checks : 3
% 133.20/21.70 % Propositional check models : 2
% 133.20/21.70 % Propositional check unsatisfiable : 0
% 133.20/21.70 % Propositional clauses : 0
% 133.20/21.70 % Propositional clauses after purity: 0
% 133.20/21.70 % Propositional unsat core size : 0
% 133.20/21.70 % Propositional preprocessing time : 0.000
% 133.20/21.70 % Propositional encoding time : 0.283
% 133.20/21.70 % Propositional solver time : 0.192
% 133.20/21.70 % Success case prop preproc time : 0.000
% 133.20/21.70 % Success case prop encoding time : 0.000
% 133.20/21.70 % Success case prop solver time : 0.000
% 133.20/21.70 % Current number of processed clauses : 6202
% 133.20/21.70 % Positive orientable unit clauses : 1588
% 133.20/21.70 % Positive unorientable unit clauses: 126
% 133.20/21.70 % Negative unit clauses : 983
% 133.20/21.70 % Non-unit-clauses : 3505
% 133.20/21.70 % Current number of unprocessed clauses: 168570
% 133.20/21.70 % ...number of literals in the above : 325472
% 133.20/21.70 % Current number of archived formulas : 0
% 133.20/21.70 % Current number of archived clauses : 6482
% 133.20/21.70 % Clause-clause subsumption calls (NU) : 4140863
% 133.20/21.70 % Rec. Clause-clause subsumption calls : 2022653
% 133.20/21.70 % Non-unit clause-clause subsumptions : 5643
% 133.20/21.70 % Unit Clause-clause subsumption calls : 265706
% 133.20/21.70 % Rewrite failures with RHS unbound : 518
% 133.20/21.70 % BW rewrite match attempts : 37876
% 133.20/21.70 % BW rewrite match successes : 1344
% 133.20/21.70 % Condensation attempts : 213752
% 133.20/21.70 % Condensation successes : 993
% 133.20/21.70 % Termbank termtop insertions : 6999646
% 133.20/21.70 % Search garbage collected termcells : 101795
% 133.20/21.70
% 133.20/21.70 % -------------------------------------------------
% 133.20/21.70 % User time : 19.712 s
% 133.20/21.70 % System time : 0.501 s
% 133.20/21.70 % Total time : 20.213 s
% 133.20/21.70 % Maximum resident set size: 42324 pages
% 133.20/21.70
% 133.20/21.70 % -------------------------------------------------
% 133.20/21.70 % User time : 88.362 s
% 133.20/21.70 % System time : 2.192 s
% 133.20/21.70 % Total time : 90.554 s
% 133.20/21.70 % Maximum resident set size: 12288 pages
% 133.20/21.70 % E exiting
%------------------------------------------------------------------------------