%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW327+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 : n002.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 03:10:18 PM UTC 2026
% Result : ContradictoryAxioms 166.35s 29.65s
% Output : CNFRefutation 166.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 85 ( 68 unt; 0 def)
% Number of atoms : 104 ( 87 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 : 22 ( 22 usr; 9 con; 0-5 aty)
% Number of variables : 147 ( 17 sgn 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X26,X6] :
( hAPP(c_Set_OCollect(X6),X26) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X26,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X6] : c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6),hAPP(c_COMBK(tc_HOL_Obool,X6),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X26,X6] : hAPP(c_Set_OCollect(X6),X26) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X26,X6] : hAPP(c_Set_OCollect(X6),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X6),c_fNot),X26)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Set_OCollect(X6),X26)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X329,X89,X6,X33] : hAPP(hAPP(c_COMBK(X33,X6),X89),X329) = X89,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_UNIV__def,axiom,
! [X6] : c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6),hAPP(c_COMBK(tc_HOL_Obool,X6),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Zero__neq__Suc,axiom,
! [X91] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X91),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X150,X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),X150)) = X150,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X26] :
( ~ hBOOL(X26)
| ~ hBOOL(hAPP(c_fNot,X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_sum__case__KK,axiom,
! [X103,X77,X117,X6,X51] : hAPP(c_Sum__Type_Osum_Osum__case(X51,X6,X117,hAPP(c_COMBK(X6,X51),X77),hAPP(c_COMBK(X6,X117),X77)),X103) = X77,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__KK) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X6] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_add__eq__self__zero,axiom,
! [X32,X91] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X91),X32) = X91
=> X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/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/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,
! [X190,X25,X26,X117,X6,X51] : hAPP(hAPP(hAPP(c_COMBB(X51,X6,X117),X26),X25),X190) = hAPP(X26,hAPP(X25,X190)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X32,X91] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X91),hAPP(c_Nat_OSuc,X32)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X91),X32)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X291,X33] : hAPP(c_List_Orev(X33),hAPP(c_List_Orev(X33),X291)) = X291,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X91] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X91),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X91,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X32] : X32 != hAPP(c_Nat_OSuc,X32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,plain,
! [X26,X6] :
( hAPP(c_Set_OCollect(X6),X26) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X26,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_20,plain,
! [X12381] : c_Orderings_Obot__class_Obot(tc_fun(X12381,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X12381),hAPP(c_COMBK(tc_HOL_Obool,X12381),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X12385,X12386] : hAPP(c_Set_OCollect(X12386),X12385) = X12385,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X12346,X12347] : hAPP(c_Set_OCollect(X12347),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12347),c_fNot),X12346)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12347,tc_HOL_Obool)),hAPP(c_Set_OCollect(X12347),X12346)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_23,plain,
! [X12375,X12376,X12377,X12378,X12380] :
( ( hAPP(c_Set_OCollect(X12380),X12378) = c_Orderings_Obot__class_Obot(tc_fun(X12380,tc_HOL_Obool))
| hBOOL(hAPP(X12378,esk319_1(X12378))) )
& ( ~ hBOOL(hAPP(X12375,X12377))
| hAPP(c_Set_OCollect(X12376),X12375) != c_Orderings_Obot__class_Obot(tc_fun(X12376,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,
! [X17653,X17654,X17655,X17656] : hAPP(hAPP(c_COMBK(X17656,X17655),X17654),X17653) = X17654,
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,
! [X12398] : c_Orderings_Otop__class_Otop(tc_fun(X12398,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X12398),hAPP(c_COMBK(tc_HOL_Obool,X12398),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_28,plain,
! [X91] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X91),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_29,plain,
! [X5682,X5683] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5683,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5683,tc_HOL_Obool)),X5682)) = X5682,
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,
! [X26] :
( ~ hBOOL(X26)
| ~ hBOOL(hAPP(c_fNot,X26)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(c_0_32,plain,
! [X5952,X5953,X5954,X5955,X5956] : hAPP(c_Sum__Type_Osum_Osum__case(X5956,X5955,X5954,hAPP(c_COMBK(X5955,X5956),X5953),hAPP(c_COMBK(X5955,X5954),X5953)),X5952) = X5953,
inference(variable_rename,[status(thm)],[fact_sum__case__KK]) ).
cnf(c_0_33,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk319_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,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_36,plain,
! [X7936] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X7936,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7936,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X7936,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
cnf(c_0_37,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_38,plain,
! [X1248,X1249] :
( X1248 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1249),X1248) != X1249 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_39,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_40,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_41,plain,
! [X1081] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1081),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
fof(c_0_42,plain,
! [X17657,X17658,X17659,X17660,X17661,X17662] : hAPP(hAPP(hAPP(c_COMBB(X17662,X17661,X17660),X17659),X17658),X17657) = hAPP(X17659,hAPP(X17658,X17657)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_43,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_44,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_45,plain,
! [X17679] :
( ~ hBOOL(X17679)
| ~ hBOOL(hAPP(c_fNot,X17679)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
cnf(c_0_46,plain,
hAPP(c_Sum__Type_Osum_Osum__case(X1,X2,X3,hAPP(c_COMBK(X2,X1),X4),hAPP(c_COMBK(X2,X3),X4)),X5) = X4,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_47,plain,
( hBOOL(hAPP(X1,esk319_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_48,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_49,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_36]) ).
cnf(c_0_50,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_37,c_0_26]) ).
cnf(c_0_51,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_38]) ).
cnf(c_0_52,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_53,plain,
! [X1254,X1255] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1255),hAPP(c_Nat_OSuc,X1254)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1255),X1254)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_54,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_56,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44]) ).
fof(c_0_57,plain,
! [X17445,X17446] : hAPP(c_List_Orev(X17446),hAPP(c_List_Orev(X17446),X17445)) = X17445,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_58,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_59,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_46]) ).
cnf(c_0_60,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_49,c_0_44]) ).
cnf(c_0_61,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_62,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_51,c_0_52]) ).
cnf(c_0_63,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_53]) ).
cnf(c_0_64,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_54,c_0_52]) ).
fof(c_0_65,plain,
! [X1245] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1245),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1245,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_66,plain,
! [X32] : X32 != hAPP(c_Nat_OSuc,X32),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_67,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_55]) ).
cnf(c_0_68,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_70,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_60]),c_0_48]),c_0_61]) ).
cnf(c_0_71,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_62,c_0_63]),c_0_64]) ).
cnf(c_0_72,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_65]) ).
fof(c_0_73,plain,
! [X465] : X465 != hAPP(c_Nat_OSuc,X465),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_66])]) ).
cnf(c_0_74,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_75,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_69,c_0_59]) ).
cnf(c_0_76,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_61]),c_0_70]) ).
cnf(c_0_77,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_71,c_0_63]) ).
cnf(c_0_78,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_72,c_0_52]) ).
cnf(c_0_79,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_80,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_81,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_82,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_83,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_84,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_80]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW327+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 21 09:50:19 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 166.35/29.65 % Version: 3.5.1
% 166.35/29.65 % Preprocessing class: FMLMSMSMSSSNFFN.
% 166.35/29.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 166.35/29.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 166.35/29.65 % Starting new_bool_3 with 300s (1) cores
% 166.35/29.65 % Starting new_bool_1 with 300s (1) cores
% 166.35/29.65 % Starting sh5l with 300s (1) cores
% 166.35/29.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3003215 completed with status 0
% 166.35/29.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 166.35/29.65 % Preprocessing class: FMLMSMSMSSSNFFN.
% 166.35/29.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 166.35/29.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 166.35/29.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 166.35/29.65 % No SInE strategy applied
% 166.35/29.65 % Search class: FGHSM-SMLM33-DFFFFFNN
% 166.35/29.65 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 166.35/29.65 % Starting SubtermCWHack with 135s (1) cores
% 166.35/29.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 166.35/29.65 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 166.35/29.65 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 166.35/29.65 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 166.35/29.65 % SAT001_CA_MinMin_p005000_rr with pid 3003232 completed with status 0
% 166.35/29.65 % Result found by SAT001_CA_MinMin_p005000_rr
% 166.35/29.65 % Preprocessing class: FMLMSMSMSSSNFFN.
% 166.35/29.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 166.35/29.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 166.35/29.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 166.35/29.65 % No SInE strategy applied
% 166.35/29.65 % Search class: FGHSM-SMLM33-DFFFFFNN
% 166.35/29.65 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 166.35/29.65 % Starting SubtermCWHack with 135s (1) cores
% 166.35/29.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 166.35/29.65 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 166.35/29.65 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 166.35/29.65 % Preprocessing time : 0.299 s
% 166.35/29.65 % Presaturation interreduction done
% 166.35/29.65
% 166.35/29.65 % Proof found!
% 166.35/29.65 % SZS status ContradictoryAxioms
% 166.35/29.65 % SZS output start CNFRefutation
% See solution above
% 166.35/29.65 % Parsed axioms : 5207
% 166.35/29.65 % Removed by relevancy pruning/SinE : 0
% 166.35/29.65 % Initial clauses : 7484
% 166.35/29.65 % Removed in clause preprocessing : 251
% 166.35/29.65 % Initial clauses in saturation : 7233
% 166.35/29.65 % Processed clauses : 23555
% 166.35/29.65 % ...of these trivial : 527
% 166.35/29.65 % ...subsumed : 7302
% 166.35/29.65 % ...remaining for further processing : 15726
% 166.35/29.65 % Other redundant clauses eliminated : 1723
% 166.35/29.65 % Clauses deleted for lack of memory : 0
% 166.35/29.65 % Backward-subsumed : 226
% 166.35/29.65 % Backward-rewritten : 484
% 166.35/29.65 % Generated clauses : 357410
% 166.35/29.65 % ...of the previous two non-redundant : 343994
% 166.35/29.65 % ...aggressively subsumed : 0
% 166.35/29.65 % Contextual simplify-reflections : 28
% 166.35/29.65 % Paramodulations : 355675
% 166.35/29.65 % Factorizations : 2
% 166.35/29.65 % NegExts : 0
% 166.35/29.65 % Equation resolutions : 1796
% 166.35/29.65 % Disequality decompositions : 0
% 166.35/29.65 % Total rewrite steps : 71998
% 166.35/29.65 % ...of those cached : 52228
% 166.35/29.65 % Propositional unsat checks : 4
% 166.35/29.65 % Propositional check models : 2
% 166.35/29.65 % Propositional check unsatisfiable : 0
% 166.35/29.65 % Propositional clauses : 0
% 166.35/29.65 % Propositional clauses after purity: 0
% 166.35/29.65 % Propositional unsat core size : 0
% 166.35/29.65 % Propositional preprocessing time : 0.000
% 166.35/29.65 % Propositional encoding time : 1.851
% 166.35/29.65 % Propositional solver time : 0.937
% 166.35/29.65 % Success case prop preproc time : 0.000
% 166.35/29.65 % Success case prop encoding time : 0.000
% 166.35/29.65 % Success case prop solver time : 0.000
% 166.35/29.65 % Current number of processed clauses : 8745
% 166.35/29.65 % Positive orientable unit clauses : 1703
% 166.35/29.65 % Positive unorientable unit clauses: 129
% 166.35/29.65 % Negative unit clauses : 1686
% 166.35/29.65 % Non-unit-clauses : 5227
% 166.35/29.65 % Current number of unprocessed clauses: 310766
% 166.35/29.65 % ...number of literals in the above : 633506
% 166.35/29.65 % Current number of archived formulas : 0
% 166.35/29.65 % Current number of archived clauses : 6531
% 166.35/29.65 % Clause-clause subsumption calls (NU) : 5707839
% 166.35/29.65 % Rec. Clause-clause subsumption calls : 3047057
% 166.35/29.65 % Non-unit clause-clause subsumptions : 4793
% 166.35/29.65 % Unit Clause-clause subsumption calls : 1207999
% 166.35/29.65 % Rewrite failures with RHS unbound : 527
% 166.35/29.65 % BW rewrite match attempts : 47822
% 166.35/29.65 % BW rewrite match successes : 1462
% 166.35/29.65 % Condensation attempts : 381933
% 166.35/29.65 % Condensation successes : 1619
% 166.35/29.65 % Termbank termtop insertions : 12568813
% 166.35/29.65 % Search garbage collected termcells : 99041
% 166.35/29.65
% 166.35/29.65 % -------------------------------------------------
% 166.35/29.65 % User time : 27.612 s
% 166.35/29.65 % System time : 0.801 s
% 166.35/29.65 % Total time : 28.413 s
% 166.35/29.65 % Maximum resident set size: 42412 pages
% 166.35/29.65
% 166.35/29.65 % -------------------------------------------------
% 166.35/29.65 % User time : 133.170 s
% 166.35/29.65 % System time : 3.400 s
% 166.35/29.65 % Total time : 136.570 s
% 166.35/29.65 % Maximum resident set size: 12544 pages
% 166.35/29.65 % E exiting
%------------------------------------------------------------------------------