%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW332+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 03:10:19 PM UTC 2026
% Result : ContradictoryAxioms 91.76s 14.93s
% Output : CNFRefutation 91.76s
% 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,
! [X6,X8] :
( hAPP(c_Set_OCollect(X8),X6) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X6,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X8] : c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X8),hAPP(c_COMBK(tc_HOL_Obool,X8),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X6,X8] : hAPP(c_Set_OCollect(X8),X6) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X6,X8] : hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8),c_fNot),X6)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_OCollect(X8),X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X312,X66,X8,X18] : hAPP(hAPP(c_COMBK(X18,X8),X66),X312) = X66,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Zero__not__Suc,axiom,
! [X59] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X59),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X20,X8] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),X20)) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X6] :
( ~ hBOOL(X6)
| ~ hBOOL(hAPP(c_fNot,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_UNIV__def,axiom,
! [X8] : c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X8),hAPP(c_COMBK(tc_HOL_Obool,X8),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_add__eq__self__zero,axiom,
! [X17,X59] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),X17) = X59
=> X17 = 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,
! [X29,X4,X6,X41,X8,X22] : hAPP(hAPP(hAPP(c_COMBB(X22,X8,X41),X6),X4),X29) = hAPP(X6,hAPP(X4,X29)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_Compl__empty__eq,axiom,
! [X8] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_add__Suc__right,axiom,
! [X17,X59] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),hAPP(c_Nat_OSuc,X17)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X249,X18] : hAPP(c_List_Orev(X18),hAPP(c_List_Orev(X18),X249)) = X249,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X59] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X59,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X17] : X17 != hAPP(c_Nat_OSuc,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_18,plain,
! [X6,X8] :
( hAPP(c_Set_OCollect(X8),X6) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X6,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_19,plain,
! [X10999] : c_Orderings_Obot__class_Obot(tc_fun(X10999,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10999),hAPP(c_COMBK(tc_HOL_Obool,X10999),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_20,plain,
! [X11018,X11019] : hAPP(c_Set_OCollect(X11019),X11018) = X11018,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X11020,X11021] : hAPP(c_Set_OCollect(X11021),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11021),c_fNot),X11020)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11021,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11021),X11020)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_22,plain,
! [X11006,X11007,X11008,X11009,X11011] :
( ( hAPP(c_Set_OCollect(X11011),X11009) = c_Orderings_Obot__class_Obot(tc_fun(X11011,tc_HOL_Obool))
| hBOOL(hAPP(X11009,esk283_1(X11009))) )
& ( ~ hBOOL(hAPP(X11006,X11008))
| hAPP(c_Set_OCollect(X11007),X11006) != c_Orderings_Obot__class_Obot(tc_fun(X11007,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,
! [X17641,X17642,X17643,X17644] : hAPP(hAPP(c_COMBK(X17644,X17643),X17642),X17641) = X17642,
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,
! [X59] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X59),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_27,plain,
! [X6432,X6433] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6433,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X6433,tc_HOL_Obool)),X6432)) = X6432,
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,
! [X6] :
( ~ hBOOL(X6)
| ~ hBOOL(hAPP(c_fNot,X6)) ),
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,esk283_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,
! [X10992] : c_Orderings_Otop__class_Otop(tc_fun(X10992,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10992),hAPP(c_COMBK(tc_HOL_Obool,X10992),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_34,plain,
! [X1184,X1185] :
( X1184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1185),X1184) != X1185 ),
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,
! [X671] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X671),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).
fof(c_0_38,plain,
! [X17645,X17646,X17647,X17648,X17649,X17650] : hAPP(hAPP(hAPP(c_COMBB(X17650,X17649,X17648),X17647),X17646),X17645) = hAPP(X17647,hAPP(X17646,X17645)),
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,
! [X17667] :
( ~ hBOOL(X17667)
| ~ hBOOL(hAPP(c_fNot,X17667)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
cnf(c_0_42,plain,
( hBOOL(hAPP(X1,esk283_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,
! [X10128] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10128,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10128,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10128,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,
! [X1190,X1191] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1191),hAPP(c_Nat_OSuc,X1190)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1191),X1190)),
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,
! [X16046,X16047] : hAPP(c_List_Orev(X16047),hAPP(c_List_Orev(X16047),X16046)) = X16046,
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,
! [X1181] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1181),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1181,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_61,plain,
! [X17] : X17 != hAPP(c_Nat_OSuc,X17),
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,
! [X799] : X799 != hAPP(c_Nat_OSuc,X799),
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
% 0.00/0.03 % Problem : SWW332+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 % Computer : n001.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Mon Sep 21 09:53:00 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.44 Running first-order theorem proving
% 0.09/0.44 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 91.76/14.93 % Version: 3.5.1
% 91.76/14.93 % Preprocessing class: FMLMSMSMSSSNFFN.
% 91.76/14.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 91.76/14.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 91.76/14.93 % Starting new_bool_3 with 300s (1) cores
% 91.76/14.93 % Starting new_bool_1 with 300s (1) cores
% 91.76/14.93 % Starting sh5l with 300s (1) cores
% 91.76/14.93 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2825883 completed with status 0
% 91.76/14.93 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 91.76/14.93 % Preprocessing class: FMLMSMSMSSSNFFN.
% 91.76/14.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 91.76/14.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 91.76/14.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 91.76/14.93 % No SInE strategy applied
% 91.76/14.93 % Search class: FGHSM-SMLM33-DFFFFFNN
% 91.76/14.93 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 91.76/14.93 % Starting SubtermCWHack with 135s (1) cores
% 91.76/14.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 91.76/14.93 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 91.76/14.93 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 91.76/14.93 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 91.76/14.93 % SAT001_CA_MinMin_p005000_rr with pid 2825893 completed with status 0
% 91.76/14.93 % Result found by SAT001_CA_MinMin_p005000_rr
% 91.76/14.93 % Preprocessing class: FMLMSMSMSSSNFFN.
% 91.76/14.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 91.76/14.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 91.76/14.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 91.76/14.93 % No SInE strategy applied
% 91.76/14.93 % Search class: FGHSM-SMLM33-DFFFFFNN
% 91.76/14.93 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 91.76/14.93 % Starting SubtermCWHack with 135s (1) cores
% 91.76/14.93 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 91.76/14.93 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 91.76/14.93 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 91.76/14.93 % Preprocessing time : 0.220 s
% 91.76/14.93 % Presaturation interreduction done
% 91.76/14.93
% 91.76/14.93 % Proof found!
% 91.76/14.93 % SZS status ContradictoryAxioms
% 91.76/14.93 % SZS output start CNFRefutation
% See solution above
% 91.76/14.93 % Parsed axioms : 5228
% 91.76/14.93 % Removed by relevancy pruning/SinE : 0
% 91.76/14.93 % Initial clauses : 7589
% 91.76/14.93 % Removed in clause preprocessing : 236
% 91.76/14.93 % Initial clauses in saturation : 7353
% 91.76/14.93 % Processed clauses : 21279
% 91.76/14.93 % ...of these trivial : 406
% 91.76/14.93 % ...subsumed : 8788
% 91.76/14.93 % ...remaining for further processing : 12085
% 91.76/14.93 % Other redundant clauses eliminated : 3772
% 91.76/14.93 % Clauses deleted for lack of memory : 0
% 91.76/14.93 % Backward-subsumed : 84
% 91.76/14.93 % Backward-rewritten : 391
% 91.76/14.93 % Generated clauses : 206771
% 91.76/14.93 % ...of the previous two non-redundant : 196690
% 91.76/14.93 % ...aggressively subsumed : 0
% 91.76/14.93 % Contextual simplify-reflections : 24
% 91.76/14.93 % Paramodulations : 203013
% 91.76/14.93 % Factorizations : 2
% 91.76/14.93 % NegExts : 0
% 91.76/14.93 % Equation resolutions : 3821
% 91.76/14.93 % Disequality decompositions : 0
% 91.76/14.93 % Total rewrite steps : 64389
% 91.76/14.93 % ...of those cached : 48305
% 91.76/14.93 % Propositional unsat checks : 3
% 91.76/14.93 % Propositional check models : 2
% 91.76/14.93 % Propositional check unsatisfiable : 0
% 91.76/14.93 % Propositional clauses : 0
% 91.76/14.93 % Propositional clauses after purity: 0
% 91.76/14.93 % Propositional unsat core size : 0
% 91.76/14.93 % Propositional preprocessing time : 0.000
% 91.76/14.93 % Propositional encoding time : 0.242
% 91.76/14.93 % Propositional solver time : 0.114
% 91.76/14.93 % Success case prop preproc time : 0.000
% 91.76/14.93 % Success case prop encoding time : 0.000
% 91.76/14.93 % Success case prop solver time : 0.000
% 91.76/14.93 % Current number of processed clauses : 5190
% 91.76/14.93 % Positive orientable unit clauses : 1521
% 91.76/14.93 % Positive unorientable unit clauses: 127
% 91.76/14.93 % Negative unit clauses : 1697
% 91.76/14.93 % Non-unit-clauses : 1845
% 91.76/14.93 % Current number of unprocessed clauses: 178540
% 91.76/14.93 % ...number of literals in the above : 317917
% 91.76/14.93 % Current number of archived formulas : 0
% 91.76/14.93 % Current number of archived clauses : 6442
% 91.76/14.93 % Clause-clause subsumption calls (NU) : 4515296
% 91.76/14.93 % Rec. Clause-clause subsumption calls : 2231676
% 91.76/14.93 % Non-unit clause-clause subsumptions : 3788
% 91.76/14.93 % Unit Clause-clause subsumption calls : 557749
% 91.76/14.93 % Rewrite failures with RHS unbound : 490
% 91.76/14.93 % BW rewrite match attempts : 40348
% 91.76/14.93 % BW rewrite match successes : 1243
% 91.76/14.93 % Condensation attempts : 228835
% 91.76/14.93 % Condensation successes : 835
% 91.76/14.93 % Termbank termtop insertions : 7709892
% 91.76/14.93 % Search garbage collected termcells : 102735
% 91.76/14.93
% 91.76/14.93 % -------------------------------------------------
% 91.76/14.93 % User time : 12.942 s
% 91.76/14.93 % System time : 0.385 s
% 91.76/14.93 % Total time : 13.328 s
% 91.76/14.93 % Maximum resident set size: 42648 pages
% 91.76/14.93
% 91.76/14.93 % -------------------------------------------------
% 91.76/14.93 % User time : 60.723 s
% 91.76/14.93 % System time : 1.697 s
% 91.76/14.93 % Total time : 62.420 s
% 91.76/14.93 % Maximum resident set size: 12288 pages
% 91.76/14.93 % E exiting
%------------------------------------------------------------------------------