%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW346+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 : n013.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 03:10:21 PM UTC 2026
% Result : ContradictoryAxioms 148.00s 30.40s
% Output : CNFRefutation 148.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 87 ( 66 unt; 0 def)
% Number of atoms : 110 ( 93 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 32 ~; 18 |; 1 &)
% ( 2 <=>; 2 =>; 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; 0-3 aty)
% Number of variables : 145 ( 19 sgn 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,
! [X24,X5] : hAPP(c_Set_OCollect(X5),X24) = X24,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__empty__eq,axiom,
! [X24,X5] :
( hAPP(c_Set_OCollect(X5),X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X24,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(help_c__COMBK__1,axiom,
! [X320,X319,X18,X5] : hAPP(hAPP(c_COMBK(X5,X18),X319),X320) = X319,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Collect__neg__eq,axiom,
! [X24,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X24)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_Zero__neq__Suc,axiom,
! [X129] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X20,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)),X20)) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X24] :
( ~ hBOOL(X24)
| ~ hBOOL(hAPP(c_fNot,X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__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/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
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_add__eq__self__zero,axiom,
! [X73,X129] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X129),X73) = X129
=> X73 = 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,
! [X35,X23,X24,X80,X5,X18] : hAPP(hAPP(hAPP(c_COMBB(X18,X5,X80),X24),X23),X35) = hAPP(X24,hAPP(X23,X35)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X73,X129] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X129),hAPP(c_Nat_OSuc,X73)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X129),X73)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X257,X5] : hAPP(c_List_Orev(X5),hAPP(c_List_Orev(X5),X257)) = X257,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X129] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X129),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X129,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X73] : X73 != hAPP(c_Nat_OSuc,X73),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,plain,
! [X1034] : c_Orderings_Obot__class_Obot(tc_fun(X1034,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1034),hAPP(c_COMBK(tc_HOL_Obool,X1034),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_20,plain,
! [X991,X992] : hAPP(c_Set_OCollect(X992),X991) = X991,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X24,X5] :
( hAPP(c_Set_OCollect(X5),X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X24,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_22,plain,
! [X17737,X17738,X17739,X17740] : hAPP(hAPP(c_COMBK(X17740,X17739),X17738),X17737) = X17738,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_23,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_24,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,plain,
! [X2785,X2786] : hAPP(c_Set_OCollect(X2786),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2786),c_fNot),X2785)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2786,tc_HOL_Obool)),hAPP(c_Set_OCollect(X2786),X2785)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_26,plain,
! [X1025,X1026,X1027,X1028,X1030] :
( ( hAPP(c_Set_OCollect(X1030),X1028) = c_Orderings_Obot__class_Obot(tc_fun(X1030,tc_HOL_Obool))
| hBOOL(hAPP(X1028,esk33_1(X1028))) )
& ( ~ hBOOL(hAPP(X1025,X1027))
| hAPP(c_Set_OCollect(X1026),X1025) != c_Orderings_Obot__class_Obot(tc_fun(X1026,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_21])])])])])]) ).
fof(c_0_27,plain,
! [X321,X322] :
( X322 = X321
| hAPP(X322,esk1_2(X321,X322)) != hAPP(X321,esk1_2(X321,X322)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_28,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,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_23,c_0_24]) ).
fof(c_0_30,plain,
! [X129] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X129),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_31,plain,
! [X2410,X2411] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2411,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2411,tc_HOL_Obool)),X2410)) = X2410,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_32,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_25]) ).
fof(c_0_33,plain,
! [X24] :
( ~ hBOOL(X24)
| ~ hBOOL(hAPP(c_fNot,X24)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_34,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk33_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_35,plain,
! [X2827] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2827,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X2827,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2827,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_36,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_38,plain,
! [X2092] : c_Orderings_Otop__class_Otop(tc_fun(X2092,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X2092),hAPP(c_COMBK(tc_HOL_Obool,X2092),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_39,plain,
! [X4760,X4761] :
( X4760 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4761),X4760) != X4761 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_40,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_41,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_42,plain,
! [X4829] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X4829),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
fof(c_0_43,plain,
! [X17741,X17742,X17743,X17744,X17745,X17746] : hAPP(hAPP(hAPP(c_COMBB(X17746,X17745,X17744),X17743),X17742),X17741) = hAPP(X17743,hAPP(X17742,X17741)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_44,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_31]) ).
cnf(c_0_45,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_32,c_0_24]),c_0_24]) ).
fof(c_0_46,plain,
! [X17763] :
( ~ hBOOL(X17763)
| ~ hBOOL(hAPP(c_fNot,X17763)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
cnf(c_0_47,plain,
( hBOOL(hAPP(X1,esk33_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_34,c_0_24]) ).
cnf(c_0_48,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_35]) ).
cnf(c_0_49,plain,
( hAPP(X1,esk1_2(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X1)) != c_fFalse
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_50,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_38]) ).
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_39]) ).
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_40,c_0_41]) ).
fof(c_0_53,plain,
! [X4385,X4386] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4386),hAPP(c_Nat_OSuc,X4385)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4386),X4385)),
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_42]) ).
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_43]) ).
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_44,c_0_45]),c_0_45]) ).
fof(c_0_57,plain,
! [X16404,X16405] : hAPP(c_List_Orev(X16405),hAPP(c_List_Orev(X16405),X16404)) = X16404,
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_46]) ).
cnf(c_0_59,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_47]),c_0_37]),c_0_28]) ).
cnf(c_0_60,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_48,c_0_45]) ).
cnf(c_0_61,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_49,c_0_37]) ).
cnf(c_0_62,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_50,c_0_24]) ).
cnf(c_0_63,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_64,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_65,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_66,plain,
! [X4778] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4778),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X4778,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_67,plain,
! [X73] : X73 != hAPP(c_Nat_OSuc,X73),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_68,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_69,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_70,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_71,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_73,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_63,c_0_64]),c_0_65]) ).
cnf(c_0_74,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_66]) ).
fof(c_0_75,plain,
! [X1543] : X1543 != hAPP(c_Nat_OSuc,X1543),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_67])]) ).
cnf(c_0_76,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_77,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_70,c_0_59]) ).
cnf(c_0_78,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_71]),c_0_72]),c_0_37]) ).
cnf(c_0_79,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_73,c_0_64]) ).
cnf(c_0_80,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_74,c_0_52]) ).
cnf(c_0_81,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_83,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82])]) ).
cnf(c_0_85,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_86,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_82]),c_0_81]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW346+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.39 % Computer : n013.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Mon Sep 21 09:47:48 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/10.44 Running first-order theorem proving
% 0.14/10.44 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
% 148.00/30.40 % Version: 3.5.1
% 148.00/30.40 % Preprocessing class: FMLMSMSMSSSNFFN.
% 148.00/30.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 148.00/30.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 148.00/30.40 % Starting new_bool_3 with 300s (1) cores
% 148.00/30.40 % Starting new_bool_1 with 300s (1) cores
% 148.00/30.40 % Starting sh5l with 300s (1) cores
% 148.00/30.40 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 480917 completed with status 0
% 148.00/30.40 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 148.00/30.40 % Preprocessing class: FMLMSMSMSSSNFFN.
% 148.00/30.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 148.00/30.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 148.00/30.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 148.00/30.40 % No SInE strategy applied
% 148.00/30.40 % Search class: FGHSM-SMLM33-DFFFFFNN
% 148.00/30.40 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 148.00/30.40 % Starting SubtermCWHack with 135s (1) cores
% 148.00/30.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 148.00/30.40 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 148.00/30.40 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 148.00/30.40 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 148.00/30.40 % SAT001_CA_MinMin_p005000_rr with pid 480927 completed with status 0
% 148.00/30.40 % Result found by SAT001_CA_MinMin_p005000_rr
% 148.00/30.40 % Preprocessing class: FMLMSMSMSSSNFFN.
% 148.00/30.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 148.00/30.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 148.00/30.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 148.00/30.40 % No SInE strategy applied
% 148.00/30.40 % Search class: FGHSM-SMLM33-DFFFFFNN
% 148.00/30.40 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 148.00/30.40 % Starting SubtermCWHack with 135s (1) cores
% 148.00/30.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 148.00/30.40 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 148.00/30.40 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 148.00/30.40 % Preprocessing time : 0.216 s
% 148.00/30.40 % Presaturation interreduction done
% 148.00/30.40
% 148.00/30.40 % Proof found!
% 148.00/30.40 % SZS status ContradictoryAxioms
% 148.00/30.40 % SZS output start CNFRefutation
% See solution above
% 148.00/30.40 % Parsed axioms : 5226
% 148.00/30.40 % Removed by relevancy pruning/SinE : 0
% 148.00/30.40 % Initial clauses : 7591
% 148.00/30.40 % Removed in clause preprocessing : 239
% 148.00/30.40 % Initial clauses in saturation : 7352
% 148.00/30.40 % Processed clauses : 21283
% 148.00/30.40 % ...of these trivial : 433
% 148.00/30.40 % ...subsumed : 8172
% 148.00/30.40 % ...remaining for further processing : 12678
% 148.00/30.40 % Other redundant clauses eliminated : 1559
% 148.00/30.40 % Clauses deleted for lack of memory : 0
% 148.00/30.40 % Backward-subsumed : 264
% 148.00/30.40 % Backward-rewritten : 386
% 148.00/30.40 % Generated clauses : 184976
% 148.00/30.40 % ...of the previous two non-redundant : 175762
% 148.00/30.40 % ...aggressively subsumed : 0
% 148.00/30.40 % Contextual simplify-reflections : 41
% 148.00/30.40 % Paramodulations : 183428
% 148.00/30.40 % Factorizations : 2
% 148.00/30.40 % NegExts : 0
% 148.00/30.40 % Equation resolutions : 1611
% 148.00/30.40 % Disequality decompositions : 0
% 148.00/30.40 % Total rewrite steps : 60140
% 148.00/30.40 % ...of those cached : 42921
% 148.00/30.40 % Propositional unsat checks : 3
% 148.00/30.40 % Propositional check models : 2
% 148.00/30.40 % Propositional check unsatisfiable : 0
% 148.00/30.40 % Propositional clauses : 0
% 148.00/30.40 % Propositional clauses after purity: 0
% 148.00/30.40 % Propositional unsat core size : 0
% 148.00/30.40 % Propositional preprocessing time : 0.000
% 148.00/30.40 % Propositional encoding time : 0.345
% 148.00/30.40 % Propositional solver time : 0.178
% 148.00/30.40 % Success case prop preproc time : 0.000
% 148.00/30.40 % Success case prop encoding time : 0.000
% 148.00/30.40 % Success case prop solver time : 0.000
% 148.00/30.40 % Current number of processed clauses : 5618
% 148.00/30.40 % Positive orientable unit clauses : 1575
% 148.00/30.40 % Positive unorientable unit clauses: 126
% 148.00/30.40 % Negative unit clauses : 833
% 148.00/30.40 % Non-unit-clauses : 3084
% 148.00/30.40 % Current number of unprocessed clauses: 158524
% 148.00/30.40 % ...number of literals in the above : 304260
% 148.00/30.40 % Current number of archived formulas : 0
% 148.00/30.40 % Current number of archived clauses : 6614
% 148.00/30.40 % Clause-clause subsumption calls (NU) : 4967598
% 148.00/30.40 % Rec. Clause-clause subsumption calls : 2293087
% 148.00/30.40 % Non-unit clause-clause subsumptions : 7010
% 148.00/30.40 % Unit Clause-clause subsumption calls : 142133
% 148.00/30.40 % Rewrite failures with RHS unbound : 561
% 148.00/30.40 % BW rewrite match attempts : 38734
% 148.00/30.40 % BW rewrite match successes : 1348
% 148.00/30.40 % Condensation attempts : 207033
% 148.00/30.40 % Condensation successes : 1387
% 148.00/30.40 % Termbank termtop insertions : 6842425
% 148.00/30.40 % Search garbage collected termcells : 101979
% 148.00/30.40
% 148.00/30.40 % -------------------------------------------------
% 148.00/30.40 % User time : 17.672 s
% 148.00/30.40 % System time : 0.468 s
% 148.00/30.40 % Total time : 18.139 s
% 148.00/30.40 % Maximum resident set size: 42588 pages
% 148.00/30.40
% 148.00/30.40 % -------------------------------------------------
% 148.00/30.40 % User time : 86.435 s
% 148.00/30.40 % System time : 2.160 s
% 148.00/30.40 % Total time : 88.595 s
% 148.00/30.40 % Maximum resident set size: 12544 pages
% 148.00/30.40 % E exiting
%------------------------------------------------------------------------------