%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW357+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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:22 PM UTC 2026
% Result : ContradictoryAxioms 122.13s 21.09s
% Output : CNFRefutation 122.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 89 ( 72 unt; 0 def)
% Number of atoms : 108 ( 91 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; 0-3 aty)
% Number of variables : 154 ( 17 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X42,X11] :
( hAPP(c_Set_OCollect(X11),X42) = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X42,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X11] : c_Orderings_Obot__class_Obot(tc_fun(X11,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11),hAPP(c_COMBK(tc_HOL_Obool,X11),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X42,X11] : hAPP(c_Set_OCollect(X11),X42) = X42,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X42,X11] : hAPP(c_Set_OCollect(X11),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11),c_fNot),X42)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_vimage__Collect__eq,axiom,
! [X42,X2,X9,X11] : hAPP(c_Set_Ovimage(X11,X9,X2),hAPP(c_Set_OCollect(X9),X42)) = hAPP(c_Set_OCollect(X11),hAPP(hAPP(c_COMBB(X9,tc_HOL_Obool,X11),X42),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
fof(help_c__COMBK__1,axiom,
! [X280,X279,X11,X33] : hAPP(hAPP(c_COMBK(X33,X11),X279),X280) = X279,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Zero__not__Suc,axiom,
! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X12,X11] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11,tc_HOL_Obool)),X12)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_vimage__id,axiom,
! [X12,X11] : hAPP(c_Set_Ovimage(X11,X11,c_Fun_Oid(X11)),X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__id) ).
fof(help_c__fNot__1,axiom,
! [X42] :
( ~ hBOOL(X42)
| ~ hBOOL(hAPP(c_fNot,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_UNIV__def,axiom,
! [X11] : c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11),hAPP(c_COMBK(tc_HOL_Obool,X11),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_add__eq__self__zero,axiom,
! [X7,X19] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X7) = X19
=> X7 = 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(fact_Compl__empty__eq,axiom,
! [X11] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_add__Suc__right,axiom,
! [X7,X19] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,X7)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_id__def,axiom,
! [X174,X33] : hAPP(c_Fun_Oid(X33),X174) = X174,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).
fof(help_c__COMBB__1,axiom,
! [X41,X46,X42,X23,X11,X9] : hAPP(hAPP(hAPP(c_COMBB(X9,X11,X23),X42),X46),X41) = hAPP(X42,hAPP(X46,X41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X19] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X7] : X7 != hAPP(c_Nat_OSuc,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_20,plain,
! [X42,X11] :
( hAPP(c_Set_OCollect(X11),X42) = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X42,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_21,plain,
! [X9844] : c_Orderings_Obot__class_Obot(tc_fun(X9844,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X9844),hAPP(c_COMBK(tc_HOL_Obool,X9844),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_22,plain,
! [X9839,X9840] : hAPP(c_Set_OCollect(X9840),X9839) = X9839,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_23,plain,
! [X9800,X9801] : hAPP(c_Set_OCollect(X9801),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X9801),c_fNot),X9800)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9801,tc_HOL_Obool)),hAPP(c_Set_OCollect(X9801),X9800)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_24,plain,
! [X9813,X9814,X9815,X9816] : hAPP(c_Set_Ovimage(X9816,X9815,X9814),hAPP(c_Set_OCollect(X9815),X9813)) = hAPP(c_Set_OCollect(X9816),hAPP(hAPP(c_COMBB(X9815,tc_HOL_Obool,X9816),X9813),X9814)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_25,plain,
! [X9833,X9834,X9835,X9836,X9838] :
( ( hAPP(c_Set_OCollect(X9838),X9836) = c_Orderings_Obot__class_Obot(tc_fun(X9838,tc_HOL_Obool))
| hBOOL(hAPP(X9836,esk250_1(X9836))) )
& ( ~ hBOOL(hAPP(X9833,X9835))
| hAPP(c_Set_OCollect(X9834),X9833) != c_Orderings_Obot__class_Obot(tc_fun(X9834,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_20])])])])])]) ).
fof(c_0_26,plain,
! [X17462,X17463,X17464,X17465] : hAPP(hAPP(c_COMBK(X17465,X17464),X17463),X17462) = X17463,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_27,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_21]) ).
cnf(c_0_28,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_29,plain,
! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X19),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_30,plain,
! [X3824,X3825] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3825,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X3825,tc_HOL_Obool)),X3824)) = X3824,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_31,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_23]) ).
fof(c_0_32,plain,
! [X10028,X10029] : hAPP(c_Set_Ovimage(X10029,X10029,c_Fun_Oid(X10029)),X10028) = X10028,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
cnf(c_0_33,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_34,plain,
! [X42] :
( ~ hBOOL(X42)
| ~ hBOOL(hAPP(c_fNot,X42)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_35,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk250_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,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_27,c_0_28]) ).
fof(c_0_38,plain,
! [X9817] : c_Orderings_Otop__class_Otop(tc_fun(X9817,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X9817),hAPP(c_COMBK(tc_HOL_Obool,X9817),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_39,plain,
! [X1328,X1329] :
( X1328 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1329),X1328) != X1329 ),
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,
! [X1645] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1645),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
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_30]) ).
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_31,c_0_28]),c_0_28]) ).
cnf(c_0_45,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_46,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_28]),c_0_28]) ).
fof(c_0_47,plain,
! [X17488] :
( ~ hBOOL(X17488)
| ~ hBOOL(hAPP(c_fNot,X17488)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
cnf(c_0_48,plain,
( hBOOL(hAPP(X1,esk250_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_35,c_0_28]) ).
cnf(c_0_49,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_50,plain,
! [X9039] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9039,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X9039,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9039,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_51,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_52,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_53,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_54,plain,
! [X1674,X1675] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1675),hAPP(c_Nat_OSuc,X1674)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1675),X1674)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_55,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_56,plain,
! [X10020,X10021] : hAPP(c_Fun_Oid(X10021),X10020) = X10020,
inference(variable_rename,[status(thm)],[fact_id__def]) ).
cnf(c_0_57,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]) ).
cnf(c_0_58,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_59,plain,
! [X17466,X17467,X17468,X17469,X17470,X17471] : hAPP(hAPP(hAPP(c_COMBB(X17471,X17470,X17469),X17468),X17467),X17466) = hAPP(X17468,hAPP(X17467,X17466)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_60,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_61,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_48]),c_0_49]),c_0_36]) ).
cnf(c_0_62,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_50]) ).
cnf(c_0_63,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_51,c_0_28]) ).
cnf(c_0_64,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_52,c_0_53]) ).
cnf(c_0_65,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_54]) ).
cnf(c_0_66,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_55,c_0_53]) ).
fof(c_0_67,plain,
! [X1325] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1325),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1325,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_68,plain,
! [X7] : X7 != hAPP(c_Nat_OSuc,X7),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_69,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_70,plain,
c_Fun_Oid(tc_HOL_Obool) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_71,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_72,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_73,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_62,c_0_44]) ).
cnf(c_0_74,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_36,c_0_63]) ).
cnf(c_0_75,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_64,c_0_65]),c_0_66]) ).
cnf(c_0_76,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_67]) ).
fof(c_0_77,plain,
! [X1634] : X1634 != hAPP(c_Nat_OSuc,X1634),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_68])]) ).
cnf(c_0_78,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_79,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_72,c_0_61]) ).
cnf(c_0_80,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_73]),c_0_74]),c_0_49]) ).
cnf(c_0_81,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_75,c_0_65]) ).
cnf(c_0_82,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_76,c_0_53]) ).
cnf(c_0_83,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_84,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_85,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_86,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84])]) ).
cnf(c_0_87,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_88,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_84]),c_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW357+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 % Computer : n018.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 09:50:44 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.55 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
% 122.13/21.09 % Version: 3.5.1
% 122.13/21.09 % Preprocessing class: FMLMSMSMSSSNFFN.
% 122.13/21.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.13/21.09 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 122.13/21.09 % Starting new_bool_3 with 300s (1) cores
% 122.13/21.09 % Starting new_bool_1 with 300s (1) cores
% 122.13/21.09 % Starting sh5l with 300s (1) cores
% 122.13/21.09 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1586252 completed with status 0
% 122.13/21.09 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 122.13/21.09 % Preprocessing class: FMLMSMSMSSSNFFN.
% 122.13/21.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.13/21.09 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 122.13/21.09 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 122.13/21.09 % No SInE strategy applied
% 122.13/21.09 % Search class: FGHSM-SMLM33-DFFFFFNN
% 122.13/21.09 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 122.13/21.09 % Starting SubtermCWHack with 135s (1) cores
% 122.13/21.09 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 122.13/21.09 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 122.13/21.09 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 122.13/21.09 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 122.13/21.09 % SAT001_CA_MinMin_p005000_rr with pid 1586262 completed with status 0
% 122.13/21.09 % Result found by SAT001_CA_MinMin_p005000_rr
% 122.13/21.09 % Preprocessing class: FMLMSMSMSSSNFFN.
% 122.13/21.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.13/21.09 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 122.13/21.09 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 122.13/21.09 % No SInE strategy applied
% 122.13/21.09 % Search class: FGHSM-SMLM33-DFFFFFNN
% 122.13/21.09 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 122.13/21.09 % Starting SubtermCWHack with 135s (1) cores
% 122.13/21.09 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 122.13/21.09 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 122.13/21.09 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 122.13/21.09 % Preprocessing time : 0.343 s
% 122.13/21.09 % Presaturation interreduction done
% 122.13/21.09
% 122.13/21.09 % Proof found!
% 122.13/21.09 % SZS status ContradictoryAxioms
% 122.13/21.09 % SZS output start CNFRefutation
% See solution above
% 122.13/21.09 % Parsed axioms : 5226
% 122.13/21.09 % Removed by relevancy pruning/SinE : 0
% 122.13/21.09 % Initial clauses : 7606
% 122.13/21.09 % Removed in clause preprocessing : 245
% 122.13/21.09 % Initial clauses in saturation : 7361
% 122.13/21.09 % Processed clauses : 21536
% 122.13/21.09 % ...of these trivial : 618
% 122.13/21.09 % ...subsumed : 8012
% 122.13/21.09 % ...remaining for further processing : 12906
% 122.13/21.09 % Other redundant clauses eliminated : 1457
% 122.13/21.09 % Clauses deleted for lack of memory : 0
% 122.13/21.09 % Backward-subsumed : 244
% 122.13/21.09 % Backward-rewritten : 606
% 122.13/21.09 % Generated clauses : 231943
% 122.13/21.09 % ...of the previous two non-redundant : 221365
% 122.13/21.09 % ...aggressively subsumed : 0
% 122.13/21.09 % Contextual simplify-reflections : 40
% 122.13/21.09 % Paramodulations : 230513
% 122.13/21.09 % Factorizations : 4
% 122.13/21.09 % NegExts : 0
% 122.13/21.09 % Equation resolutions : 1492
% 122.13/21.09 % Disequality decompositions : 0
% 122.13/21.09 % Total rewrite steps : 62169
% 122.13/21.09 % ...of those cached : 46197
% 122.13/21.09 % Propositional unsat checks : 3
% 122.13/21.09 % Propositional check models : 2
% 122.13/21.09 % Propositional check unsatisfiable : 0
% 122.13/21.09 % Propositional clauses : 0
% 122.13/21.09 % Propositional clauses after purity: 0
% 122.13/21.09 % Propositional unsat core size : 0
% 122.13/21.09 % Propositional preprocessing time : 0.000
% 122.13/21.09 % Propositional encoding time : 0.285
% 122.13/21.09 % Propositional solver time : 0.129
% 122.13/21.09 % Success case prop preproc time : 0.000
% 122.13/21.09 % Success case prop encoding time : 0.000
% 122.13/21.09 % Success case prop solver time : 0.000
% 122.13/21.09 % Current number of processed clauses : 5613
% 122.13/21.09 % Positive orientable unit clauses : 1674
% 122.13/21.09 % Positive unorientable unit clauses: 126
% 122.13/21.09 % Negative unit clauses : 848
% 122.13/21.09 % Non-unit-clauses : 2965
% 122.13/21.09 % Current number of unprocessed clauses: 196339
% 122.13/21.09 % ...number of literals in the above : 380323
% 122.13/21.09 % Current number of archived formulas : 0
% 122.13/21.09 % Current number of archived clauses : 6832
% 122.13/21.09 % Clause-clause subsumption calls (NU) : 5233279
% 122.13/21.09 % Rec. Clause-clause subsumption calls : 2364908
% 122.13/21.09 % Non-unit clause-clause subsumptions : 7131
% 122.13/21.09 % Unit Clause-clause subsumption calls : 205549
% 122.13/21.09 % Rewrite failures with RHS unbound : 367
% 122.13/21.09 % BW rewrite match attempts : 41300
% 122.13/21.09 % BW rewrite match successes : 1325
% 122.13/21.09 % Condensation attempts : 254696
% 122.13/21.09 % Condensation successes : 1321
% 122.13/21.09 % Termbank termtop insertions : 7554378
% 122.13/21.09 % Search garbage collected termcells : 102626
% 122.13/21.09
% 122.13/21.09 % -------------------------------------------------
% 122.13/21.09 % User time : 17.895 s
% 122.13/21.09 % System time : 0.516 s
% 122.13/21.09 % Total time : 18.411 s
% 122.13/21.09 % Maximum resident set size: 42588 pages
% 122.13/21.09
% 122.13/21.09 % -------------------------------------------------
% 122.13/21.09 % User time : 81.341 s
% 122.13/21.09 % System time : 2.215 s
% 122.13/21.09 % Total time : 83.556 s
% 122.13/21.09 % Maximum resident set size: 12288 pages
% 122.13/21.09 % E exiting
%------------------------------------------------------------------------------