%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW293+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 : n014.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 03:10:14 PM UTC 2026
% Result : ContradictoryAxioms 84.16s 13.62s
% Output : CNFRefutation 84.16s
% 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,
! [X19,X10] :
( hAPP(c_Set_OCollect(X10),X19) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [X10] : c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X19,X10] : hAPP(c_Set_OCollect(X10),X19) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X19,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X19)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X335,X87,X10,X94] : hAPP(hAPP(c_COMBK(X94,X10),X87),X335) = X87,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_UNIV__def,axiom,
! [X10] : c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Zero__neq__Suc,axiom,
! [X97] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X154,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X154)) = X154,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X19] :
( ~ hBOOL(X19)
| ~ hBOOL(hAPP(c_fNot,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_sum__case__KK,axiom,
! [X16,X39,X125,X10,X13] : hAPP(c_Sum__Type_Osum_Osum__case(X13,X10,X125,hAPP(c_COMBK(X10,X13),X39),hAPP(c_COMBK(X10,X125),X39)),X16) = X39,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__KK) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_add__eq__self__zero,axiom,
! [X42,X97] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42) = X97
=> X42 = 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,
! [X196,X17,X19,X125,X10,X13] : hAPP(hAPP(hAPP(c_COMBB(X13,X10,X125),X19),X17),X196) = hAPP(X19,hAPP(X17,X196)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X42,X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),hAPP(c_Nat_OSuc,X42)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X297,X94] : hAPP(c_List_Orev(X94),hAPP(c_List_Orev(X94),X297)) = X297,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X97] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X97),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X42] : X42 != hAPP(c_Nat_OSuc,X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,plain,
! [X19,X10] :
( hAPP(c_Set_OCollect(X10),X19) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_20,plain,
! [X12415] : c_Orderings_Obot__class_Obot(tc_fun(X12415,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X12415),hAPP(c_COMBK(tc_HOL_Obool,X12415),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X12416,X12417] : hAPP(c_Set_OCollect(X12417),X12416) = X12416,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X12373,X12374] : hAPP(c_Set_OCollect(X12374),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X12374),c_fNot),X12373)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X12374,tc_HOL_Obool)),hAPP(c_Set_OCollect(X12374),X12373)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_23,plain,
! [X12409,X12410,X12411,X12412,X12414] :
( ( hAPP(c_Set_OCollect(X12414),X12412) = c_Orderings_Obot__class_Obot(tc_fun(X12414,tc_HOL_Obool))
| hBOOL(hAPP(X12412,esk310_1(X12412))) )
& ( ~ hBOOL(hAPP(X12409,X12411))
| hAPP(c_Set_OCollect(X12410),X12409) != c_Orderings_Obot__class_Obot(tc_fun(X12410,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,
! [X17685,X17686,X17687,X17688] : hAPP(hAPP(c_COMBK(X17688,X17687),X17686),X17685) = X17686,
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,
! [X12390] : c_Orderings_Otop__class_Otop(tc_fun(X12390,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X12390),hAPP(c_COMBK(tc_HOL_Obool,X12390),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_28,plain,
! [X97] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X97),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_29,plain,
! [X5664,X5665] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5665,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5665,tc_HOL_Obool)),X5664)) = X5664,
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,
! [X19] :
( ~ hBOOL(X19)
| ~ hBOOL(hAPP(c_fNot,X19)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
fof(c_0_32,plain,
! [X6070,X6071,X6072,X6073,X6074] : hAPP(c_Sum__Type_Osum_Osum__case(X6074,X6073,X6072,hAPP(c_COMBK(X6073,X6074),X6071),hAPP(c_COMBK(X6073,X6072),X6071)),X6070) = X6071,
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,esk310_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,
! [X11456] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11456,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X11456,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X11456,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,
! [X1326,X1327] :
( X1326 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1327),X1326) != X1327 ),
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,
! [X1272] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1272),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_28])]) ).
fof(c_0_42,plain,
! [X17689,X17690,X17691,X17692,X17693,X17694] : hAPP(hAPP(hAPP(c_COMBB(X17694,X17693,X17692),X17691),X17690),X17689) = hAPP(X17691,hAPP(X17690,X17689)),
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,
! [X17711] :
( ~ hBOOL(X17711)
| ~ hBOOL(hAPP(c_fNot,X17711)) ),
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,esk310_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,
! [X1332,X1333] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1333),hAPP(c_Nat_OSuc,X1332)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1333),X1332)),
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,
! [X17516,X17517] : hAPP(c_List_Orev(X17517),hAPP(c_List_Orev(X17517),X17516)) = X17516,
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,
! [X1323] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1323),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1323,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_66,plain,
! [X42] : X42 != hAPP(c_Nat_OSuc,X42),
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,
! [X1357] : X1357 != hAPP(c_Nat_OSuc,X1357),
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
% 0.00/0.04 % Problem : SWW293+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n014.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 09:46:04 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.53 Running first-order theorem proving
% 0.27/0.53 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
% 84.16/13.62 % Version: 3.5.1
% 84.16/13.62 % Preprocessing class: FMLMSMSMSSSNFFN.
% 84.16/13.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.16/13.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 84.16/13.62 % Starting new_bool_3 with 300s (1) cores
% 84.16/13.62 % Starting new_bool_1 with 300s (1) cores
% 84.16/13.62 % Starting sh5l with 300s (1) cores
% 84.16/13.62 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3765842 completed with status 0
% 84.16/13.62 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 84.16/13.62 % Preprocessing class: FMLMSMSMSSSNFFN.
% 84.16/13.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.16/13.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 84.16/13.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 84.16/13.62 % No SInE strategy applied
% 84.16/13.62 % Search class: FGHSM-SMLM33-DFFFFFNN
% 84.16/13.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 84.16/13.62 % Starting SubtermCWHack with 136s (1) cores
% 84.16/13.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 84.16/13.62 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 84.16/13.62 % Starting SAT001_CA_MinMin_p005000_rr with 136s (1) cores
% 84.16/13.62 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 84.16/13.62 % SAT001_CA_MinMin_p005000_rr with pid 3766007 completed with status 0
% 84.16/13.62 % Result found by SAT001_CA_MinMin_p005000_rr
% 84.16/13.62 % Preprocessing class: FMLMSMSMSSSNFFN.
% 84.16/13.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.16/13.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 84.16/13.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 84.16/13.62 % No SInE strategy applied
% 84.16/13.62 % Search class: FGHSM-SMLM33-DFFFFFNN
% 84.16/13.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 84.16/13.62 % Starting SubtermCWHack with 136s (1) cores
% 84.16/13.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 84.16/13.62 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 84.16/13.62 % Starting SAT001_CA_MinMin_p005000_rr with 136s (1) cores
% 84.16/13.62 % Preprocessing time : 0.213 s
% 84.16/13.62 % Presaturation interreduction done
% 84.16/13.62
% 84.16/13.62 % Proof found!
% 84.16/13.62 % SZS status ContradictoryAxioms
% 84.16/13.62 % SZS output start CNFRefutation
% See solution above
% 84.16/13.62 % Parsed axioms : 5205
% 84.16/13.62 % Removed by relevancy pruning/SinE : 0
% 84.16/13.62 % Initial clauses : 7485
% 84.16/13.62 % Removed in clause preprocessing : 252
% 84.16/13.62 % Initial clauses in saturation : 7233
% 84.16/13.62 % Processed clauses : 21626
% 84.16/13.62 % ...of these trivial : 363
% 84.16/13.62 % ...subsumed : 8139
% 84.16/13.62 % ...remaining for further processing : 13124
% 84.16/13.62 % Other redundant clauses eliminated : 2132
% 84.16/13.62 % Clauses deleted for lack of memory : 0
% 84.16/13.62 % Backward-subsumed : 146
% 84.16/13.62 % Backward-rewritten : 446
% 84.16/13.62 % Generated clauses : 204963
% 84.16/13.62 % ...of the previous two non-redundant : 194911
% 84.16/13.62 % ...aggressively subsumed : 0
% 84.16/13.62 % Contextual simplify-reflections : 27
% 84.16/13.62 % Paramodulations : 202826
% 84.16/13.62 % Factorizations : 2
% 84.16/13.62 % NegExts : 0
% 84.16/13.62 % Equation resolutions : 2198
% 84.16/13.62 % Disequality decompositions : 0
% 84.16/13.62 % Total rewrite steps : 62790
% 84.16/13.62 % ...of those cached : 46382
% 84.16/13.62 % Propositional unsat checks : 3
% 84.16/13.62 % Propositional check models : 2
% 84.16/13.62 % Propositional check unsatisfiable : 0
% 84.16/13.62 % Propositional clauses : 0
% 84.16/13.62 % Propositional clauses after purity: 0
% 84.16/13.62 % Propositional unsat core size : 0
% 84.16/13.62 % Propositional preprocessing time : 0.000
% 84.16/13.62 % Propositional encoding time : 0.207
% 84.16/13.62 % Propositional solver time : 0.101
% 84.16/13.62 % Success case prop preproc time : 0.000
% 84.16/13.62 % Success case prop encoding time : 0.000
% 84.16/13.62 % Success case prop solver time : 0.000
% 84.16/13.62 % Current number of processed clauses : 6261
% 84.16/13.62 % Positive orientable unit clauses : 1629
% 84.16/13.62 % Positive unorientable unit clauses: 130
% 84.16/13.62 % Negative unit clauses : 1210
% 84.16/13.62 % Non-unit-clauses : 3292
% 84.16/13.62 % Current number of unprocessed clauses: 174791
% 84.16/13.62 % ...number of literals in the above : 312718
% 84.16/13.62 % Current number of archived formulas : 0
% 84.16/13.62 % Current number of archived clauses : 6412
% 84.16/13.62 % Clause-clause subsumption calls (NU) : 5772326
% 84.16/13.62 % Rec. Clause-clause subsumption calls : 2389547
% 84.16/13.62 % Non-unit clause-clause subsumptions : 3324
% 84.16/13.62 % Unit Clause-clause subsumption calls : 365045
% 84.16/13.62 % Rewrite failures with RHS unbound : 590
% 84.16/13.62 % BW rewrite match attempts : 44836
% 84.16/13.62 % BW rewrite match successes : 1261
% 84.16/13.62 % Condensation attempts : 227481
% 84.16/13.62 % Condensation successes : 670
% 84.16/13.62 % Termbank termtop insertions : 7177387
% 84.16/13.62 % Search garbage collected termcells : 99123
% 84.16/13.62
% 84.16/13.62 % -------------------------------------------------
% 84.16/13.62 % User time : 11.821 s
% 84.16/13.62 % System time : 0.383 s
% 84.16/13.62 % Total time : 12.204 s
% 84.16/13.62 % Maximum resident set size: 42412 pages
% 84.16/13.62
% 84.16/13.62 % -------------------------------------------------
% 84.16/13.62 % User time : 56.369 s
% 84.16/13.62 % System time : 1.623 s
% 84.16/13.62 % Total time : 57.992 s
% 84.16/13.62 % Maximum resident set size: 12288 pages
% 84.16/13.62 % E exiting
%------------------------------------------------------------------------------