%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW370+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 : n026.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 03:10:24 PM UTC 2026
% Result : ContradictoryAxioms 121.33s 19.87s
% Output : CNFRefutation 121.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 82 ( 65 unt; 0 def)
% Number of atoms : 101 ( 84 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,
! [X18,X5] :
( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
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,
! [X18,X5] : hAPP(c_Set_OCollect(X5),X18) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X18,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X18)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X320,X21,X28,X5] : hAPP(hAPP(c_COMBK(X5,X28),X21),X320) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
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_Zero__not__Suc,axiom,
! [X81] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X29,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)),X29)) = X29,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X18] :
( ~ hBOOL(X18)
| ~ hBOOL(hAPP(c_fNot,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_Compl__UNIV__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_add__eq__self__zero,axiom,
! [X54,X81] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X81),X54) = X81
=> X54 = 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,
! [X44,X16,X18,X96,X5,X28] : hAPP(hAPP(hAPP(c_COMBB(X28,X5,X96),X18),X16),X44) = hAPP(X18,hAPP(X16,X44)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X54,X81] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X81),hAPP(c_Nat_OSuc,X54)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X81),X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X273,X5] : hAPP(c_List_Orev(X5),hAPP(c_List_Orev(X5),X273)) = X273,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X81] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X81),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X81,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X54] : X54 != hAPP(c_Nat_OSuc,X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_18,plain,
! [X18,X5] :
( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_19,plain,
! [X11232] : c_Orderings_Obot__class_Obot(tc_fun(X11232,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11232),hAPP(c_COMBK(tc_HOL_Obool,X11232),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_20,plain,
! [X11230,X11231] : hAPP(c_Set_OCollect(X11231),X11230) = X11230,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X11221,X11222] : hAPP(c_Set_OCollect(X11222),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11222),c_fNot),X11221)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11222,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11222),X11221)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_22,plain,
! [X11239,X11240,X11241,X11242,X11244] :
( ( hAPP(c_Set_OCollect(X11244),X11242) = c_Orderings_Obot__class_Obot(tc_fun(X11244,tc_HOL_Obool))
| hBOOL(hAPP(X11242,esk286_1(X11242))) )
& ( ~ hBOOL(hAPP(X11239,X11241))
| hAPP(c_Set_OCollect(X11240),X11239) != c_Orderings_Obot__class_Obot(tc_fun(X11240,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,
! [X17663,X17664,X17665,X17666] : hAPP(hAPP(c_COMBK(X17666,X17665),X17664),X17663) = X17664,
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,
! [X11254] : c_Orderings_Otop__class_Otop(tc_fun(X11254,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11254),hAPP(c_COMBK(tc_HOL_Obool,X11254),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_27,plain,
! [X81] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X81),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_28,plain,
! [X2933,X2934] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2934,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2934,tc_HOL_Obool)),X2933)) = X2933,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_29,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_30,plain,
! [X18] :
( ~ hBOOL(X18)
| ~ hBOOL(hAPP(c_fNot,X18)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_31,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk286_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,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_34,plain,
! [X10418] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10418,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10418,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10418,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).
cnf(c_0_35,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_26]) ).
fof(c_0_36,plain,
! [X2397,X2398] :
( X2397 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2398),X2397) != X2398 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_37,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_38,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_39,plain,
! [X770] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X770),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
fof(c_0_40,plain,
! [X17667,X17668,X17669,X17670,X17671,X17672] : hAPP(hAPP(hAPP(c_COMBB(X17672,X17671,X17670),X17669),X17668),X17667) = hAPP(X17669,hAPP(X17668,X17667)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_41,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_28]) ).
cnf(c_0_42,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_29,c_0_25]),c_0_25]) ).
fof(c_0_43,plain,
! [X17689] :
( ~ hBOOL(X17689)
| ~ hBOOL(hAPP(c_fNot,X17689)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
cnf(c_0_44,plain,
( hBOOL(hAPP(X1,esk286_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_45,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_46,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_34]) ).
cnf(c_0_47,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_35,c_0_25]) ).
cnf(c_0_48,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_36]) ).
cnf(c_0_49,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_50,plain,
! [X2407,X2408] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2408),hAPP(c_Nat_OSuc,X2407)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2408),X2407)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_51,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,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_41,c_0_42]),c_0_42]) ).
fof(c_0_54,plain,
! [X16551,X16552] : hAPP(c_List_Orev(X16552),hAPP(c_List_Orev(X16552),X16551)) = X16551,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_55,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_56,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_44]),c_0_45]),c_0_32]) ).
cnf(c_0_57,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_46,c_0_42]) ).
cnf(c_0_58,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_32,c_0_47]) ).
cnf(c_0_59,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_48,c_0_49]) ).
cnf(c_0_60,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_50]) ).
cnf(c_0_61,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_51,c_0_49]) ).
fof(c_0_62,plain,
! [X2401] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2401),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2401,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_63,plain,
! [X54] : X54 != hAPP(c_Nat_OSuc,X54),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_64,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_52]) ).
cnf(c_0_65,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_67,plain,
hAPP(c_fNot,c_fTrue) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_57]),c_0_45]),c_0_58]) ).
cnf(c_0_68,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_59,c_0_60]),c_0_61]) ).
cnf(c_0_69,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_62]) ).
fof(c_0_70,plain,
! [X784] : X784 != hAPP(c_Nat_OSuc,X784),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_63])]) ).
cnf(c_0_71,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_66,c_0_56]) ).
cnf(c_0_73,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_58]),c_0_67]) ).
cnf(c_0_74,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_68,c_0_60]) ).
cnf(c_0_75,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_69,c_0_49]) ).
cnf(c_0_76,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_78,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_80,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_81,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_77]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW370+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 21 09:52:23 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 Running first-order theorem proving
% 0.16/0.44 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
% 121.33/19.87 % Version: 3.5.1
% 121.33/19.87 % Preprocessing class: FMLMSLSMSSSNFFN.
% 121.33/19.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 121.33/19.87 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 121.33/19.87 % Starting new_bool_3 with 300s (1) cores
% 121.33/19.87 % Starting new_bool_1 with 300s (1) cores
% 121.33/19.87 % Starting sh5l with 300s (1) cores
% 121.33/19.87 % SAT001_MinMin_p005000_rr_RG with pid 1974019 completed with status 0
% 121.33/19.87 % Result found by SAT001_MinMin_p005000_rr_RG
% 121.33/19.87 % Preprocessing class: FMLMSLSMSSSNFFN.
% 121.33/19.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 121.33/19.87 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 121.33/19.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 121.33/19.87 % No SInE strategy applied
% 121.33/19.87 % Search class: FGHSM-SMLM33-DFFFFFNN
% 121.33/19.87 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 121.33/19.87 % Starting SubtermCWHack with 135s (1) cores
% 121.33/19.87 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 121.33/19.87 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 121.33/19.87 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 121.33/19.87 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 121.33/19.87 % SAT001_CA_MinMin_p005000_rr with pid 1974060 completed with status 0
% 121.33/19.87 % Result found by SAT001_CA_MinMin_p005000_rr
% 121.33/19.87 % Preprocessing class: FMLMSLSMSSSNFFN.
% 121.33/19.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 121.33/19.87 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 121.33/19.87 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 121.33/19.87 % No SInE strategy applied
% 121.33/19.87 % Search class: FGHSM-SMLM33-DFFFFFNN
% 121.33/19.87 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 121.33/19.87 % Starting SubtermCWHack with 135s (1) cores
% 121.33/19.87 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 121.33/19.87 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 121.33/19.87 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 121.33/19.87 % Preprocessing time : 0.313 s
% 121.33/19.87 % Presaturation interreduction done
% 121.33/19.87
% 121.33/19.87 % Proof found!
% 121.33/19.87 % SZS status ContradictoryAxioms
% 121.33/19.87 % SZS output start CNFRefutation
% See solution above
% 121.33/19.87 % Parsed axioms : 5241
% 121.33/19.87 % Removed by relevancy pruning/SinE : 0
% 121.33/19.87 % Initial clauses : 7563
% 121.33/19.87 % Removed in clause preprocessing : 231
% 121.33/19.87 % Initial clauses in saturation : 7332
% 121.33/19.87 % Processed clauses : 20903
% 121.33/19.87 % ...of these trivial : 392
% 121.33/19.87 % ...subsumed : 7382
% 121.33/19.87 % ...remaining for further processing : 13129
% 121.33/19.87 % Other redundant clauses eliminated : 1522
% 121.33/19.87 % Clauses deleted for lack of memory : 0
% 121.33/19.87 % Backward-subsumed : 277
% 121.33/19.87 % Backward-rewritten : 387
% 121.33/19.87 % Generated clauses : 184150
% 121.33/19.87 % ...of the previous two non-redundant : 174131
% 121.33/19.87 % ...aggressively subsumed : 0
% 121.33/19.87 % Contextual simplify-reflections : 48
% 121.33/19.87 % Paramodulations : 182644
% 121.33/19.87 % Factorizations : 2
% 121.33/19.87 % NegExts : 0
% 121.33/19.87 % Equation resolutions : 1570
% 121.33/19.87 % Disequality decompositions : 0
% 121.33/19.87 % Total rewrite steps : 60892
% 121.33/19.87 % ...of those cached : 43197
% 121.33/19.87 % Propositional unsat checks : 3
% 121.33/19.87 % Propositional check models : 2
% 121.33/19.87 % Propositional check unsatisfiable : 0
% 121.33/19.87 % Propositional clauses : 0
% 121.33/19.87 % Propositional clauses after purity: 0
% 121.33/19.87 % Propositional unsat core size : 0
% 121.33/19.87 % Propositional preprocessing time : 0.000
% 121.33/19.87 % Propositional encoding time : 0.297
% 121.33/19.87 % Propositional solver time : 0.189
% 121.33/19.87 % Success case prop preproc time : 0.000
% 121.33/19.87 % Success case prop encoding time : 0.000
% 121.33/19.87 % Success case prop solver time : 0.000
% 121.33/19.87 % Current number of processed clauses : 6067
% 121.33/19.87 % Positive orientable unit clauses : 1580
% 121.33/19.87 % Positive unorientable unit clauses: 129
% 121.33/19.87 % Negative unit clauses : 860
% 121.33/19.87 % Non-unit-clauses : 3498
% 121.33/19.87 % Current number of unprocessed clauses: 155810
% 121.33/19.87 % ...number of literals in the above : 314548
% 121.33/19.87 % Current number of archived formulas : 0
% 121.33/19.87 % Current number of archived clauses : 6605
% 121.33/19.87 % Clause-clause subsumption calls (NU) : 5725429
% 121.33/19.87 % Rec. Clause-clause subsumption calls : 2426311
% 121.33/19.87 % Non-unit clause-clause subsumptions : 5784
% 121.33/19.87 % Unit Clause-clause subsumption calls : 143575
% 121.33/19.87 % Rewrite failures with RHS unbound : 580
% 121.33/19.87 % BW rewrite match attempts : 37801
% 121.33/19.87 % BW rewrite match successes : 1176
% 121.33/19.87 % Condensation attempts : 205829
% 121.33/19.87 % Condensation successes : 1046
% 121.33/19.87 % Termbank termtop insertions : 6281355
% 121.33/19.87 % Search garbage collected termcells : 101651
% 121.33/19.87
% 121.33/19.87 % -------------------------------------------------
% 121.33/19.87 % User time : 18.139 s
% 121.33/19.87 % System time : 0.497 s
% 121.33/19.87 % Total time : 18.636 s
% 121.33/19.87 % Maximum resident set size: 42948 pages
% 121.33/19.87
% 121.33/19.87 % -------------------------------------------------
% 121.33/19.87 % User time : 79.866 s
% 121.33/19.87 % System time : 2.145 s
% 121.33/19.87 % Total time : 82.011 s
% 121.33/19.87 % Maximum resident set size: 12288 pages
% 121.33/19.87 % E exiting
%------------------------------------------------------------------------------