%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW373+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 90.98s 15.17s
% Output : CNFRefutation 90.98s
% 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 : 135 ( 16 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__empty__eq,axiom,
! [X19,X5] :
( hAPP(c_Set_OCollect(X5),X19) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X19,X5] : hAPP(c_Set_OCollect(X5),X19) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X19,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X19)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(help_c__COMBK__1,axiom,
! [X328,X27,X20,X5] : hAPP(hAPP(c_COMBK(X5,X20),X27),X328) = X27,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Zero__not__Suc,axiom,
! [X109] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X109),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X10,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)),X10)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X19] :
( ~ hBOOL(X19)
| ~ hBOOL(hAPP(c_fNot,X19)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_add__eq__self__zero,axiom,
! [X108,X109] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),X108) = X109
=> X108 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(help_c__COMBB__1,axiom,
! [X49,X18,X19,X82,X5,X20] : hAPP(hAPP(hAPP(c_COMBB(X20,X5,X82),X19),X18),X49) = hAPP(X19,hAPP(X18,X49)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X108,X109] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),hAPP(c_Nat_OSuc,X108)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),X108)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_converse__converse,axiom,
! [X186,X5,X20] : hAPP(c_Relation_Oconverse(X20,X5),hAPP(c_Relation_Oconverse(X5,X20),X186)) = X186,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X109] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X109,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X108] : X108 != hAPP(c_Nat_OSuc,X108),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_18,plain,
! [X19,X5] :
( hAPP(c_Set_OCollect(X5),X19) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X19,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_19,plain,
! [X11945] : c_Orderings_Obot__class_Obot(tc_fun(X11945,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11945),hAPP(c_COMBK(tc_HOL_Obool,X11945),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_20,plain,
! [X11981,X11982] : hAPP(c_Set_OCollect(X11982),X11981) = X11981,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X11979,X11980] : hAPP(c_Set_OCollect(X11980),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11980),c_fNot),X11979)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11980,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11980),X11979)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_22,plain,
! [X11946,X11947,X11948,X11949,X11951] :
( ( hAPP(c_Set_OCollect(X11951),X11949) = c_Orderings_Obot__class_Obot(tc_fun(X11951,tc_HOL_Obool))
| hBOOL(hAPP(X11949,esk304_1(X11949))) )
& ( ~ hBOOL(hAPP(X11946,X11948))
| hAPP(c_Set_OCollect(X11947),X11946) != c_Orderings_Obot__class_Obot(tc_fun(X11947,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,
! [X17659,X17660,X17661,X17662] : hAPP(hAPP(c_COMBK(X17662,X17661),X17660),X17659) = X17660,
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,
! [X11938] : c_Orderings_Otop__class_Otop(tc_fun(X11938,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11938),hAPP(c_COMBK(tc_HOL_Obool,X11938),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_27,plain,
! [X109] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X109),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_28,plain,
! [X1761,X1762] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1762,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1762,tc_HOL_Obool)),X1761)) = X1761,
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,
! [X19] :
( ~ hBOOL(X19)
| ~ hBOOL(hAPP(c_fNot,X19)) ),
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,esk304_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,
! [X1960] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1960,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1960,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X1960,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,
! [X3458,X3459] :
( X3458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3459),X3458) != X3459 ),
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,
! [X3442] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3442),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_27])]) ).
fof(c_0_40,plain,
! [X17663,X17664,X17665,X17666,X17667,X17668] : hAPP(hAPP(hAPP(c_COMBB(X17668,X17667,X17666),X17665),X17664),X17663) = hAPP(X17665,hAPP(X17664,X17663)),
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,
! [X17685] :
( ~ hBOOL(X17685)
| ~ hBOOL(hAPP(c_fNot,X17685)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
cnf(c_0_44,plain,
( hBOOL(hAPP(X1,esk304_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,
! [X3235,X3236] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3236),hAPP(c_Nat_OSuc,X3235)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3236),X3235)),
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,
! [X16953,X16954,X16955] : hAPP(c_Relation_Oconverse(X16955,X16954),hAPP(c_Relation_Oconverse(X16954,X16955),X16953)) = X16953,
inference(variable_rename,[status(thm)],[fact_converse__converse]) ).
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,
! [X3455] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3455),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3455,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_63,plain,
! [X108] : X108 != hAPP(c_Nat_OSuc,X108),
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_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
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,
! [X3201] : X3201 != hAPP(c_Nat_OSuc,X3201),
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 : SWW373+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 09:49:40 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 90.98/15.17 % Version: 3.5.1
% 90.98/15.17 % Preprocessing class: FMLMSLSMSSSNFFN.
% 90.98/15.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 90.98/15.17 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 90.98/15.17 % Starting new_bool_3 with 300s (1) cores
% 90.98/15.17 % Starting new_bool_1 with 300s (1) cores
% 90.98/15.17 % Starting sh5l with 300s (1) cores
% 90.98/15.17 % SAT001_MinMin_p005000_rr_RG with pid 1600825 completed with status 0
% 90.98/15.17 % Result found by SAT001_MinMin_p005000_rr_RG
% 90.98/15.17 % Preprocessing class: FMLMSLSMSSSNFFN.
% 90.98/15.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 90.98/15.17 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 90.98/15.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 90.98/15.17 % No SInE strategy applied
% 90.98/15.17 % Search class: FGHSM-SMLM33-DFFFFFNN
% 90.98/15.17 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 90.98/15.17 % Starting SubtermCWHack with 135s (1) cores
% 90.98/15.17 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 90.98/15.17 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 90.98/15.17 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 90.98/15.17 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 90.98/15.17 % SAT001_MinMin_p005000_rr_RG with pid 1600841 completed with status 0
% 90.98/15.17 % Result found by SAT001_MinMin_p005000_rr_RG
% 90.98/15.17 % Preprocessing class: FMLMSLSMSSSNFFN.
% 90.98/15.17 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 90.98/15.17 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 90.98/15.17 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 90.98/15.17 % No SInE strategy applied
% 90.98/15.17 % Search class: FGHSM-SMLM33-DFFFFFNN
% 90.98/15.17 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 90.98/15.17 % Starting SubtermCWHack with 135s (1) cores
% 90.98/15.17 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 90.98/15.17 % Preprocessing time : 0.185 s
% 90.98/15.17 % Presaturation interreduction done
% 90.98/15.17
% 90.98/15.17 % Proof found!
% 90.98/15.17 % SZS status ContradictoryAxioms
% 90.98/15.17 % SZS output start CNFRefutation
% See solution above
% 90.98/15.17 % Parsed axioms : 5250
% 90.98/15.17 % Removed by relevancy pruning/SinE : 0
% 90.98/15.17 % Initial clauses : 7572
% 90.98/15.17 % Removed in clause preprocessing : 235
% 90.98/15.17 % Initial clauses in saturation : 7337
% 90.98/15.17 % Processed clauses : 23984
% 90.98/15.17 % ...of these trivial : 498
% 90.98/15.17 % ...subsumed : 9608
% 90.98/15.17 % ...remaining for further processing : 13878
% 90.98/15.17 % Other redundant clauses eliminated : 1585
% 90.98/15.17 % Clauses deleted for lack of memory : 0
% 90.98/15.17 % Backward-subsumed : 239
% 90.98/15.17 % Backward-rewritten : 458
% 90.98/15.17 % Generated clauses : 271344
% 90.98/15.17 % ...of the previous two non-redundant : 260534
% 90.98/15.17 % ...aggressively subsumed : 0
% 90.98/15.17 % Contextual simplify-reflections : 60
% 90.98/15.17 % Paramodulations : 269756
% 90.98/15.17 % Factorizations : 12
% 90.98/15.17 % NegExts : 0
% 90.98/15.17 % Equation resolutions : 1642
% 90.98/15.17 % Disequality decompositions : 0
% 90.98/15.17 % Total rewrite steps : 66694
% 90.98/15.17 % ...of those cached : 48986
% 90.98/15.17 % Propositional unsat checks : 3
% 90.98/15.17 % Propositional check models : 2
% 90.98/15.17 % Propositional check unsatisfiable : 0
% 90.98/15.17 % Propositional clauses : 0
% 90.98/15.17 % Propositional clauses after purity: 0
% 90.98/15.17 % Propositional unsat core size : 0
% 90.98/15.17 % Propositional preprocessing time : 0.000
% 90.98/15.17 % Propositional encoding time : 0.214
% 90.98/15.17 % Propositional solver time : 0.091
% 90.98/15.17 % Success case prop preproc time : 0.000
% 90.98/15.17 % Success case prop encoding time : 0.000
% 90.98/15.17 % Success case prop solver time : 0.000
% 90.98/15.17 % Current number of processed clauses : 6769
% 90.98/15.17 % Positive orientable unit clauses : 1673
% 90.98/15.17 % Positive unorientable unit clauses: 133
% 90.98/15.17 % Negative unit clauses : 918
% 90.98/15.17 % Non-unit-clauses : 4045
% 90.98/15.17 % Current number of unprocessed clauses: 223242
% 90.98/15.17 % ...number of literals in the above : 421177
% 90.98/15.17 % Current number of archived formulas : 0
% 90.98/15.17 % Current number of archived clauses : 6663
% 90.98/15.17 % Clause-clause subsumption calls (NU) : 4388028
% 90.98/15.17 % Rec. Clause-clause subsumption calls : 2433140
% 90.98/15.17 % Non-unit clause-clause subsumptions : 7341
% 90.98/15.17 % Unit Clause-clause subsumption calls : 202956
% 90.98/15.17 % Rewrite failures with RHS unbound : 0
% 90.98/15.17 % BW rewrite match attempts : 42988
% 90.98/15.17 % BW rewrite match successes : 1442
% 90.98/15.17 % Condensation attempts : 0
% 90.98/15.17 % Condensation successes : 0
% 90.98/15.17 % Termbank termtop insertions : 7938374
% 90.98/15.17 % Search garbage collected termcells : 100427
% 90.98/15.17
% 90.98/15.17 % -------------------------------------------------
% 90.98/15.17 % User time : 13.714 s
% 90.98/15.17 % System time : 0.369 s
% 90.98/15.17 % Total time : 14.083 s
% 90.98/15.17 % Maximum resident set size: 42688 pages
% 90.98/15.17
% 90.98/15.17 % -------------------------------------------------
% 90.98/15.17 % User time : 59.818 s
% 90.98/15.17 % System time : 1.607 s
% 90.98/15.17 % Total time : 61.425 s
% 90.98/15.17 % Maximum resident set size: 12544 pages
% 90.98/15.17 % E exiting
%------------------------------------------------------------------------------