%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW309+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 : n001.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 03:10:16 PM UTC 2026
% Result : ContradictoryAxioms 132.60s 22.92s
% Output : CNFRefutation 132.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 88 ( 68 unt; 0 def)
% Number of atoms : 116 ( 93 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 63 ( 35 ~; 21 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 146 ( 19 sgn 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_empty__def,axiom,
! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X10,X5] : hAPP(c_Set_OCollect(X5),X10) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__empty__eq,axiom,
! [X10,X5] :
( hAPP(c_Set_OCollect(X5),X10) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X10,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(help_c__COMBK__1,axiom,
! [X311,X310,X5,X66] : hAPP(hAPP(c_COMBK(X66,X5),X310),X311) = X310,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Collect__neg__eq,axiom,
! [X10,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X10)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_Zero__not__Suc,axiom,
! [X116] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X116),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X23,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)),X23)) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X10] :
( ~ hBOOL(X10)
| ~ hBOOL(hAPP(c_fNot,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_Compl__empty__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_UNIV__def,axiom,
! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fTrue)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(help_c__COMBB__1,axiom,
! [X35,X27,X10,X51,X5,X21] : hAPP(hAPP(hAPP(c_COMBB(X21,X5,X51),X10),X27),X35) = hAPP(X10,hAPP(X27,X35)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__0__iff,axiom,
! [X6,X26,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X26 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X26),X6)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_add__Suc__right,axiom,
! [X115,X116] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X116),hAPP(c_Nat_OSuc,X115)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X116),X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X233,X66] : hAPP(c_List_Orev(X66),hAPP(c_List_Orev(X66),X233)) = X233,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X116] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X116),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X116,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X115] : X115 != hAPP(c_Nat_OSuc,X115),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_20,plain,
! [X477] : c_Orderings_Obot__class_Obot(tc_fun(X477,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X477),hAPP(c_COMBK(tc_HOL_Obool,X477),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X463,X464] : hAPP(c_Set_OCollect(X464),X463) = X463,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X10,X5] :
( hAPP(c_Set_OCollect(X5),X10) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X10,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_23,plain,
! [X17594,X17595,X17596,X17597] : hAPP(hAPP(c_COMBK(X17597,X17596),X17595),X17594) = X17595,
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_20]) ).
cnf(c_0_25,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X1852,X1853] : hAPP(c_Set_OCollect(X1853),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1853),c_fNot),X1852)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1853,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1853),X1852)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_27,plain,
! [X471,X472,X473,X474,X476] :
( ( hAPP(c_Set_OCollect(X476),X474) = c_Orderings_Obot__class_Obot(tc_fun(X476,tc_HOL_Obool))
| hBOOL(hAPP(X474,esk12_1(X474))) )
& ( ~ hBOOL(hAPP(X471,X473))
| hAPP(c_Set_OCollect(X472),X471) != c_Orderings_Obot__class_Obot(tc_fun(X472,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_22])])])])])]) ).
fof(c_0_28,plain,
! [X312,X313] :
( X313 = X312
| hAPP(X313,esk1_2(X312,X313)) != hAPP(X312,esk1_2(X312,X313)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
cnf(c_0_29,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,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_31,plain,
! [X116] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X116),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_32,plain,
! [X1663,X1664] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1664,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1664,tc_HOL_Obool)),X1663)) = X1663,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_33,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_26]) ).
fof(c_0_34,plain,
! [X10] :
( ~ hBOOL(X10)
| ~ hBOOL(hAPP(c_fNot,X10)) ),
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,esk12_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_36,plain,
! [X1858] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1858,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1858,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1858,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_37,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_39,plain,
! [X1389] : c_Orderings_Otop__class_Otop(tc_fun(X1389,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1389),hAPP(c_COMBK(tc_HOL_Obool,X1389),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_40,plain,
! [X6350] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X6350),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
cnf(c_0_41,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_42,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_43,plain,
! [X17598,X17599,X17600,X17601,X17602,X17603] : hAPP(hAPP(hAPP(c_COMBB(X17603,X17602,X17601),X17600),X17599),X17598) = hAPP(X17600,hAPP(X17599,X17598)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_44,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_25]),c_0_25]) ).
fof(c_0_46,plain,
! [X17620] :
( ~ hBOOL(X17620)
| ~ hBOOL(hAPP(c_fNot,X17620)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
cnf(c_0_47,plain,
( hBOOL(hAPP(X1,esk12_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_35,c_0_25]) ).
cnf(c_0_48,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,plain,
( hAPP(X1,esk1_2(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X1)) != c_fFalse
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_50,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_51,plain,
! [X6299,X6300,X6301] :
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6301)
| X6300 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6301),X6300),X6299)
| X6299 != c_Groups_Ozero__class_Ozero(X6301) )
& ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X6301)
| X6299 = c_Groups_Ozero__class_Ozero(X6301)
| X6300 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X6301),X6300),X6299) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])])]) ).
fof(c_0_52,plain,
! [X5864,X5865] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5865),hAPP(c_Nat_OSuc,X5864)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5865),X5864)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_53,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_55,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_56,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_45]) ).
fof(c_0_57,plain,
! [X15936,X15937] : hAPP(c_List_Orev(X15937),hAPP(c_List_Orev(X15937),X15936)) = X15936,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_58,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_47]),c_0_38]),c_0_29]) ).
cnf(c_0_60,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_61,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_49,c_0_38]) ).
cnf(c_0_62,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_50,c_0_25]) ).
cnf(c_0_63,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_64,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_65,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(c_0_66,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_67,plain,
! [X6369] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6369),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X6369,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_68,plain,
! [X115] : X115 != hAPP(c_Nat_OSuc,X115),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_69,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_70,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_71,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_72,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_73,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_29,c_0_62]) ).
cnf(c_0_74,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_54]),c_0_65])]),c_0_66]) ).
cnf(c_0_75,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_76,plain,
! [X5835] : X5835 != hAPP(c_Nat_OSuc,X5835),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_68])]) ).
cnf(c_0_77,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_78,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_71,c_0_59]) ).
cnf(c_0_79,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_72]),c_0_73]),c_0_38]) ).
cnf(c_0_80,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_74,c_0_64]) ).
cnf(c_0_81,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_75,c_0_54]) ).
cnf(c_0_82,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_83,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_84,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83])]) ).
cnf(c_0_86,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_87,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_83]),c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW309+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 09:52:29 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 132.60/22.92 % Version: 3.5.1
% 132.60/22.92 % Preprocessing class: FMLMSMSMSSSNFFN.
% 132.60/22.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 132.60/22.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 132.60/22.92 % Starting new_bool_3 with 300s (1) cores
% 132.60/22.92 % Starting new_bool_1 with 300s (1) cores
% 132.60/22.92 % Starting sh5l with 300s (1) cores
% 132.60/22.92 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2825304 completed with status 0
% 132.60/22.92 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 132.60/22.92 % Preprocessing class: FMLMSMSMSSSNFFN.
% 132.60/22.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 132.60/22.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 132.60/22.92 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 132.60/22.92 % No SInE strategy applied
% 132.60/22.92 % Search class: FGHSM-SMLM33-DFFFFFNN
% 132.60/22.92 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 132.60/22.92 % Starting SubtermCWHack with 135s (1) cores
% 132.60/22.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 132.60/22.92 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 132.60/22.92 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 132.60/22.92 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 132.60/22.92 % SAT001_CA_MinMin_p005000_rr with pid 2825347 completed with status 0
% 132.60/22.92 % Result found by SAT001_CA_MinMin_p005000_rr
% 132.60/22.92 % Preprocessing class: FMLMSMSMSSSNFFN.
% 132.60/22.92 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 132.60/22.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 132.60/22.92 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 132.60/22.92 % No SInE strategy applied
% 132.60/22.92 % Search class: FGHSM-SMLM33-DFFFFFNN
% 132.60/22.92 % Scheduled 7 strats onto 5 cores with 1498 seconds (1498 total)
% 132.60/22.92 % Starting SubtermCWHack with 135s (1) cores
% 132.60/22.92 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 132.60/22.92 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 132.60/22.92 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 132.60/22.92 % Preprocessing time : 0.368 s
% 132.60/22.92 % Presaturation interreduction done
% 132.60/22.92
% 132.60/22.92 % Proof found!
% 132.60/22.92 % SZS status ContradictoryAxioms
% 132.60/22.92 % SZS output start CNFRefutation
% See solution above
% 132.60/22.92 % Parsed axioms : 5228
% 132.60/22.92 % Removed by relevancy pruning/SinE : 0
% 132.60/22.92 % Initial clauses : 7572
% 132.60/22.92 % Removed in clause preprocessing : 230
% 132.60/22.92 % Initial clauses in saturation : 7342
% 132.60/22.92 % Processed clauses : 21431
% 132.60/22.92 % ...of these trivial : 426
% 132.60/22.92 % ...subsumed : 7683
% 132.60/22.92 % ...remaining for further processing : 13322
% 132.60/22.92 % Other redundant clauses eliminated : 1405
% 132.60/22.92 % Clauses deleted for lack of memory : 0
% 132.60/22.92 % Backward-subsumed : 248
% 132.60/22.92 % Backward-rewritten : 421
% 132.60/22.92 % Generated clauses : 192916
% 132.60/22.92 % ...of the previous two non-redundant : 183804
% 132.60/22.92 % ...aggressively subsumed : 0
% 132.60/22.92 % Contextual simplify-reflections : 35
% 132.60/22.92 % Paramodulations : 191525
% 132.60/22.92 % Factorizations : 2
% 132.60/22.92 % NegExts : 0
% 132.60/22.92 % Equation resolutions : 1455
% 132.60/22.92 % Disequality decompositions : 0
% 132.60/22.92 % Total rewrite steps : 62346
% 132.60/22.92 % ...of those cached : 44005
% 132.60/22.92 % Propositional unsat checks : 3
% 132.60/22.92 % Propositional check models : 2
% 132.60/22.92 % Propositional check unsatisfiable : 0
% 132.60/22.92 % Propositional clauses : 0
% 132.60/22.92 % Propositional clauses after purity: 0
% 132.60/22.92 % Propositional unsat core size : 0
% 132.60/22.92 % Propositional preprocessing time : 0.000
% 132.60/22.92 % Propositional encoding time : 0.327
% 132.60/22.92 % Propositional solver time : 0.182
% 132.60/22.92 % Success case prop preproc time : 0.000
% 132.60/22.92 % Success case prop encoding time : 0.000
% 132.60/22.92 % Success case prop solver time : 0.000
% 132.60/22.92 % Current number of processed clauses : 6234
% 132.60/22.92 % Positive orientable unit clauses : 1602
% 132.60/22.92 % Positive unorientable unit clauses: 128
% 132.60/22.92 % Negative unit clauses : 926
% 132.60/22.92 % Non-unit-clauses : 3578
% 132.60/22.92 % Current number of unprocessed clauses: 169311
% 132.60/22.92 % ...number of literals in the above : 324630
% 132.60/22.92 % Current number of archived formulas : 0
% 132.60/22.92 % Current number of archived clauses : 6641
% 132.60/22.92 % Clause-clause subsumption calls (NU) : 5941202
% 132.60/22.92 % Rec. Clause-clause subsumption calls : 2660638
% 132.60/22.92 % Non-unit clause-clause subsumptions : 5993
% 132.60/22.92 % Unit Clause-clause subsumption calls : 251334
% 132.60/22.92 % Rewrite failures with RHS unbound : 555
% 132.60/22.92 % BW rewrite match attempts : 37568
% 132.60/22.92 % BW rewrite match successes : 1341
% 132.60/22.92 % Condensation attempts : 215190
% 132.60/22.92 % Condensation successes : 1029
% 132.60/22.92 % Termbank termtop insertions : 7056405
% 132.60/22.92 % Search garbage collected termcells : 101620
% 132.60/22.92
% 132.60/22.92 % -------------------------------------------------
% 132.60/22.92 % User time : 19.929 s
% 132.60/22.92 % System time : 0.536 s
% 132.60/22.92 % Total time : 20.464 s
% 132.60/22.92 % Maximum resident set size: 42592 pages
% 132.60/22.92
% 132.60/22.92 % -------------------------------------------------
% 132.60/22.92 % User time : 90.550 s
% 132.60/22.92 % System time : 2.589 s
% 132.60/22.92 % Total time : 93.139 s
% 132.60/22.92 % Maximum resident set size: 12544 pages
% 132.60/22.92 % E exiting
%------------------------------------------------------------------------------