%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW307+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 : n016.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 92.79s 22.23s
% Output : CNFRefutation 92.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 87 ( 66 unt; 0 def)
% Number of atoms : 110 ( 93 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 32 ~; 18 |; 1 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 145 ( 19 sgn 77 !; 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/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X24,X5] : hAPP(c_Set_OCollect(X5),X24) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__empty__eq,axiom,
! [X24,X5] :
( hAPP(c_Set_OCollect(X5),X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X24,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(help_c__COMBK__1,axiom,
! [X311,X310,X5,X54] : hAPP(hAPP(c_COMBK(X54,X5),X310),X311) = X310,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_Collect__neg__eq,axiom,
! [X24,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X24)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X24)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_Zero__neq__Suc,axiom,
! [X99] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X99),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X19,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)),X19)) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X24] :
( ~ hBOOL(X24)
| ~ hBOOL(hAPP(c_fNot,X24)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_add__eq__self__zero,axiom,
! [X98,X99] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98) = X99
=> X98 = 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,
! [X32,X23,X24,X38,X5,X17] : hAPP(hAPP(hAPP(c_COMBB(X17,X5,X38),X24),X23),X32) = hAPP(X24,hAPP(X23,X32)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X98,X99] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),hAPP(c_Nat_OSuc,X98)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X229,X54] : hAPP(c_List_Orev(X54),hAPP(c_List_Orev(X54),X229)) = X229,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X99] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X99,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X98] : X98 != hAPP(c_Nat_OSuc,X98),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_19,plain,
! [X488] : c_Orderings_Obot__class_Obot(tc_fun(X488,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X488),hAPP(c_COMBK(tc_HOL_Obool,X488),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_20,plain,
! [X452,X453] : hAPP(c_Set_OCollect(X453),X452) = X452,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_21,plain,
! [X24,X5] :
( hAPP(c_Set_OCollect(X5),X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X24,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_22,plain,
! [X17625,X17626,X17627,X17628] : hAPP(hAPP(c_COMBK(X17628,X17627),X17626),X17625) = X17626,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_23,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_24,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,plain,
! [X1766,X1767] : hAPP(c_Set_OCollect(X1767),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1767),c_fNot),X1766)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1767,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1767),X1766)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_26,plain,
! [X482,X483,X484,X485,X487] :
( ( hAPP(c_Set_OCollect(X487),X485) = c_Orderings_Obot__class_Obot(tc_fun(X487,tc_HOL_Obool))
| hBOOL(hAPP(X485,esk12_1(X485))) )
& ( ~ hBOOL(hAPP(X482,X484))
| hAPP(c_Set_OCollect(X483),X482) != c_Orderings_Obot__class_Obot(tc_fun(X483,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_21])])])])])]) ).
fof(c_0_27,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_28,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,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_23,c_0_24]) ).
fof(c_0_30,plain,
! [X99] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X99),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_31,plain,
! [X1456,X1457] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1457,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1457,tc_HOL_Obool)),X1456)) = X1456,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_32,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_25]) ).
fof(c_0_33,plain,
! [X24] :
( ~ hBOOL(X24)
| ~ hBOOL(hAPP(c_fNot,X24)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_34,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_26]) ).
fof(c_0_35,plain,
! [X1801] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1801,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1801,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1801,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_36,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_38,plain,
! [X1235] : c_Orderings_Otop__class_Otop(tc_fun(X1235,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1235),hAPP(c_COMBK(tc_HOL_Obool,X1235),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_39,plain,
! [X3444,X3445] :
( X3444 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3445),X3444) != X3445 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_40,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_41,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_42,plain,
! [X3433] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X3433),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_30])]) ).
fof(c_0_43,plain,
! [X17629,X17630,X17631,X17632,X17633,X17634] : hAPP(hAPP(hAPP(c_COMBB(X17634,X17633,X17632),X17631),X17630),X17629) = hAPP(X17631,hAPP(X17630,X17629)),
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_31]) ).
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_32,c_0_24]),c_0_24]) ).
fof(c_0_46,plain,
! [X17651] :
( ~ hBOOL(X17651)
| ~ hBOOL(hAPP(c_fNot,X17651)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
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_34,c_0_24]) ).
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_35]) ).
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_36,c_0_37]) ).
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_38]) ).
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_39]) ).
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_40,c_0_41]) ).
fof(c_0_53,plain,
! [X2792,X2793] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2793),hAPP(c_Nat_OSuc,X2792)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2793),X2792)),
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_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,
! [X15912,X15913] : hAPP(c_List_Orev(X15913),hAPP(c_List_Orev(X15913),X15912)) = X15912,
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_28,c_0_47]),c_0_37]),c_0_28]) ).
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_37]) ).
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_24]) ).
cnf(c_0_63,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_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_53]) ).
cnf(c_0_65,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_66,plain,
! [X3448] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3448),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3448,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_67,plain,
! [X98] : X98 != hAPP(c_Nat_OSuc,X98),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_68,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_69,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_70,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_71,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_72,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_73,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_63,c_0_64]),c_0_65]) ).
cnf(c_0_74,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_66]) ).
fof(c_0_75,plain,
! [X2797] : X2797 != hAPP(c_Nat_OSuc,X2797),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_67])]) ).
cnf(c_0_76,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_77,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_70,c_0_59]) ).
cnf(c_0_78,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_71]),c_0_72]),c_0_37]) ).
cnf(c_0_79,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_73,c_0_64]) ).
cnf(c_0_80,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_74,c_0_52]) ).
cnf(c_0_81,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_83,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82])]) ).
cnf(c_0_85,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_86,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_82]),c_0_81]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW307+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.40 % Computer : n016.cluster.edu
% 0.15/5.40 % Model : x86_64 x86_64
% 0.15/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.40 % Memory : 8046.5625MB
% 0.15/5.40 % OS : Linux 6.8.0-71-generic
% 0.15/5.41 % CPULimit : 300
% 0.15/5.41 % WCLimit : 300
% 0.15/5.41 % DateTime : Mon Sep 21 09:51:43 UTC 2026
% 0.15/5.41 % CPUTime :
% 0.15/5.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.49 Running first-order theorem proving
% 0.15/5.49 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
% 92.79/22.23 % Version: 3.5.1
% 92.79/22.23 % Preprocessing class: FMLMSMSMSSSNFFN.
% 92.79/22.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 92.79/22.23 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 92.79/22.23 % Starting new_bool_3 with 300s (1) cores
% 92.79/22.23 % Starting new_bool_1 with 300s (1) cores
% 92.79/22.23 % Starting sh5l with 300s (1) cores
% 92.79/22.23 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2154108 completed with status 0
% 92.79/22.23 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 92.79/22.23 % Preprocessing class: FMLMSMSMSSSNFFN.
% 92.79/22.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 92.79/22.23 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 92.79/22.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 92.79/22.23 % No SInE strategy applied
% 92.79/22.23 % Search class: FGHSM-SMLM33-DFFFFFNN
% 92.79/22.23 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 92.79/22.23 % Starting SubtermCWHack with 135s (1) cores
% 92.79/22.23 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 92.79/22.23 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 92.79/22.23 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 92.79/22.23 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 92.79/22.23 % SAT001_CA_MinMin_p005000_rr with pid 2154118 completed with status 0
% 92.79/22.23 % Result found by SAT001_CA_MinMin_p005000_rr
% 92.79/22.23 % Preprocessing class: FMLMSMSMSSSNFFN.
% 92.79/22.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 92.79/22.23 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 92.79/22.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 92.79/22.23 % No SInE strategy applied
% 92.79/22.23 % Search class: FGHSM-SMLM33-DFFFFFNN
% 92.79/22.23 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 92.79/22.23 % Starting SubtermCWHack with 135s (1) cores
% 92.79/22.23 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 150s (1) cores
% 92.79/22.23 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 92.79/22.23 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 92.79/22.23 % Preprocessing time : 0.322 s
% 92.79/22.23 % Presaturation interreduction done
% 92.79/22.23
% 92.79/22.23 % Proof found!
% 92.79/22.23 % SZS status ContradictoryAxioms
% 92.79/22.23 % SZS output start CNFRefutation
% See solution above
% 92.79/22.23 % Parsed axioms : 5230
% 92.79/22.23 % Removed by relevancy pruning/SinE : 0
% 92.79/22.23 % Initial clauses : 7571
% 92.79/22.23 % Removed in clause preprocessing : 229
% 92.79/22.23 % Initial clauses in saturation : 7342
% 92.79/22.23 % Processed clauses : 21250
% 92.79/22.23 % ...of these trivial : 445
% 92.79/22.23 % ...subsumed : 7656
% 92.79/22.23 % ...remaining for further processing : 13149
% 92.79/22.23 % Other redundant clauses eliminated : 1378
% 92.79/22.23 % Clauses deleted for lack of memory : 0
% 92.79/22.23 % Backward-subsumed : 425
% 92.79/22.23 % Backward-rewritten : 412
% 92.79/22.23 % Generated clauses : 189041
% 92.79/22.23 % ...of the previous two non-redundant : 180359
% 92.79/22.23 % ...aggressively subsumed : 0
% 92.79/22.23 % Contextual simplify-reflections : 31
% 92.79/22.23 % Paramodulations : 187676
% 92.79/22.23 % Factorizations : 2
% 92.79/22.23 % NegExts : 0
% 92.79/22.23 % Equation resolutions : 1428
% 92.79/22.23 % Disequality decompositions : 0
% 92.79/22.23 % Total rewrite steps : 63642
% 92.79/22.23 % ...of those cached : 45483
% 92.79/22.23 % Propositional unsat checks : 3
% 92.79/22.23 % Propositional check models : 2
% 92.79/22.23 % Propositional check unsatisfiable : 0
% 92.79/22.23 % Propositional clauses : 0
% 92.79/22.23 % Propositional clauses after purity: 0
% 92.79/22.23 % Propositional unsat core size : 0
% 92.79/22.23 % Propositional preprocessing time : 0.000
% 92.79/22.23 % Propositional encoding time : 0.282
% 92.79/22.23 % Propositional solver time : 0.138
% 92.79/22.23 % Success case prop preproc time : 0.000
% 92.79/22.23 % Success case prop encoding time : 0.000
% 92.79/22.23 % Success case prop solver time : 0.000
% 92.79/22.23 % Current number of processed clauses : 5880
% 92.79/22.23 % Positive orientable unit clauses : 1601
% 92.79/22.23 % Positive unorientable unit clauses: 130
% 92.79/22.23 % Negative unit clauses : 833
% 92.79/22.23 % Non-unit-clauses : 3316
% 92.79/22.23 % Current number of unprocessed clauses: 164964
% 92.79/22.23 % ...number of literals in the above : 316191
% 92.79/22.23 % Current number of archived formulas : 0
% 92.79/22.23 % Current number of archived clauses : 6819
% 92.79/22.23 % Clause-clause subsumption calls (NU) : 4444023
% 92.79/22.23 % Rec. Clause-clause subsumption calls : 2288841
% 92.79/22.23 % Non-unit clause-clause subsumptions : 6561
% 92.79/22.23 % Unit Clause-clause subsumption calls : 218531
% 92.79/22.23 % Rewrite failures with RHS unbound : 558
% 92.79/22.23 % BW rewrite match attempts : 36278
% 92.79/22.23 % BW rewrite match successes : 1396
% 92.79/22.23 % Condensation attempts : 211117
% 92.79/22.23 % Condensation successes : 1186
% 92.79/22.23 % Termbank termtop insertions : 7062534
% 92.79/22.23 % Search garbage collected termcells : 101872
% 92.79/22.23
% 92.79/22.23 % -------------------------------------------------
% 92.79/22.23 % User time : 13.620 s
% 92.79/22.23 % System time : 0.403 s
% 92.79/22.23 % Total time : 14.023 s
% 92.79/22.23 % Maximum resident set size: 42028 pages
% 92.79/22.23
% 92.79/22.23 % -------------------------------------------------
% 92.79/22.23 % User time : 63.274 s
% 92.79/22.23 % System time : 1.879 s
% 92.79/22.23 % Total time : 65.153 s
% 92.79/22.23 % Maximum resident set size: 12288 pages
% 92.79/22.23 % E exiting
%------------------------------------------------------------------------------