%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW396+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 : n003.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 03:10:27 PM UTC 2026
% Result : ContradictoryAxioms 72.41s 12.45s
% Output : CNFRefutation 72.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 26
% Syntax : Number of formulae : 118 ( 83 unt; 0 def)
% Number of atoms : 155 ( 111 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 45 ~; 30 |; 1 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-3 aty)
% Number of variables : 229 ( 40 sgn 121 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__mem__eq,axiom,
! [X26,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X26)) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_Collect__def,axiom,
! [X7,X5] : hAPP(c_Set_OCollect(X5),X7) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_all__not__in__conv,axiom,
! [X26,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X26))
<=> X26 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(help_c__COMBC__1,axiom,
! [X41,X8,X7,X5,X81,X24] : hAPP(hAPP(hAPP(c_COMBC(X24,X81,X5),X7),X8),X41) = hAPP(hAPP(X7,X41),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__fconj__2,axiom,
! [X8,X7] :
( hBOOL(X7)
| ~ hBOOL(hAPP(hAPP(c_fconj,X7),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(fact_bot__fun__def,axiom,
! [X23,X24,X5] :
( class_Orderings_Obot(X5)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X24,X5)),X23) = c_Orderings_Obot__class_Obot(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(arity_fun__Orderings_Obot,axiom,
! [X321,X322] :
( class_Orderings_Obot(X322)
=> class_Orderings_Obot(tc_fun(X321,X322)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
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_bot2E,axiom,
! [X34,X23,X24,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X24,tc_HOL_Obool))),X23),X34)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
fof(help_c__COMBK__1,axiom,
! [X324,X323,X5,X101] : hAPP(hAPP(c_COMBK(X101,X5),X323),X324) = X323,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(fact_Collect__neg__eq,axiom,
! [X7,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X7)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X7)),
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,
! [X115] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X115),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_double__complement,axiom,
! [X26,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)),X26)) = X26,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X7] :
( ~ hBOOL(X7)
| ~ hBOOL(hAPP(c_fNot,X7)) ),
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_add__eq__self__zero,axiom,
! [X63,X115] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),X63) = X115
=> X63 = 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,
! [X41,X8,X7,X81,X5,X24] : hAPP(hAPP(hAPP(c_COMBB(X24,X5,X81),X7),X8),X41) = hAPP(X7,hAPP(X8,X41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__Suc__right,axiom,
! [X63,X115] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),hAPP(c_Nat_OSuc,X63)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),X63)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X262,X101] : hAPP(c_List_Orev(X101),hAPP(c_List_Orev(X101),X262)) = X262,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X115] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X115),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X115,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X63] : X63 != hAPP(c_Nat_OSuc,X63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_26,plain,
! [X1205,X1206] : hAPP(c_Set_OCollect(X1206),hAPP(hAPP(c_COMBC(X1206,tc_fun(X1206,tc_HOL_Obool),tc_HOL_Obool),c_member(X1206)),X1205)) = X1205,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_27,plain,
! [X1203,X1204] : hAPP(c_Set_OCollect(X1204),X1203) = X1203,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_28,plain,
! [X26,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X26))
<=> X26 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).
fof(c_0_29,plain,
! [X17739,X17740,X17741,X17742,X17743,X17744] : hAPP(hAPP(hAPP(c_COMBC(X17744,X17743,X17742),X17741),X17740),X17739) = hAPP(hAPP(X17741,X17739),X17740),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_30,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_32,plain,
! [X8,X7] :
( hBOOL(X7)
| ~ hBOOL(hAPP(hAPP(c_fconj,X7),X8)) ),
inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).
fof(c_0_33,plain,
! [X1428,X1429,X1431,X1432,X1433] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1432),X1433),X1431))
| X1431 != c_Orderings_Obot__class_Obot(tc_fun(X1432,tc_HOL_Obool)) )
& ( X1428 = c_Orderings_Obot__class_Obot(tc_fun(X1429,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1429),esk43_2(X1428,X1429)),X1428)) ) ),
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_28])])])])])]) ).
cnf(c_0_34,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_36,plain,
! [X376,X377,X378] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X377,X378)),X376) = c_Orderings_Obot__class_Obot(X378)
| ~ class_Orderings_Obot(X378) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])])]) ).
fof(c_0_37,plain,
! [X17696,X17697] :
( class_Orderings_Obot(tc_fun(X17696,X17697))
| ~ class_Orderings_Obot(X17697) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])])]) ).
fof(c_0_38,plain,
! [X1491] : c_Orderings_Obot__class_Obot(tc_fun(X1491,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1491),hAPP(c_COMBK(tc_HOL_Obool,X1491),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_39,plain,
! [X34,X23,X24,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X24,tc_HOL_Obool))),X23),X34)),
inference(fof_simplification,[status(thm)],[fact_bot2E]) ).
fof(c_0_40,plain,
! [X17759,X17760] :
( hBOOL(X17760)
| ~ hBOOL(hAPP(hAPP(c_fconj,X17760),X17759)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_32])]) ).
cnf(c_0_41,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X1),esk43_2(X2,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,plain,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(tc_fun(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_45,plain,
! [X17729,X17730,X17731,X17732] : hAPP(hAPP(c_COMBK(X17732,X17731),X17730),X17729) = X17730,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_46,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_38]) ).
fof(c_0_47,plain,
! [X4029,X4030,X4031,X4032] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4032,tc_fun(X4031,tc_HOL_Obool))),X4030),X4029)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_39])]) ).
cnf(c_0_48,plain,
( ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2))
| hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
( hBOOL(hAPP(X1,esk43_2(X1,X2)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,plain,
( ~ class_Orderings_Obot(X3)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,X3))),X4) = c_Orderings_Obot__class_Obot(tc_fun(X2,X3)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
cnf(c_0_52,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,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_46,c_0_31]) ).
cnf(c_0_54,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,plain,
( hBOOL(X1)
| hAPP(c_fconj,X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_58,plain,
! [X4565,X4566] : hAPP(c_Set_OCollect(X4566),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4566),c_fNot),X4565)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4566,tc_HOL_Obool)),hAPP(c_Set_OCollect(X4566),X4565)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
cnf(c_0_59,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_fconj,c_fFalse),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]) ).
fof(c_0_60,plain,
! [X325,X326] :
( X326 = X325
| hAPP(X326,esk1_2(X325,X326)) != hAPP(X325,esk1_2(X325,X326)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
fof(c_0_61,plain,
! [X115] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X115),
inference(fof_simplification,[status(thm)],[fact_Zero__not__Suc]) ).
fof(c_0_62,plain,
! [X4431,X4432] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4432,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4432,tc_HOL_Obool)),X4431)) = X4431,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_63,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_58]) ).
fof(c_0_64,plain,
! [X7] :
( ~ hBOOL(X7)
| ~ hBOOL(hAPP(c_fNot,X7)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_65,plain,
( hBOOL(hAPP(X1,esk43_2(X1,X2)))
| X1 = hAPP(c_fconj,c_fFalse) ),
inference(rw,[status(thm)],[c_0_49,c_0_59]) ).
fof(c_0_66,plain,
! [X4590] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4590,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4590,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X4590,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_67,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_68,plain,
! [X2776] : c_Orderings_Otop__class_Otop(tc_fun(X2776,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X2776),hAPP(c_COMBK(tc_HOL_Obool,X2776),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_69,plain,
! [X7615,X7616] :
( X7615 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7616),X7615) != X7616 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])])]) ).
cnf(c_0_70,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_71,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_72,plain,
! [X7599] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X7599),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_61])]) ).
fof(c_0_73,plain,
! [X17733,X17734,X17735,X17736,X17737,X17738] : hAPP(hAPP(hAPP(c_COMBB(X17738,X17737,X17736),X17735),X17734),X17733) = hAPP(X17735,hAPP(X17734,X17733)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_74,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_62]) ).
cnf(c_0_75,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_63,c_0_31]),c_0_31]) ).
fof(c_0_76,plain,
! [X17755] :
( ~ hBOOL(X17755)
| ~ hBOOL(hAPP(c_fNot,X17755)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_64])]) ).
cnf(c_0_77,plain,
( hBOOL(X3)
| hAPP(c_COMBK(X1,X2),X3) = hAPP(c_fconj,c_fFalse) ),
inference(spm,[status(thm)],[c_0_65,c_0_52]) ).
cnf(c_0_78,plain,
hAPP(hAPP(c_fconj,c_fFalse),X1) = c_fFalse,
inference(rw,[status(thm)],[c_0_57,c_0_59]) ).
cnf(c_0_79,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_66]) ).
cnf(c_0_80,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_67,c_0_57]) ).
cnf(c_0_81,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_68]) ).
cnf(c_0_82,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_69]) ).
cnf(c_0_83,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
fof(c_0_84,plain,
! [X6690,X6691] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6691),hAPP(c_Nat_OSuc,X6690)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6691),X6690)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_85,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_86,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_87,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_74,c_0_75]),c_0_75]) ).
fof(c_0_88,plain,
! [X16516,X16517] : hAPP(c_List_Orev(X16517),hAPP(c_List_Orev(X16517),X16516)) = X16516,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_89,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_90,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_77]),c_0_78]) ).
cnf(c_0_91,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_79,c_0_75]) ).
cnf(c_0_92,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_80,c_0_57]) ).
cnf(c_0_93,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_81,c_0_31]) ).
cnf(c_0_94,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_82,c_0_83]) ).
cnf(c_0_95,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_84]) ).
cnf(c_0_96,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_85,c_0_83]) ).
fof(c_0_97,plain,
! [X7612] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X7612),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X7612,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_98,plain,
! [X63] : X63 != hAPP(c_Nat_OSuc,X63),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_99,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_86]) ).
cnf(c_0_100,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_101,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_102,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_91,c_0_92]) ).
cnf(c_0_103,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_52,c_0_93]) ).
cnf(c_0_104,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_94,c_0_95]),c_0_96]) ).
cnf(c_0_105,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_97]) ).
fof(c_0_106,plain,
! [X2215] : X2215 != hAPP(c_Nat_OSuc,X2215),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_98])]) ).
cnf(c_0_107,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_108,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_101,c_0_90]) ).
cnf(c_0_109,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_102]),c_0_103]),c_0_57]) ).
cnf(c_0_110,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_104,c_0_95]) ).
cnf(c_0_111,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_105,c_0_83]) ).
cnf(c_0_112,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_113,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_114,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_115,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113])]) ).
cnf(c_0_116,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_117,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_113]),c_0_112]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW396+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 09:52:33 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 72.41/12.45 % Version: 3.5.1
% 72.41/12.45 % Preprocessing class: FMLMSLSMSSSNFFN.
% 72.41/12.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 72.41/12.45 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 72.41/12.45 % Starting new_bool_3 with 300s (1) cores
% 72.41/12.45 % Starting new_bool_1 with 300s (1) cores
% 72.41/12.45 % Starting sh5l with 300s (1) cores
% 72.41/12.45 % SAT001_MinMin_p005000_rr_RG with pid 3997133 completed with status 0
% 72.41/12.45 % Result found by SAT001_MinMin_p005000_rr_RG
% 72.41/12.45 % Preprocessing class: FMLMSLSMSSSNFFN.
% 72.41/12.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 72.41/12.45 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 72.41/12.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 72.41/12.45 % No SInE strategy applied
% 72.41/12.45 % Search class: FGHSM-SMLM33-DFFFFFNN
% 72.41/12.45 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 72.41/12.45 % Starting SubtermCWHack with 135s (1) cores
% 72.41/12.45 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 72.41/12.45 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 72.41/12.45 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 72.41/12.45 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 135s (1) cores
% 72.41/12.45 % SAT001_CA_MinMin_p005000_rr with pid 3997143 completed with status 0
% 72.41/12.45 % Result found by SAT001_CA_MinMin_p005000_rr
% 72.41/12.45 % Preprocessing class: FMLMSLSMSSSNFFN.
% 72.41/12.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 72.41/12.45 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 72.41/12.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 72.41/12.45 % No SInE strategy applied
% 72.41/12.45 % Search class: FGHSM-SMLM33-DFFFFFNN
% 72.41/12.45 % Scheduled 7 strats onto 5 cores with 1499 seconds (1499 total)
% 72.41/12.45 % Starting SubtermCWHack with 135s (1) cores
% 72.41/12.45 % Starting SAT001_MinMin_p005000_rr_RG with 150s (1) cores
% 72.41/12.45 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 135s (1) cores
% 72.41/12.45 % Starting SAT001_CA_MinMin_p005000_rr with 135s (1) cores
% 72.41/12.45 % Preprocessing time : 0.325 s
% 72.41/12.45 % Presaturation interreduction done
% 72.41/12.45
% 72.41/12.45 % Proof found!
% 72.41/12.45 % SZS status ContradictoryAxioms
% 72.41/12.45 % SZS output start CNFRefutation
% See solution above
% 72.41/12.45 % Parsed axioms : 5225
% 72.41/12.45 % Removed by relevancy pruning/SinE : 0
% 72.41/12.45 % Initial clauses : 7582
% 72.41/12.45 % Removed in clause preprocessing : 239
% 72.41/12.45 % Initial clauses in saturation : 7343
% 72.41/12.45 % Processed clauses : 17801
% 72.41/12.45 % ...of these trivial : 425
% 72.41/12.45 % ...subsumed : 6034
% 72.41/12.45 % ...remaining for further processing : 11342
% 72.41/12.45 % Other redundant clauses eliminated : 917
% 72.41/12.45 % Clauses deleted for lack of memory : 0
% 72.41/12.45 % Backward-subsumed : 206
% 72.41/12.45 % Backward-rewritten : 799
% 72.41/12.45 % Generated clauses : 90222
% 72.41/12.45 % ...of the previous two non-redundant : 84989
% 72.41/12.45 % ...aggressively subsumed : 0
% 72.41/12.45 % Contextual simplify-reflections : 33
% 72.41/12.45 % Paramodulations : 89324
% 72.41/12.45 % Factorizations : 2
% 72.41/12.45 % NegExts : 0
% 72.41/12.45 % Equation resolutions : 961
% 72.41/12.45 % Disequality decompositions : 0
% 72.41/12.45 % Total rewrite steps : 27780
% 72.41/12.45 % ...of those cached : 19944
% 72.41/12.45 % Propositional unsat checks : 3
% 72.41/12.45 % Propositional check models : 2
% 72.41/12.45 % Propositional check unsatisfiable : 0
% 72.41/12.45 % Propositional clauses : 0
% 72.41/12.45 % Propositional clauses after purity: 0
% 72.41/12.45 % Propositional unsat core size : 0
% 72.41/12.45 % Propositional preprocessing time : 0.000
% 72.41/12.45 % Propositional encoding time : 0.272
% 72.41/12.45 % Propositional solver time : 0.126
% 72.41/12.45 % Success case prop preproc time : 0.000
% 72.41/12.45 % Success case prop encoding time : 0.000
% 72.41/12.45 % Success case prop solver time : 0.000
% 72.41/12.45 % Current number of processed clauses : 3926
% 72.41/12.45 % Positive orientable unit clauses : 1439
% 72.41/12.45 % Positive unorientable unit clauses: 43
% 72.41/12.45 % Negative unit clauses : 570
% 72.41/12.45 % Non-unit-clauses : 1874
% 72.41/12.45 % Current number of unprocessed clauses: 74256
% 72.41/12.45 % ...number of literals in the above : 134702
% 72.41/12.45 % Current number of archived formulas : 0
% 72.41/12.45 % Current number of archived clauses : 6971
% 72.41/12.45 % Clause-clause subsumption calls (NU) : 4965346
% 72.41/12.45 % Rec. Clause-clause subsumption calls : 2362847
% 72.41/12.45 % Non-unit clause-clause subsumptions : 3768
% 72.41/12.45 % Unit Clause-clause subsumption calls : 140691
% 72.41/12.45 % Rewrite failures with RHS unbound : 452
% 72.41/12.45 % BW rewrite match attempts : 36227
% 72.41/12.45 % BW rewrite match successes : 1093
% 72.41/12.45 % Condensation attempts : 109625
% 72.41/12.45 % Condensation successes : 394
% 72.41/12.45 % Termbank termtop insertions : 4088686
% 72.41/12.45 % Search garbage collected termcells : 101993
% 72.41/12.45
% 72.41/12.45 % -------------------------------------------------
% 72.41/12.45 % User time : 10.787 s
% 72.41/12.45 % System time : 0.302 s
% 72.41/12.45 % Total time : 11.089 s
% 72.41/12.45 % Maximum resident set size: 43156 pages
% 72.41/12.45
% 72.41/12.45 % -------------------------------------------------
% 72.41/12.45 % User time : 47.539 s
% 72.41/12.45 % System time : 1.320 s
% 72.41/12.45 % Total time : 48.860 s
% 72.41/12.45 % Maximum resident set size: 12288 pages
% 72.41/12.45 % E exiting
%------------------------------------------------------------------------------