TSTP Solution File: SWW366+1 by Enigma---0.5.1
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%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SWW366+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 00:02:06 EDT 2022
% Result : ContradictoryAxioms 88.03s 13.99s
% Output : CNFRefutation 88.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 85 ( 70 unt; 0 def)
% Number of atoms : 102 ( 88 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 24 ~; 14 |; 1 &)
% ( 1 <=>; 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 : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 148 ( 17 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_empty__def,axiom,
! [X11] : c_Orderings_Obot__class_Obot(tc_fun(X11,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11),hAPP(c_COMBK(tc_HOL_Obool,X11),c_fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X44,X11] : hAPP(c_Set_OCollect(X11),X44) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__neg__eq,axiom,
! [X44,X11] : hAPP(c_Set_OCollect(X11),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11),c_fNot),X44)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11),X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_vimage__Collect__eq,axiom,
! [X44,X2,X9,X11] : hAPP(c_Set_Ovimage(X11,X9,X2),hAPP(c_Set_OCollect(X9),X44)) = hAPP(c_Set_OCollect(X11),hAPP(hAPP(c_COMBB(X9,tc_HOL_Obool,X11),X44),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).
fof(fact_Collect__empty__eq,axiom,
! [X44,X11] :
( hAPP(c_Set_OCollect(X11),X44) = c_Orderings_Obot__class_Obot(tc_fun(X11,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X44,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(help_c__COMBK__1,axiom,
! [X280,X279,X11,X27] : hAPP(hAPP(c_COMBK(X27,X11),X279),X280) = X279,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_double__complement,axiom,
! [X13,X11] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11,tc_HOL_Obool)),X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(fact_vimage__id,axiom,
! [X13,X11] : hAPP(c_Set_Ovimage(X11,X11,c_Fun_Oid(X11)),X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__id) ).
fof(fact_UNIV__def,axiom,
! [X11] : c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11),hAPP(c_COMBK(tc_HOL_Obool,X11),c_fTrue)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_add__eq__self__zero,axiom,
! [X25,X24] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25) = X24
=> X25 = 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(fact_Zero__not__Suc,axiom,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(help_c__fNot__1,axiom,
! [X44] :
( ~ hBOOL(hAPP(c_fNot,X44))
| ~ hBOOL(X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_Compl__empty__eq,axiom,
! [X11] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X11,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X11,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_add__Suc__right,axiom,
! [X25,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_id__def,axiom,
! [X190,X27] : hAPP(c_Fun_Oid(X27),X190) = X190,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).
fof(help_c__COMBB__1,axiom,
! [X29,X43,X44,X19,X11,X9] : hAPP(hAPP(hAPP(c_COMBB(X9,X11,X19),X44),X43),X29) = hAPP(X44,hAPP(X43,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X25] : X25 != hAPP(c_Nat_OSuc,X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_20,plain,
! [X11051] : c_Orderings_Obot__class_Obot(tc_fun(X11051,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11051),hAPP(c_COMBK(tc_HOL_Obool,X11051),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_21,plain,
! [X11049,X11050] : hAPP(c_Set_OCollect(X11050),X11049) = X11049,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_22,plain,
! [X11064,X11065] : hAPP(c_Set_OCollect(X11065),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X11065),c_fNot),X11064)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X11065,tc_HOL_Obool)),hAPP(c_Set_OCollect(X11065),X11064)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_23,plain,
! [X11066,X11067,X11068,X11069] : hAPP(c_Set_Ovimage(X11069,X11068,X11067),hAPP(c_Set_OCollect(X11068),X11066)) = hAPP(c_Set_OCollect(X11069),hAPP(hAPP(c_COMBB(X11068,tc_HOL_Obool,X11069),X11066),X11067)),
inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(c_0_24,plain,
! [X11052,X11053,X11054,X11055,X11057] :
( ( hAPP(c_Set_OCollect(X11053),X11052) != c_Orderings_Obot__class_Obot(tc_fun(X11053,tc_HOL_Obool))
| ~ hBOOL(hAPP(X11052,X11054)) )
& ( hBOOL(hAPP(X11055,esk278_1(X11055)))
| hAPP(c_Set_OCollect(X11057),X11055) = c_Orderings_Obot__class_Obot(tc_fun(X11057,tc_HOL_Obool)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq])])])])])]) ).
fof(c_0_25,plain,
! [X17462,X17463,X17464,X17465] : hAPP(hAPP(c_COMBK(X17465,X17464),X17463),X17462) = X17463,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_26,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_27,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_28,plain,
! [X4942,X4943] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4943,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4943,tc_HOL_Obool)),X4942)) = X4942,
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_22]) ).
fof(c_0_30,plain,
! [X11254,X11255] : hAPP(c_Set_Ovimage(X11255,X11255,c_Fun_Oid(X11255)),X11254) = X11254,
inference(variable_rename,[status(thm)],[fact_vimage__id]) ).
cnf(c_0_31,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Set_OCollect(X2),X4)) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( hBOOL(hAPP(X1,esk278_1(X1)))
| hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,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_26,c_0_27]) ).
fof(c_0_35,plain,
! [X11036] : c_Orderings_Otop__class_Otop(tc_fun(X11036,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X11036),hAPP(c_COMBK(tc_HOL_Obool,X11036),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_36,plain,
! [X2054,X2055] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2055),X2054) != X2055
| X2054 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
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,
! [X2038] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2038),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
cnf(c_0_40,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_41,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_27]),c_0_27]) ).
cnf(c_0_42,plain,
hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X2,tc_HOL_Obool,X1),X4),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_27]),c_0_27]) ).
fof(c_0_44,plain,
! [X17488] :
( ~ hBOOL(hAPP(c_fNot,X17488))
| ~ hBOOL(X17488) ),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[help_c__fNot__1])]) ).
cnf(c_0_45,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk278_1(X1))) ),
inference(rw,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_46,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_47,plain,
! [X9638] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9638,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X9638,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9638,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_48,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_35]) ).
cnf(c_0_49,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_50,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_51,plain,
! [X1416,X1417] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1417),hAPP(c_Nat_OSuc,X1416)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1417),X1416)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_52,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_53,plain,
! [X11258,X11259] : hAPP(c_Fun_Oid(X11259),X11258) = X11258,
inference(variable_rename,[status(thm)],[fact_id__def]) ).
cnf(c_0_54,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_40,c_0_41]),c_0_41]) ).
cnf(c_0_55,plain,
hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X1),X2),c_Fun_Oid(X1)) = X2,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_56,plain,
! [X17466,X17467,X17468,X17469,X17470,X17471] : hAPP(hAPP(hAPP(c_COMBB(X17471,X17470,X17469),X17468),X17467),X17466) = hAPP(X17468,hAPP(X17467,X17466)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_57,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_58,plain,
( c_fFalse = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_45]),c_0_46]),c_0_33]) ).
cnf(c_0_59,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_47]) ).
cnf(c_0_60,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_48,c_0_27]) ).
cnf(c_0_61,plain,
( X1 = hAPP(c_Int_Onat,c_Int_OPls)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2 ),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_62,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_51]) ).
cnf(c_0_63,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_52,c_0_50]) ).
fof(c_0_64,plain,
! [X2051] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2051),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2051,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
cnf(c_0_65,plain,
hAPP(c_Fun_Oid(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_66,plain,
c_Fun_Oid(tc_HOL_Obool) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_HOL_Obool),c_fNot),c_fNot),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_67,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,plain,
( hAPP(c_fNot,X1) = c_fFalse
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_69,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_59,c_0_41]) ).
cnf(c_0_70,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_33,c_0_60]) ).
cnf(c_0_71,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_61,c_0_62]),c_0_63]) ).
cnf(c_0_72,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_64]) ).
fof(c_0_73,plain,
! [X655] : X655 != hAPP(c_Nat_OSuc,X655),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_74,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]) ).
cnf(c_0_75,plain,
( hAPP(c_fNot,X1) = c_fFalse
| c_fFalse = X1 ),
inference(spm,[status(thm)],[c_0_68,c_0_58]) ).
cnf(c_0_76,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_69]),c_0_70]),c_0_46]) ).
cnf(c_0_77,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_71,c_0_62]) ).
cnf(c_0_78,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_72,c_0_50]) ).
cnf(c_0_79,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_80,plain,
( c_fFalse = X1
| c_fTrue = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_81,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_82,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_83,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_84,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_80]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SWW366+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.09 % Command : enigmatic-eprover.py %s %d 1
% 0.09/0.29 % Computer : n018.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Sat Jun 4 19:06:19 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.15/0.45 # ENIGMATIC: Selected SinE mode:
% 0.49/0.70 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.49/0.70 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.49/0.70 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.49/0.70 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 88.03/13.99 # ENIGMATIC: Solved by autoschedule:
% 88.03/13.99 # No SInE strategy applied
% 88.03/13.99 # Trying AutoSched0 for 150 seconds
% 88.03/13.99 # AutoSched0-Mode selected heuristic SAT001_MinMin_x000000_rr
% 88.03/13.99 # and selection function SelectMaxLComplexAvoidPosPred.
% 88.03/13.99 #
% 88.03/13.99 # Preprocessing time : 1.402 s
% 88.03/13.99 # Presaturation interreduction done
% 88.03/13.99
% 88.03/13.99 # Proof found!
% 88.03/13.99 # SZS status ContradictoryAxioms
% 88.03/13.99 # SZS output start CNFRefutation
% See solution above
% 88.03/13.99 # Training examples: 0 positive, 0 negative
% 88.03/13.99
% 88.03/13.99 # -------------------------------------------------
% 88.03/13.99 # User time : 9.716 s
% 88.03/13.99 # System time : 0.206 s
% 88.03/13.99 # Total time : 9.922 s
% 88.03/13.99 # Maximum resident set size: 10796 pages
% 88.03/13.99
%------------------------------------------------------------------------------