TSTP Solution File: LCL518+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL518+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n014.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 : 300s
% DateTime : Fri Sep 1 17:23:36 EDT 2023
% Result : Theorem 0.19s 0.60s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 138
% Syntax : Number of formulae : 467 ( 88 unt; 0 def)
% Number of atoms : 1040 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 963 ( 390 ~; 337 |; 94 &)
% ( 109 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 103 ( 101 usr; 101 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 607 (; 442 !; 165 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2401,plain,
$false,
inference(avatar_smt_refutation,[],[f265,f270,f275,f280,f285,f290,f295,f300,f305,f310,f315,f316,f317,f318,f319,f320,f321,f322,f323,f324,f329,f337,f343,f351,f357,f362,f368,f376,f382,f388,f396,f402,f410,f416,f424,f430,f441,f447,f455,f461,f469,f475,f483,f489,f523,f528,f543,f608,f667,f721,f794,f799,f822,f949,f1125,f1178,f1262,f1416,f1581,f1735,f1800,f1947,f2284,f2394,f2395]) ).
fof(f2395,plain,
spl55_46,
inference(avatar_contradiction_clause,[],[f2386]) ).
fof(f2386,plain,
( $false
| spl55_46 ),
inference(resolution,[],[f2360,f522]) ).
fof(f522,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| spl55_46 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f520,plain,
( spl55_46
<=> is_a_theorem(implies(or(sK0,sK0),sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_46])]) ).
fof(f2360,plain,
! [X5] : is_a_theorem(implies(or(X5,X5),X5)),
inference(forward_demodulation,[],[f2349,f241]) ).
fof(f241,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181]) ).
fof(f181,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',op_implies_or) ).
fof(f180,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',principia_op_equiv) ).
fof(f179,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',rosser_op_equiv) ).
fof(f178,plain,
op_implies_or,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
op_implies_or,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',principia_op_implies_or) ).
fof(f177,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',rosser_op_implies_and) ).
fof(f176,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',rosser_op_or) ).
fof(f175,plain,
op_and,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
op_and,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',principia_op_and) ).
fof(f174,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',rosser_kn1) ).
fof(f173,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',rosser_kn3) ).
fof(f172,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',rosser_modus_ponens) ).
fof(f171,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',substitution_of_equivalents) ).
fof(f170,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',rosser_kn2) ).
fof(f169,plain,
~ r1,
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
~ r1,
inference(flattening,[],[f44]) ).
fof(f44,negated_conjecture,
~ r1,
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
r1,
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',principia_r1) ).
fof(f2349,plain,
! [X5] : is_a_theorem(or(not(or(X5,X5)),X5)),
inference(resolution,[],[f2339,f2221]) ).
fof(f2221,plain,
! [X0,X1] :
( ~ is_a_theorem(or(or(X1,X1),X0))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f2220,f503]) ).
fof(f503,plain,
! [X2,X3] : or(X2,X3) = implies(not(X2),X3),
inference(superposition,[],[f244,f242]) ).
fof(f242,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182]) ).
fof(f182,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',op_implies_and) ).
fof(f244,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184]) ).
fof(f184,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',op_or) ).
fof(f243,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183]) ).
fof(f183,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',op_and) ).
fof(f2220,plain,
! [X0,X1] :
( ~ is_a_theorem(or(implies(not(X1),X1),X0))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f2194,f491]) ).
fof(f491,plain,
! [X2,X0,X1] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2),
inference(superposition,[],[f241,f242]) ).
fof(f2194,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(and(not(X1),not(X1)),X0)) ),
inference(resolution,[],[f2183,f516]) ).
fof(f516,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f249,f503]) ).
fof(f249,plain,
! [X1] : is_a_theorem(implies(X1,and(X1,X1))),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228]) ).
fof(f228,plain,
! [X1] :
( is_a_theorem(implies(X1,and(X1,X1)))
| ~ kn1 ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
( ( kn1
| ~ is_a_theorem(implies(sK45,and(sK45,sK45))) )
& ( ! [X1] : is_a_theorem(implies(X1,and(X1,X1)))
| ~ kn1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f150,f151]) ).
fof(f151,plain,
( ? [X0] : ~ is_a_theorem(implies(X0,and(X0,X0)))
=> ~ is_a_theorem(implies(sK45,and(sK45,sK45))) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
( ( kn1
| ? [X0] : ~ is_a_theorem(implies(X0,and(X0,X0))) )
& ( ! [X1] : is_a_theorem(implies(X1,and(X1,X1)))
| ~ kn1 ) ),
inference(rectify,[],[f149]) ).
fof(f149,plain,
( ( kn1
| ? [X0] : ~ is_a_theorem(implies(X0,and(X0,X0))) )
& ( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
( kn1
<=> ! [X3] : is_a_theorem(implies(X3,and(X3,X3))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',kn1) ).
fof(f248,plain,
kn1,
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229]) ).
fof(f229,plain,
( kn1
| ~ is_a_theorem(implies(sK45,and(sK45,sK45))) ),
inference(cnf_transformation,[],[f152]) ).
fof(f247,plain,
~ r1,
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226]) ).
fof(f226,plain,
! [X1] :
( is_a_theorem(implies(or(X1,X1),X1))
| ~ r1 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( ( r1
| ~ is_a_theorem(implies(or(sK44,sK44),sK44)) )
& ( ! [X1] : is_a_theorem(implies(or(X1,X1),X1))
| ~ r1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f146,f147]) ).
fof(f147,plain,
( ? [X0] : ~ is_a_theorem(implies(or(X0,X0),X0))
=> ~ is_a_theorem(implies(or(sK44,sK44),sK44)) ),
introduced(choice_axiom,[]) ).
fof(f146,plain,
( ( r1
| ? [X0] : ~ is_a_theorem(implies(or(X0,X0),X0)) )
& ( ! [X1] : is_a_theorem(implies(or(X1,X1),X1))
| ~ r1 ) ),
inference(rectify,[],[f145]) ).
fof(f145,plain,
( ( r1
| ? [X0] : ~ is_a_theorem(implies(or(X0,X0),X0)) )
& ( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
( r1
<=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',r1) ).
fof(f246,plain,
~ is_a_theorem(implies(or(sK44,sK44),sK44)),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227]) ).
fof(f227,plain,
( r1
| ~ is_a_theorem(implies(or(sK44,sK44),sK44)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f224,plain,
! [X3,X4,X5] :
( is_a_theorem(implies(implies(X3,X5),implies(implies(X4,X5),implies(or(X3,X4),X5))))
| ~ or_3 ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ( or_3
| ~ is_a_theorem(implies(implies(sK41,sK43),implies(implies(sK42,sK43),implies(or(sK41,sK42),sK43)))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X5),implies(implies(X4,X5),implies(or(X3,X4),X5))))
| ~ or_3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43])],[f142,f143]) ).
fof(f143,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
=> ~ is_a_theorem(implies(implies(sK41,sK43),implies(implies(sK42,sK43),implies(or(sK41,sK42),sK43)))) ),
introduced(choice_axiom,[]) ).
fof(f142,plain,
( ( or_3
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X5),implies(implies(X4,X5),implies(or(X3,X4),X5))))
| ~ or_3 ) ),
inference(rectify,[],[f141]) ).
fof(f141,plain,
( ( or_3
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,axiom,
( or_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',or_3) ).
fof(f225,plain,
( or_3
| ~ is_a_theorem(implies(implies(sK41,sK43),implies(implies(sK42,sK43),implies(or(sK41,sK42),sK43)))) ),
inference(cnf_transformation,[],[f144]) ).
fof(f222,plain,
! [X3,X4,X5] :
( is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5))))
| ~ r4 ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( ( r4
| ~ is_a_theorem(implies(or(sK38,or(sK39,sK40)),or(sK39,or(sK38,sK40)))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5))))
| ~ r4 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39,sK40])],[f138,f139]) ).
fof(f139,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
=> ~ is_a_theorem(implies(or(sK38,or(sK39,sK40)),or(sK39,or(sK38,sK40)))) ),
introduced(choice_axiom,[]) ).
fof(f138,plain,
( ( r4
| ? [X0,X1,X2] : ~ is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5))))
| ~ r4 ) ),
inference(rectify,[],[f137]) ).
fof(f137,plain,
( ( r4
| ? [X0,X1,X2] : ~ is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) )
& ( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
( r4
<=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
( r4
<=> ! [X3,X4,X5] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5)))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',r4) ).
fof(f223,plain,
( r4
| ~ is_a_theorem(implies(or(sK38,or(sK39,sK40)),or(sK39,or(sK38,sK40)))) ),
inference(cnf_transformation,[],[f140]) ).
fof(f220,plain,
! [X3,X4,X5] :
( is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5))))
| ~ cn1 ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( ( cn1
| ~ is_a_theorem(implies(implies(sK35,sK36),implies(implies(sK36,sK37),implies(sK35,sK37)))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5))))
| ~ cn1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37])],[f134,f135]) ).
fof(f135,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> ~ is_a_theorem(implies(implies(sK35,sK36),implies(implies(sK36,sK37),implies(sK35,sK37)))) ),
introduced(choice_axiom,[]) ).
fof(f134,plain,
( ( cn1
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5))))
| ~ cn1 ) ),
inference(rectify,[],[f133]) ).
fof(f133,plain,
( ( cn1
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
( cn1
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
( cn1
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5)))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',cn1) ).
fof(f221,plain,
( cn1
| ~ is_a_theorem(implies(implies(sK35,sK36),implies(implies(sK36,sK37),implies(sK35,sK37)))) ),
inference(cnf_transformation,[],[f136]) ).
fof(f218,plain,
! [X3,X4,X5] :
( is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( ( implies_3
| ~ is_a_theorem(implies(implies(sK32,sK33),implies(implies(sK33,sK34),implies(sK32,sK34)))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5))))
| ~ implies_3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34])],[f130,f131]) ).
fof(f131,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> ~ is_a_theorem(implies(implies(sK32,sK33),implies(implies(sK33,sK34),implies(sK32,sK34)))) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
( ( implies_3
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5))))
| ~ implies_3 ) ),
inference(rectify,[],[f129]) ).
fof(f129,plain,
( ( implies_3
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',implies_3) ).
fof(f219,plain,
( implies_3
| ~ is_a_theorem(implies(implies(sK32,sK33),implies(implies(sK33,sK34),implies(sK32,sK34)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f216,plain,
! [X3,X4,X5] :
( is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5))))
| ~ r5 ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
( ( r5
| ~ is_a_theorem(implies(implies(sK30,sK31),implies(or(sK29,sK30),or(sK29,sK31)))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5))))
| ~ r5 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f126,f127]) ).
fof(f127,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
=> ~ is_a_theorem(implies(implies(sK30,sK31),implies(or(sK29,sK30),or(sK29,sK31)))) ),
introduced(choice_axiom,[]) ).
fof(f126,plain,
( ( r5
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5))))
| ~ r5 ) ),
inference(rectify,[],[f125]) ).
fof(f125,plain,
( ( r5
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
( r5
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5)))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',r5) ).
fof(f217,plain,
( r5
| ~ is_a_theorem(implies(implies(sK30,sK31),implies(or(sK29,sK30),or(sK29,sK31)))) ),
inference(cnf_transformation,[],[f128]) ).
fof(f214,plain,
! [X2,X3] :
( is_a_theorem(implies(implies(X2,X3),implies(implies(X3,X2),equiv(X2,X3))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
( ( equivalence_3
| ~ is_a_theorem(implies(implies(sK27,sK28),implies(implies(sK28,sK27),equiv(sK27,sK28)))) )
& ( ! [X2,X3] : is_a_theorem(implies(implies(X2,X3),implies(implies(X3,X2),equiv(X2,X3))))
| ~ equivalence_3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f122,f123]) ).
fof(f123,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
=> ~ is_a_theorem(implies(implies(sK27,sK28),implies(implies(sK28,sK27),equiv(sK27,sK28)))) ),
introduced(choice_axiom,[]) ).
fof(f122,plain,
( ( equivalence_3
| ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) )
& ( ! [X2,X3] : is_a_theorem(implies(implies(X2,X3),implies(implies(X3,X2),equiv(X2,X3))))
| ~ equivalence_3 ) ),
inference(rectify,[],[f121]) ).
fof(f121,plain,
( ( equivalence_3
| ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) )
& ( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',equivalence_3) ).
fof(f215,plain,
( equivalence_3
| ~ is_a_theorem(implies(implies(sK27,sK28),implies(implies(sK28,sK27),equiv(sK27,sK28)))) ),
inference(cnf_transformation,[],[f124]) ).
fof(f212,plain,
! [X2,X3] :
( is_a_theorem(implies(implies(X2,implies(X2,X3)),implies(X2,X3)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
( ( implies_2
| ~ is_a_theorem(implies(implies(sK25,implies(sK25,sK26)),implies(sK25,sK26))) )
& ( ! [X2,X3] : is_a_theorem(implies(implies(X2,implies(X2,X3)),implies(X2,X3)))
| ~ implies_2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f118,f119]) ).
fof(f119,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
=> ~ is_a_theorem(implies(implies(sK25,implies(sK25,sK26)),implies(sK25,sK26))) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
( ( implies_2
| ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) )
& ( ! [X2,X3] : is_a_theorem(implies(implies(X2,implies(X2,X3)),implies(X2,X3)))
| ~ implies_2 ) ),
inference(rectify,[],[f117]) ).
fof(f117,plain,
( ( implies_2
| ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) )
& ( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',implies_2) ).
fof(f213,plain,
( implies_2
| ~ is_a_theorem(implies(implies(sK25,implies(sK25,sK26)),implies(sK25,sK26))) ),
inference(cnf_transformation,[],[f120]) ).
fof(f210,plain,
! [X2,X3] :
( is_a_theorem(implies(implies(not(X3),not(X2)),implies(X2,X3)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
( ( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK24),not(sK23)),implies(sK23,sK24))) )
& ( ! [X2,X3] : is_a_theorem(implies(implies(not(X3),not(X2)),implies(X2,X3)))
| ~ modus_tollens ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f114,f115]) ).
fof(f115,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
=> ~ is_a_theorem(implies(implies(not(sK24),not(sK23)),implies(sK23,sK24))) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
( ( modus_tollens
| ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) )
& ( ! [X2,X3] : is_a_theorem(implies(implies(not(X3),not(X2)),implies(X2,X3)))
| ~ modus_tollens ) ),
inference(rectify,[],[f113]) ).
fof(f113,plain,
( ( modus_tollens
| ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) )
& ( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',modus_tollens) ).
fof(f211,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK24),not(sK23)),implies(sK23,sK24))) ),
inference(cnf_transformation,[],[f116]) ).
fof(f208,plain,
! [X2,X3] :
( is_a_theorem(implies(or(X2,X3),or(X3,X2)))
| ~ r3 ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
( ( r3
| ~ is_a_theorem(implies(or(sK21,sK22),or(sK22,sK21))) )
& ( ! [X2,X3] : is_a_theorem(implies(or(X2,X3),or(X3,X2)))
| ~ r3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f110,f111]) ).
fof(f111,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
=> ~ is_a_theorem(implies(or(sK21,sK22),or(sK22,sK21))) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
( ( r3
| ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) )
& ( ! [X2,X3] : is_a_theorem(implies(or(X2,X3),or(X3,X2)))
| ~ r3 ) ),
inference(rectify,[],[f109]) ).
fof(f109,plain,
( ( r3
| ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) )
& ( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
( r3
<=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',r3) ).
fof(f209,plain,
( r3
| ~ is_a_theorem(implies(or(sK21,sK22),or(sK22,sK21))) ),
inference(cnf_transformation,[],[f112]) ).
fof(f206,plain,
! [X2,X3] :
( is_a_theorem(implies(equiv(X2,X3),implies(X2,X3)))
| ~ equivalence_1 ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
( ( equivalence_1
| ~ is_a_theorem(implies(equiv(sK19,sK20),implies(sK19,sK20))) )
& ( ! [X2,X3] : is_a_theorem(implies(equiv(X2,X3),implies(X2,X3)))
| ~ equivalence_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f106,f107]) ).
fof(f107,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
=> ~ is_a_theorem(implies(equiv(sK19,sK20),implies(sK19,sK20))) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
( ( equivalence_1
| ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) )
& ( ! [X2,X3] : is_a_theorem(implies(equiv(X2,X3),implies(X2,X3)))
| ~ equivalence_1 ) ),
inference(rectify,[],[f105]) ).
fof(f105,plain,
( ( equivalence_1
| ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) )
& ( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,axiom,
( equivalence_1
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',equivalence_1) ).
fof(f207,plain,
( equivalence_1
| ~ is_a_theorem(implies(equiv(sK19,sK20),implies(sK19,sK20))) ),
inference(cnf_transformation,[],[f108]) ).
fof(f204,plain,
! [X2,X3] :
( is_a_theorem(implies(equiv(X2,X3),implies(X3,X2)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
( ( equivalence_2
| ~ is_a_theorem(implies(equiv(sK17,sK18),implies(sK18,sK17))) )
& ( ! [X2,X3] : is_a_theorem(implies(equiv(X2,X3),implies(X3,X2)))
| ~ equivalence_2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f102,f103]) ).
fof(f103,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
=> ~ is_a_theorem(implies(equiv(sK17,sK18),implies(sK18,sK17))) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
( ( equivalence_2
| ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) )
& ( ! [X2,X3] : is_a_theorem(implies(equiv(X2,X3),implies(X3,X2)))
| ~ equivalence_2 ) ),
inference(rectify,[],[f101]) ).
fof(f101,plain,
( ( equivalence_2
| ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) )
& ( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',equivalence_2) ).
fof(f205,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv(sK17,sK18),implies(sK18,sK17))) ),
inference(cnf_transformation,[],[f104]) ).
fof(f202,plain,
! [X2,X3] :
( is_a_theorem(implies(X2,implies(X3,and(X2,X3))))
| ~ and_3 ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
( ( and_3
| ~ is_a_theorem(implies(sK15,implies(sK16,and(sK15,sK16)))) )
& ( ! [X2,X3] : is_a_theorem(implies(X2,implies(X3,and(X2,X3))))
| ~ and_3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f98,f99]) ).
fof(f99,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
=> ~ is_a_theorem(implies(sK15,implies(sK16,and(sK15,sK16)))) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
( ( and_3
| ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) )
& ( ! [X2,X3] : is_a_theorem(implies(X2,implies(X3,and(X2,X3))))
| ~ and_3 ) ),
inference(rectify,[],[f97]) ).
fof(f97,plain,
( ( and_3
| ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',and_3) ).
fof(f203,plain,
( and_3
| ~ is_a_theorem(implies(sK15,implies(sK16,and(sK15,sK16)))) ),
inference(cnf_transformation,[],[f100]) ).
fof(f200,plain,
! [X2,X3] :
( is_a_theorem(implies(X2,implies(not(X2),X3)))
| ~ cn2 ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( ( cn2
| ~ is_a_theorem(implies(sK13,implies(not(sK13),sK14))) )
& ( ! [X2,X3] : is_a_theorem(implies(X2,implies(not(X2),X3)))
| ~ cn2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f94,f95]) ).
fof(f95,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(not(X0),X1)))
=> ~ is_a_theorem(implies(sK13,implies(not(sK13),sK14))) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
( ( cn2
| ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(not(X0),X1))) )
& ( ! [X2,X3] : is_a_theorem(implies(X2,implies(not(X2),X3)))
| ~ cn2 ) ),
inference(rectify,[],[f93]) ).
fof(f93,plain,
( ( cn2
| ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(not(X0),X1))) )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
( cn2
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
( cn2
<=> ! [X3,X4] : is_a_theorem(implies(X3,implies(not(X3),X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',cn2) ).
fof(f201,plain,
( cn2
| ~ is_a_theorem(implies(sK13,implies(not(sK13),sK14))) ),
inference(cnf_transformation,[],[f96]) ).
fof(f198,plain,
! [X2,X3] :
( is_a_theorem(implies(and(X2,X3),X3))
| ~ and_2 ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
( ( and_2
| ~ is_a_theorem(implies(and(sK11,sK12),sK12)) )
& ( ! [X2,X3] : is_a_theorem(implies(and(X2,X3),X3))
| ~ and_2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f90,f91]) ).
fof(f91,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X1))
=> ~ is_a_theorem(implies(and(sK11,sK12),sK12)) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
( ( and_2
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X1)) )
& ( ! [X2,X3] : is_a_theorem(implies(and(X2,X3),X3))
| ~ and_2 ) ),
inference(rectify,[],[f89]) ).
fof(f89,plain,
( ( and_2
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X1)) )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',and_2) ).
fof(f199,plain,
( and_2
| ~ is_a_theorem(implies(and(sK11,sK12),sK12)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f196,plain,
! [X2,X3] :
( is_a_theorem(implies(and(X2,X3),X2))
| ~ and_1 ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( ( and_1
| ~ is_a_theorem(implies(and(sK9,sK10),sK9)) )
& ( ! [X2,X3] : is_a_theorem(implies(and(X2,X3),X2))
| ~ and_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f86,f87]) ).
fof(f87,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0))
=> ~ is_a_theorem(implies(and(sK9,sK10),sK9)) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
( ( and_1
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) )
& ( ! [X2,X3] : is_a_theorem(implies(and(X2,X3),X2))
| ~ and_1 ) ),
inference(rectify,[],[f85]) ).
fof(f85,plain,
( ( and_1
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',and_1) ).
fof(f197,plain,
( and_1
| ~ is_a_theorem(implies(and(sK9,sK10),sK9)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f194,plain,
! [X2,X3] :
( is_a_theorem(implies(X2,implies(X3,X2)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
( ( implies_1
| ~ is_a_theorem(implies(sK7,implies(sK8,sK7))) )
& ( ! [X2,X3] : is_a_theorem(implies(X2,implies(X3,X2)))
| ~ implies_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f82,f83]) ).
fof(f83,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,X0)))
=> ~ is_a_theorem(implies(sK7,implies(sK8,sK7))) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( ( implies_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,X0))) )
& ( ! [X2,X3] : is_a_theorem(implies(X2,implies(X3,X2)))
| ~ implies_1 ) ),
inference(rectify,[],[f81]) ).
fof(f81,plain,
( ( implies_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,implies(X1,X0))) )
& ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',implies_1) ).
fof(f195,plain,
( implies_1
| ~ is_a_theorem(implies(sK7,implies(sK8,sK7))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f192,plain,
! [X2,X3] :
( is_a_theorem(implies(X3,or(X2,X3)))
| ~ r2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
( ( r2
| ~ is_a_theorem(implies(sK6,or(sK5,sK6))) )
& ( ! [X2,X3] : is_a_theorem(implies(X3,or(X2,X3)))
| ~ r2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f78,f79]) ).
fof(f79,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1)))
=> ~ is_a_theorem(implies(sK6,or(sK5,sK6))) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
( ( r2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) )
& ( ! [X2,X3] : is_a_theorem(implies(X3,or(X2,X3)))
| ~ r2 ) ),
inference(rectify,[],[f77]) ).
fof(f77,plain,
( ( r2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) )
& ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
( r2
<=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',r2) ).
fof(f193,plain,
( r2
| ~ is_a_theorem(implies(sK6,or(sK5,sK6))) ),
inference(cnf_transformation,[],[f80]) ).
fof(f190,plain,
! [X2,X3] :
( is_a_theorem(implies(X2,or(X2,X3)))
| ~ or_1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( ( or_1
| ~ is_a_theorem(implies(sK3,or(sK3,sK4))) )
& ( ! [X2,X3] : is_a_theorem(implies(X2,or(X2,X3)))
| ~ or_1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f74,f75]) ).
fof(f75,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X0,or(X0,X1)))
=> ~ is_a_theorem(implies(sK3,or(sK3,sK4))) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
( ( or_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,or(X0,X1))) )
& ( ! [X2,X3] : is_a_theorem(implies(X2,or(X2,X3)))
| ~ or_1 ) ),
inference(rectify,[],[f73]) ).
fof(f73,plain,
( ( or_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,or(X0,X1))) )
& ( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',or_1) ).
fof(f191,plain,
( or_1
| ~ is_a_theorem(implies(sK3,or(sK3,sK4))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f188,plain,
! [X2,X3] :
( is_a_theorem(implies(X3,or(X2,X3)))
| ~ or_2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( ( or_2
| ~ is_a_theorem(implies(sK2,or(sK1,sK2))) )
& ( ! [X2,X3] : is_a_theorem(implies(X3,or(X2,X3)))
| ~ or_2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f70,f71]) ).
fof(f71,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1)))
=> ~ is_a_theorem(implies(sK2,or(sK1,sK2))) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
( ( or_2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) )
& ( ! [X2,X3] : is_a_theorem(implies(X3,or(X2,X3)))
| ~ or_2 ) ),
inference(rectify,[],[f69]) ).
fof(f69,plain,
( ( or_2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) )
& ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',or_2) ).
fof(f189,plain,
( or_2
| ~ is_a_theorem(implies(sK2,or(sK1,sK2))) ),
inference(cnf_transformation,[],[f72]) ).
fof(f186,plain,
! [X1] :
( is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ cn3 ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
( ( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) )
& ( ! [X1] : is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ cn3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f66,f67]) ).
fof(f67,plain,
( ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0))
=> ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
( ( cn3
| ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0)) )
& ( ! [X1] : is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ cn3 ) ),
inference(rectify,[],[f65]) ).
fof(f65,plain,
( ( cn3
| ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0)) )
& ( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
( cn3
<=> ! [X3] : is_a_theorem(implies(implies(not(X3),X3),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',cn3) ).
fof(f187,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f245,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185]) ).
fof(f185,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',op_equiv) ).
fof(f2183,plain,
! [X8,X6,X7] :
( ~ is_a_theorem(or(X6,X7))
| is_a_theorem(or(X8,X6))
| ~ is_a_theorem(implies(X7,X8)) ),
inference(resolution,[],[f2154,f258]) ).
fof(f258,plain,
! [X2,X3] :
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(X3)
| ~ is_a_theorem(X2) ),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231,f250,f230,f251,f234,f252,f233,f253,f232,f254,f238,f255,f237,f256,f236,f257,f235]) ).
fof(f235,plain,
! [X2,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(X2)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
( ( modus_ponens
| ( ~ is_a_theorem(sK51)
& is_a_theorem(implies(sK50,sK51))
& is_a_theorem(sK50) ) )
& ( ! [X2,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(X2) )
| ~ modus_ponens ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51])],[f162,f163]) ).
fof(f163,plain,
( ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> ( ~ is_a_theorem(sK51)
& is_a_theorem(implies(sK50,sK51))
& is_a_theorem(sK50) ) ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
( ( modus_ponens
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) ) )
& ( ! [X2,X3] :
( is_a_theorem(X3)
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(X2) )
| ~ modus_ponens ) ),
inference(rectify,[],[f161]) ).
fof(f161,plain,
( ( modus_ponens
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) ) )
& ( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
( modus_ponens
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
( modus_ponens
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',modus_ponens) ).
fof(f257,plain,
modus_ponens,
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231,f250,f230,f251,f234,f252,f233,f253,f232,f254,f238,f255,f237,f256,f236]) ).
fof(f236,plain,
( modus_ponens
| is_a_theorem(sK50) ),
inference(cnf_transformation,[],[f164]) ).
fof(f256,plain,
modus_ponens,
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231,f250,f230,f251,f234,f252,f233,f253,f232,f254,f238,f255,f237]) ).
fof(f237,plain,
( modus_ponens
| is_a_theorem(implies(sK50,sK51)) ),
inference(cnf_transformation,[],[f164]) ).
fof(f255,plain,
modus_ponens,
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231,f250,f230,f251,f234,f252,f233,f253,f232,f254,f238]) ).
fof(f238,plain,
( modus_ponens
| ~ is_a_theorem(sK51) ),
inference(cnf_transformation,[],[f164]) ).
fof(f254,plain,
! [X2,X3] :
( ~ is_a_theorem(equiv(X2,X3))
| X2 = X3 ),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231,f250,f230,f251,f234,f252,f233,f253,f232]) ).
fof(f232,plain,
! [X2,X3] :
( X2 = X3
| ~ is_a_theorem(equiv(X2,X3))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
( ( substitution_of_equivalents
| ( sK48 != sK49
& is_a_theorem(equiv(sK48,sK49)) ) )
& ( ! [X2,X3] :
( X2 = X3
| ~ is_a_theorem(equiv(X2,X3)) )
| ~ substitution_of_equivalents ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49])],[f158,f159]) ).
fof(f159,plain,
( ? [X0,X1] :
( X0 != X1
& is_a_theorem(equiv(X0,X1)) )
=> ( sK48 != sK49
& is_a_theorem(equiv(sK48,sK49)) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
( ( substitution_of_equivalents
| ? [X0,X1] :
( X0 != X1
& is_a_theorem(equiv(X0,X1)) ) )
& ( ! [X2,X3] :
( X2 = X3
| ~ is_a_theorem(equiv(X2,X3)) )
| ~ substitution_of_equivalents ) ),
inference(rectify,[],[f157]) ).
fof(f157,plain,
( ( substitution_of_equivalents
| ? [X0,X1] :
( X0 != X1
& is_a_theorem(equiv(X0,X1)) ) )
& ( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
( substitution_of_equivalents
<=> ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',substitution_of_equivalents) ).
fof(f253,plain,
substitution_of_equivalents,
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231,f250,f230,f251,f234,f252,f233]) ).
fof(f233,plain,
( substitution_of_equivalents
| is_a_theorem(equiv(sK48,sK49)) ),
inference(cnf_transformation,[],[f160]) ).
fof(f252,plain,
substitution_of_equivalents,
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231,f250,f230,f251,f234]) ).
fof(f234,plain,
( substitution_of_equivalents
| sK48 != sK49 ),
inference(cnf_transformation,[],[f160]) ).
fof(f251,plain,
! [X2,X3] : is_a_theorem(implies(and(X2,X3),X2)),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231,f250,f230]) ).
fof(f230,plain,
! [X2,X3] :
( is_a_theorem(implies(and(X2,X3),X2))
| ~ kn2 ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
( ( kn2
| ~ is_a_theorem(implies(and(sK46,sK47),sK46)) )
& ( ! [X2,X3] : is_a_theorem(implies(and(X2,X3),X2))
| ~ kn2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47])],[f154,f155]) ).
fof(f155,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0))
=> ~ is_a_theorem(implies(and(sK46,sK47),sK46)) ),
introduced(choice_axiom,[]) ).
fof(f154,plain,
( ( kn2
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) )
& ( ! [X2,X3] : is_a_theorem(implies(and(X2,X3),X2))
| ~ kn2 ) ),
inference(rectify,[],[f153]) ).
fof(f153,plain,
( ( kn2
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
( kn2
<=> ! [X3,X4] : is_a_theorem(implies(and(X3,X4),X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',kn2) ).
fof(f250,plain,
kn2,
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231]) ).
fof(f231,plain,
( kn2
| ~ is_a_theorem(implies(and(sK46,sK47),sK46)) ),
inference(cnf_transformation,[],[f156]) ).
fof(f2154,plain,
! [X3,X4,X5] :
( is_a_theorem(implies(implies(X3,X4),or(X4,X5)))
| ~ is_a_theorem(or(X5,X3)) ),
inference(resolution,[],[f2136,f258]) ).
fof(f2136,plain,
! [X3,X4,X5] : is_a_theorem(implies(or(X4,X5),implies(implies(X5,X3),or(X3,X4)))),
inference(forward_demodulation,[],[f2135,f503]) ).
fof(f2135,plain,
! [X3,X4,X5] : is_a_theorem(implies(implies(not(X4),X5),implies(implies(X5,X3),or(X3,X4)))),
inference(forward_demodulation,[],[f2124,f508]) ).
fof(f508,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(forward_demodulation,[],[f497,f242]) ).
fof(f497,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2))),
inference(superposition,[],[f244,f242]) ).
fof(f2124,plain,
! [X3,X4,X5] : is_a_theorem(implies(implies(not(X4),X5),or(and(X5,not(X3)),or(X3,X4)))),
inference(superposition,[],[f1991,f244]) ).
fof(f1991,plain,
! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),or(and(X4,X5),not(and(X5,X3))))),
inference(forward_demodulation,[],[f260,f503]) ).
fof(f260,plain,
! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(not(and(X4,X5)),not(and(X5,X3))))),
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231,f250,f230,f251,f234,f252,f233,f253,f232,f254,f238,f255,f237,f256,f236,f257,f235,f258,f240,f259,f239]) ).
fof(f239,plain,
! [X3,X4,X5] :
( is_a_theorem(implies(implies(X3,X4),implies(not(and(X4,X5)),not(and(X5,X3)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
( ( kn3
| ~ is_a_theorem(implies(implies(sK52,sK53),implies(not(and(sK53,sK54)),not(and(sK54,sK52))))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(not(and(X4,X5)),not(and(X5,X3)))))
| ~ kn3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53,sK54])],[f166,f167]) ).
fof(f167,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
=> ~ is_a_theorem(implies(implies(sK52,sK53),implies(not(and(sK53,sK54)),not(and(sK54,sK52))))) ),
introduced(choice_axiom,[]) ).
fof(f166,plain,
( ( kn3
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) )
& ( ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(not(and(X4,X5)),not(and(X5,X3)))))
| ~ kn3 ) ),
inference(rectify,[],[f165]) ).
fof(f165,plain,
( ( kn3
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) )
& ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
( kn3
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(not(and(X4,X5)),not(and(X5,X3))))) ),
file('/export/starexec/sandbox2/tmp/tmp.Tr01fWJkbN/Vampire---4.8_28830',kn3) ).
fof(f259,plain,
kn3,
inference(global_subsumption,[],[f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f241,f182,f242,f183,f243,f184,f244,f185,f245,f187,f186,f189,f188,f191,f190,f193,f192,f195,f194,f197,f196,f199,f198,f201,f200,f203,f202,f205,f204,f207,f206,f209,f208,f211,f210,f213,f212,f215,f214,f217,f216,f219,f218,f221,f220,f223,f222,f225,f224,f227,f246,f226,f247,f229,f248,f228,f249,f231,f250,f230,f251,f234,f252,f233,f253,f232,f254,f238,f255,f237,f256,f236,f257,f235,f258,f240]) ).
fof(f240,plain,
( kn3
| ~ is_a_theorem(implies(implies(sK52,sK53),implies(not(and(sK53,sK54)),not(and(sK54,sK52))))) ),
inference(cnf_transformation,[],[f168]) ).
fof(f2339,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[],[f2305,f503]) ).
fof(f2305,plain,
! [X4] : is_a_theorem(implies(X4,X4)),
inference(forward_demodulation,[],[f2287,f241]) ).
fof(f2287,plain,
! [X4] : is_a_theorem(or(not(X4),X4)),
inference(resolution,[],[f2221,f1221]) ).
fof(f1221,plain,
! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X0))),
inference(superposition,[],[f1184,f503]) ).
fof(f1184,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[],[f251,f491]) ).
fof(f2394,plain,
spl55_12,
inference(avatar_contradiction_clause,[],[f2387]) ).
fof(f2387,plain,
( $false
| spl55_12 ),
inference(resolution,[],[f2360,f328]) ).
fof(f328,plain,
( ~ is_a_theorem(implies(or(sK44,sK44),sK44))
| spl55_12 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f326,plain,
( spl55_12
<=> is_a_theorem(implies(or(sK44,sK44),sK44)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_12])]) ).
fof(f2284,plain,
( ~ spl55_68
| spl55_69 ),
inference(avatar_split_clause,[],[f224,f2282,f2278]) ).
fof(f2278,plain,
( spl55_68
<=> or_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_68])]) ).
fof(f2282,plain,
( spl55_69
<=> ! [X4,X5,X3] : is_a_theorem(implies(implies(X3,X5),implies(implies(X4,X5),implies(or(X3,X4),X5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_69])]) ).
fof(f1947,plain,
( ~ spl55_67
| spl55_65 ),
inference(avatar_split_clause,[],[f1905,f1794,f1944]) ).
fof(f1944,plain,
( spl55_67
<=> is_a_theorem(implies(or(sK38,or(sK39,sK40)),or(sK39,or(sK38,sK40)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_67])]) ).
fof(f1794,plain,
( spl55_65
<=> r4 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_65])]) ).
fof(f1905,plain,
( ~ is_a_theorem(implies(or(sK38,or(sK39,sK40)),or(sK39,or(sK38,sK40))))
| spl55_65 ),
inference(subsumption_resolution,[],[f223,f1796]) ).
fof(f1796,plain,
( ~ r4
| spl55_65 ),
inference(avatar_component_clause,[],[f1794]) ).
fof(f1800,plain,
( ~ spl55_65
| spl55_66 ),
inference(avatar_split_clause,[],[f222,f1798,f1794]) ).
fof(f1798,plain,
( spl55_66
<=> ! [X4,X5,X3] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_66])]) ).
fof(f1735,plain,
( ~ spl55_64
| spl55_63 ),
inference(avatar_split_clause,[],[f1730,f1578,f1732]) ).
fof(f1732,plain,
( spl55_64
<=> is_a_theorem(implies(implies(sK35,sK36),implies(implies(sK36,sK37),implies(sK35,sK37)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_64])]) ).
fof(f1578,plain,
( spl55_63
<=> cn1 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_63])]) ).
fof(f1730,plain,
( ~ is_a_theorem(implies(implies(sK35,sK36),implies(implies(sK36,sK37),implies(sK35,sK37))))
| spl55_63 ),
inference(subsumption_resolution,[],[f221,f1580]) ).
fof(f1580,plain,
( ~ cn1
| spl55_63 ),
inference(avatar_component_clause,[],[f1578]) ).
fof(f1581,plain,
( ~ spl55_63
| spl55_61 ),
inference(avatar_split_clause,[],[f220,f1260,f1578]) ).
fof(f1260,plain,
( spl55_61
<=> ! [X4,X5,X3] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_61])]) ).
fof(f1416,plain,
( ~ spl55_62
| spl55_60 ),
inference(avatar_split_clause,[],[f1394,f1256,f1413]) ).
fof(f1413,plain,
( spl55_62
<=> is_a_theorem(implies(implies(sK32,sK33),implies(implies(sK33,sK34),implies(sK32,sK34)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_62])]) ).
fof(f1256,plain,
( spl55_60
<=> implies_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_60])]) ).
fof(f1394,plain,
( ~ is_a_theorem(implies(implies(sK32,sK33),implies(implies(sK33,sK34),implies(sK32,sK34))))
| spl55_60 ),
inference(subsumption_resolution,[],[f219,f1258]) ).
fof(f1258,plain,
( ~ implies_3
| spl55_60 ),
inference(avatar_component_clause,[],[f1256]) ).
fof(f1262,plain,
( ~ spl55_60
| spl55_61 ),
inference(avatar_split_clause,[],[f218,f1260,f1256]) ).
fof(f1178,plain,
( ~ spl55_59
| spl55_57 ),
inference(avatar_split_clause,[],[f1169,f1119,f1175]) ).
fof(f1175,plain,
( spl55_59
<=> is_a_theorem(implies(implies(sK30,sK31),implies(or(sK29,sK30),or(sK29,sK31)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_59])]) ).
fof(f1119,plain,
( spl55_57
<=> r5 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_57])]) ).
fof(f1169,plain,
( ~ is_a_theorem(implies(implies(sK30,sK31),implies(or(sK29,sK30),or(sK29,sK31))))
| spl55_57 ),
inference(subsumption_resolution,[],[f217,f1121]) ).
fof(f1121,plain,
( ~ r5
| spl55_57 ),
inference(avatar_component_clause,[],[f1119]) ).
fof(f1125,plain,
( ~ spl55_57
| spl55_58 ),
inference(avatar_split_clause,[],[f216,f1123,f1119]) ).
fof(f1123,plain,
( spl55_58
<=> ! [X4,X5,X3] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_58])]) ).
fof(f949,plain,
( ~ spl55_56
| spl55_54 ),
inference(avatar_split_clause,[],[f886,f816,f946]) ).
fof(f946,plain,
( spl55_56
<=> is_a_theorem(implies(implies(sK27,sK28),implies(implies(sK28,sK27),equiv(sK27,sK28)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_56])]) ).
fof(f816,plain,
( spl55_54
<=> equivalence_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_54])]) ).
fof(f886,plain,
( ~ is_a_theorem(implies(implies(sK27,sK28),implies(implies(sK28,sK27),equiv(sK27,sK28))))
| spl55_54 ),
inference(subsumption_resolution,[],[f215,f818]) ).
fof(f818,plain,
( ~ equivalence_3
| spl55_54 ),
inference(avatar_component_clause,[],[f816]) ).
fof(f822,plain,
( ~ spl55_54
| spl55_55 ),
inference(avatar_split_clause,[],[f214,f820,f816]) ).
fof(f820,plain,
( spl55_55
<=> ! [X2,X3] : is_a_theorem(implies(implies(X2,X3),implies(implies(X3,X2),equiv(X2,X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_55])]) ).
fof(f799,plain,
( ~ spl55_41
| spl55_42 ),
inference(avatar_contradiction_clause,[],[f795]) ).
fof(f795,plain,
( $false
| ~ spl55_41
| spl55_42 ),
inference(resolution,[],[f468,f474]) ).
fof(f474,plain,
( ~ is_a_theorem(implies(equiv(sK19,sK20),implies(sK19,sK20)))
| spl55_42 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f472,plain,
( spl55_42
<=> is_a_theorem(implies(equiv(sK19,sK20),implies(sK19,sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_42])]) ).
fof(f468,plain,
( ! [X2,X3] : is_a_theorem(implies(equiv(X2,X3),implies(X2,X3)))
| ~ spl55_41 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f467,plain,
( spl55_41
<=> ! [X2,X3] : is_a_theorem(implies(equiv(X2,X3),implies(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_41])]) ).
fof(f794,plain,
spl55_41,
inference(avatar_split_clause,[],[f783,f467]) ).
fof(f783,plain,
! [X2,X3] : is_a_theorem(implies(equiv(X2,X3),implies(X2,X3))),
inference(superposition,[],[f251,f245]) ).
fof(f721,plain,
( ~ spl55_53
| spl55_51 ),
inference(avatar_split_clause,[],[f716,f661,f718]) ).
fof(f718,plain,
( spl55_53
<=> is_a_theorem(implies(implies(sK25,implies(sK25,sK26)),implies(sK25,sK26))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_53])]) ).
fof(f661,plain,
( spl55_51
<=> implies_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_51])]) ).
fof(f716,plain,
( ~ is_a_theorem(implies(implies(sK25,implies(sK25,sK26)),implies(sK25,sK26)))
| spl55_51 ),
inference(subsumption_resolution,[],[f213,f663]) ).
fof(f663,plain,
( ~ implies_2
| spl55_51 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f667,plain,
( ~ spl55_51
| spl55_52 ),
inference(avatar_split_clause,[],[f212,f665,f661]) ).
fof(f665,plain,
( spl55_52
<=> ! [X2,X3] : is_a_theorem(implies(implies(X2,implies(X2,X3)),implies(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_52])]) ).
fof(f608,plain,
( ~ spl55_50
| spl55_48 ),
inference(avatar_split_clause,[],[f596,f537,f605]) ).
fof(f605,plain,
( spl55_50
<=> is_a_theorem(implies(or(sK24,not(sK23)),implies(sK23,sK24))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_50])]) ).
fof(f537,plain,
( spl55_48
<=> modus_tollens ),
introduced(avatar_definition,[new_symbols(naming,[spl55_48])]) ).
fof(f596,plain,
( ~ is_a_theorem(implies(or(sK24,not(sK23)),implies(sK23,sK24)))
| spl55_48 ),
inference(forward_demodulation,[],[f595,f503]) ).
fof(f595,plain,
( ~ is_a_theorem(implies(implies(not(sK24),not(sK23)),implies(sK23,sK24)))
| spl55_48 ),
inference(subsumption_resolution,[],[f211,f539]) ).
fof(f539,plain,
( ~ modus_tollens
| spl55_48 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f543,plain,
( ~ spl55_48
| spl55_49 ),
inference(avatar_split_clause,[],[f529,f541,f537]) ).
fof(f541,plain,
( spl55_49
<=> ! [X2,X3] : is_a_theorem(implies(or(X3,not(X2)),implies(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_49])]) ).
fof(f529,plain,
! [X2,X3] :
( is_a_theorem(implies(or(X3,not(X2)),implies(X2,X3)))
| ~ modus_tollens ),
inference(forward_demodulation,[],[f210,f503]) ).
fof(f528,plain,
( ~ spl55_47
| spl55_33 ),
inference(avatar_split_clause,[],[f515,f427,f525]) ).
fof(f525,plain,
( spl55_47
<=> is_a_theorem(implies(sK13,or(sK13,sK14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_47])]) ).
fof(f427,plain,
( spl55_33
<=> is_a_theorem(implies(sK13,implies(not(sK13),sK14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_33])]) ).
fof(f515,plain,
( ~ is_a_theorem(implies(sK13,or(sK13,sK14)))
| spl55_33 ),
inference(superposition,[],[f429,f503]) ).
fof(f429,plain,
( ~ is_a_theorem(implies(sK13,implies(not(sK13),sK14)))
| spl55_33 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f523,plain,
( ~ spl55_46
| spl55_30 ),
inference(avatar_split_clause,[],[f514,f413,f520]) ).
fof(f413,plain,
( spl55_30
<=> is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_30])]) ).
fof(f514,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| spl55_30 ),
inference(superposition,[],[f415,f503]) ).
fof(f415,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| spl55_30 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f489,plain,
( ~ spl55_45
| spl55_43 ),
inference(avatar_split_clause,[],[f484,f477,f486]) ).
fof(f486,plain,
( spl55_45
<=> is_a_theorem(implies(or(sK21,sK22),or(sK22,sK21))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_45])]) ).
fof(f477,plain,
( spl55_43
<=> r3 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_43])]) ).
fof(f484,plain,
( ~ is_a_theorem(implies(or(sK21,sK22),or(sK22,sK21)))
| spl55_43 ),
inference(subsumption_resolution,[],[f209,f479]) ).
fof(f479,plain,
( ~ r3
| spl55_43 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f483,plain,
( ~ spl55_43
| spl55_44 ),
inference(avatar_split_clause,[],[f208,f481,f477]) ).
fof(f481,plain,
( spl55_44
<=> ! [X2,X3] : is_a_theorem(implies(or(X2,X3),or(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_44])]) ).
fof(f475,plain,
( ~ spl55_42
| spl55_40 ),
inference(avatar_split_clause,[],[f470,f463,f472]) ).
fof(f463,plain,
( spl55_40
<=> equivalence_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_40])]) ).
fof(f470,plain,
( ~ is_a_theorem(implies(equiv(sK19,sK20),implies(sK19,sK20)))
| spl55_40 ),
inference(subsumption_resolution,[],[f207,f465]) ).
fof(f465,plain,
( ~ equivalence_1
| spl55_40 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f469,plain,
( ~ spl55_40
| spl55_41 ),
inference(avatar_split_clause,[],[f206,f467,f463]) ).
fof(f461,plain,
( ~ spl55_39
| spl55_37 ),
inference(avatar_split_clause,[],[f456,f449,f458]) ).
fof(f458,plain,
( spl55_39
<=> is_a_theorem(implies(equiv(sK17,sK18),implies(sK18,sK17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_39])]) ).
fof(f449,plain,
( spl55_37
<=> equivalence_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_37])]) ).
fof(f456,plain,
( ~ is_a_theorem(implies(equiv(sK17,sK18),implies(sK18,sK17)))
| spl55_37 ),
inference(subsumption_resolution,[],[f205,f451]) ).
fof(f451,plain,
( ~ equivalence_2
| spl55_37 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f455,plain,
( ~ spl55_37
| spl55_38 ),
inference(avatar_split_clause,[],[f204,f453,f449]) ).
fof(f453,plain,
( spl55_38
<=> ! [X2,X3] : is_a_theorem(implies(equiv(X2,X3),implies(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_38])]) ).
fof(f447,plain,
( ~ spl55_36
| spl55_34 ),
inference(avatar_split_clause,[],[f442,f435,f444]) ).
fof(f444,plain,
( spl55_36
<=> is_a_theorem(implies(sK15,implies(sK16,and(sK15,sK16)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_36])]) ).
fof(f435,plain,
( spl55_34
<=> and_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_34])]) ).
fof(f442,plain,
( ~ is_a_theorem(implies(sK15,implies(sK16,and(sK15,sK16))))
| spl55_34 ),
inference(subsumption_resolution,[],[f203,f437]) ).
fof(f437,plain,
( ~ and_3
| spl55_34 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f441,plain,
( ~ spl55_34
| spl55_35 ),
inference(avatar_split_clause,[],[f202,f439,f435]) ).
fof(f439,plain,
( spl55_35
<=> ! [X2,X3] : is_a_theorem(implies(X2,implies(X3,and(X2,X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_35])]) ).
fof(f430,plain,
( ~ spl55_33
| spl55_31 ),
inference(avatar_split_clause,[],[f425,f418,f427]) ).
fof(f418,plain,
( spl55_31
<=> cn2 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_31])]) ).
fof(f425,plain,
( ~ is_a_theorem(implies(sK13,implies(not(sK13),sK14)))
| spl55_31 ),
inference(subsumption_resolution,[],[f201,f420]) ).
fof(f420,plain,
( ~ cn2
| spl55_31 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f424,plain,
( ~ spl55_31
| spl55_32 ),
inference(avatar_split_clause,[],[f200,f422,f418]) ).
fof(f422,plain,
( spl55_32
<=> ! [X2,X3] : is_a_theorem(implies(X2,implies(not(X2),X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_32])]) ).
fof(f416,plain,
( ~ spl55_30
| spl55_28 ),
inference(avatar_split_clause,[],[f411,f404,f413]) ).
fof(f404,plain,
( spl55_28
<=> cn3 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_28])]) ).
fof(f411,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| spl55_28 ),
inference(subsumption_resolution,[],[f187,f406]) ).
fof(f406,plain,
( ~ cn3
| spl55_28 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f410,plain,
( ~ spl55_28
| spl55_29 ),
inference(avatar_split_clause,[],[f186,f408,f404]) ).
fof(f408,plain,
( spl55_29
<=> ! [X1] : is_a_theorem(implies(implies(not(X1),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_29])]) ).
fof(f402,plain,
( ~ spl55_27
| spl55_25 ),
inference(avatar_split_clause,[],[f397,f390,f399]) ).
fof(f399,plain,
( spl55_27
<=> is_a_theorem(implies(and(sK11,sK12),sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_27])]) ).
fof(f390,plain,
( spl55_25
<=> and_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_25])]) ).
fof(f397,plain,
( ~ is_a_theorem(implies(and(sK11,sK12),sK12))
| spl55_25 ),
inference(subsumption_resolution,[],[f199,f392]) ).
fof(f392,plain,
( ~ and_2
| spl55_25 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f396,plain,
( ~ spl55_25
| spl55_26 ),
inference(avatar_split_clause,[],[f198,f394,f390]) ).
fof(f394,plain,
( spl55_26
<=> ! [X2,X3] : is_a_theorem(implies(and(X2,X3),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_26])]) ).
fof(f388,plain,
spl55_24,
inference(avatar_split_clause,[],[f383,f385]) ).
fof(f385,plain,
( spl55_24
<=> and_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_24])]) ).
fof(f383,plain,
and_1,
inference(subsumption_resolution,[],[f197,f251]) ).
fof(f382,plain,
( ~ spl55_23
| spl55_21 ),
inference(avatar_split_clause,[],[f377,f370,f379]) ).
fof(f379,plain,
( spl55_23
<=> is_a_theorem(implies(sK7,implies(sK8,sK7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_23])]) ).
fof(f370,plain,
( spl55_21
<=> implies_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_21])]) ).
fof(f377,plain,
( ~ is_a_theorem(implies(sK7,implies(sK8,sK7)))
| spl55_21 ),
inference(subsumption_resolution,[],[f195,f372]) ).
fof(f372,plain,
( ~ implies_1
| spl55_21 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f376,plain,
( ~ spl55_21
| spl55_22 ),
inference(avatar_split_clause,[],[f194,f374,f370]) ).
fof(f374,plain,
( spl55_22
<=> ! [X2,X3] : is_a_theorem(implies(X2,implies(X3,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_22])]) ).
fof(f368,plain,
( ~ spl55_20
| spl55_19 ),
inference(avatar_split_clause,[],[f363,f359,f365]) ).
fof(f365,plain,
( spl55_20
<=> is_a_theorem(implies(sK6,or(sK5,sK6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_20])]) ).
fof(f359,plain,
( spl55_19
<=> r2 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_19])]) ).
fof(f363,plain,
( ~ is_a_theorem(implies(sK6,or(sK5,sK6)))
| spl55_19 ),
inference(subsumption_resolution,[],[f193,f361]) ).
fof(f361,plain,
( ~ r2
| spl55_19 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f362,plain,
( ~ spl55_19
| spl55_14 ),
inference(avatar_split_clause,[],[f192,f335,f359]) ).
fof(f335,plain,
( spl55_14
<=> ! [X2,X3] : is_a_theorem(implies(X3,or(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_14])]) ).
fof(f357,plain,
( ~ spl55_18
| spl55_16 ),
inference(avatar_split_clause,[],[f352,f345,f354]) ).
fof(f354,plain,
( spl55_18
<=> is_a_theorem(implies(sK3,or(sK3,sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_18])]) ).
fof(f345,plain,
( spl55_16
<=> or_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_16])]) ).
fof(f352,plain,
( ~ is_a_theorem(implies(sK3,or(sK3,sK4)))
| spl55_16 ),
inference(subsumption_resolution,[],[f191,f347]) ).
fof(f347,plain,
( ~ or_1
| spl55_16 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f351,plain,
( ~ spl55_16
| spl55_17 ),
inference(avatar_split_clause,[],[f190,f349,f345]) ).
fof(f349,plain,
( spl55_17
<=> ! [X2,X3] : is_a_theorem(implies(X2,or(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_17])]) ).
fof(f343,plain,
( ~ spl55_15
| spl55_13 ),
inference(avatar_split_clause,[],[f338,f331,f340]) ).
fof(f340,plain,
( spl55_15
<=> is_a_theorem(implies(sK2,or(sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl55_15])]) ).
fof(f331,plain,
( spl55_13
<=> or_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_13])]) ).
fof(f338,plain,
( ~ is_a_theorem(implies(sK2,or(sK1,sK2)))
| spl55_13 ),
inference(subsumption_resolution,[],[f189,f333]) ).
fof(f333,plain,
( ~ or_2
| spl55_13 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f337,plain,
( ~ spl55_13
| spl55_14 ),
inference(avatar_split_clause,[],[f188,f335,f331]) ).
fof(f329,plain,
~ spl55_12,
inference(avatar_split_clause,[],[f246,f326]) ).
fof(f324,plain,
spl55_5,
inference(avatar_split_clause,[],[f259,f282]) ).
fof(f282,plain,
( spl55_5
<=> kn3 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_5])]) ).
fof(f323,plain,
spl55_4,
inference(avatar_split_clause,[],[f257,f277]) ).
fof(f277,plain,
( spl55_4
<=> modus_ponens ),
introduced(avatar_definition,[new_symbols(naming,[spl55_4])]) ).
fof(f322,plain,
spl55_4,
inference(avatar_split_clause,[],[f256,f277]) ).
fof(f321,plain,
spl55_4,
inference(avatar_split_clause,[],[f255,f277]) ).
fof(f320,plain,
spl55_3,
inference(avatar_split_clause,[],[f253,f272]) ).
fof(f272,plain,
( spl55_3
<=> substitution_of_equivalents ),
introduced(avatar_definition,[new_symbols(naming,[spl55_3])]) ).
fof(f319,plain,
spl55_3,
inference(avatar_split_clause,[],[f252,f272]) ).
fof(f318,plain,
spl55_2,
inference(avatar_split_clause,[],[f250,f267]) ).
fof(f267,plain,
( spl55_2
<=> kn2 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_2])]) ).
fof(f317,plain,
spl55_6,
inference(avatar_split_clause,[],[f248,f287]) ).
fof(f287,plain,
( spl55_6
<=> kn1 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_6])]) ).
fof(f316,plain,
spl55_11,
inference(avatar_split_clause,[],[f180,f312]) ).
fof(f312,plain,
( spl55_11
<=> op_equiv ),
introduced(avatar_definition,[new_symbols(naming,[spl55_11])]) ).
fof(f315,plain,
spl55_11,
inference(avatar_split_clause,[],[f179,f312]) ).
fof(f310,plain,
spl55_10,
inference(avatar_split_clause,[],[f178,f307]) ).
fof(f307,plain,
( spl55_10
<=> op_implies_or ),
introduced(avatar_definition,[new_symbols(naming,[spl55_10])]) ).
fof(f305,plain,
spl55_9,
inference(avatar_split_clause,[],[f177,f302]) ).
fof(f302,plain,
( spl55_9
<=> op_implies_and ),
introduced(avatar_definition,[new_symbols(naming,[spl55_9])]) ).
fof(f300,plain,
spl55_8,
inference(avatar_split_clause,[],[f176,f297]) ).
fof(f297,plain,
( spl55_8
<=> op_or ),
introduced(avatar_definition,[new_symbols(naming,[spl55_8])]) ).
fof(f295,plain,
spl55_7,
inference(avatar_split_clause,[],[f175,f292]) ).
fof(f292,plain,
( spl55_7
<=> op_and ),
introduced(avatar_definition,[new_symbols(naming,[spl55_7])]) ).
fof(f290,plain,
spl55_6,
inference(avatar_split_clause,[],[f174,f287]) ).
fof(f285,plain,
spl55_5,
inference(avatar_split_clause,[],[f173,f282]) ).
fof(f280,plain,
spl55_4,
inference(avatar_split_clause,[],[f172,f277]) ).
fof(f275,plain,
spl55_3,
inference(avatar_split_clause,[],[f171,f272]) ).
fof(f270,plain,
spl55_2,
inference(avatar_split_clause,[],[f170,f267]) ).
fof(f265,plain,
~ spl55_1,
inference(avatar_split_clause,[],[f169,f262]) ).
fof(f262,plain,
( spl55_1
<=> r1 ),
introduced(avatar_definition,[new_symbols(naming,[spl55_1])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.17 % Problem : LCL518+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.18 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.38 % Computer : n014.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Wed Aug 30 14:44:14 EDT 2023
% 0.15/0.38 % CPUTime :
% 0.19/0.42 % (28974)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42 % (29000)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.19/0.42 % (28978)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.19/0.42 % (28979)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.19/0.42 % (28985)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.19/0.42 % (28989)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.19/0.42 % (28991)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.19/0.42 % (28976)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.19/0.43 TRYING [1]
% 0.19/0.43 TRYING [2]
% 0.19/0.44 TRYING [1]
% 0.19/0.44 TRYING [2]
% 0.19/0.45 TRYING [3]
% 0.19/0.47 TRYING [3]
% 0.19/0.49 TRYING [4]
% 0.19/0.56 TRYING [4]
% 0.19/0.59 % (28979)First to succeed.
% 0.19/0.60 % (28979)Refutation found. Thanks to Tanya!
% 0.19/0.60 % SZS status Theorem for Vampire---4
% 0.19/0.60 % SZS output start Proof for Vampire---4
% See solution above
% 0.19/0.60 % (28979)------------------------------
% 0.19/0.60 % (28979)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.19/0.60 % (28979)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.19/0.60 % (28979)Termination reason: Refutation
% 0.19/0.60
% 0.19/0.60 % (28979)Memory used [KB]: 7419
% 0.19/0.60 % (28979)Time elapsed: 0.176 s
% 0.19/0.60 % (28979)------------------------------
% 0.19/0.60 % (28979)------------------------------
% 0.19/0.60 % (28974)Success in time 0.222 s
% 0.19/0.61 % Vampire---4.8 exiting
%------------------------------------------------------------------------------