TSTP Solution File: LCL528+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL528+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 : n007.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 : Thu Aug 31 08:24:27 EDT 2023
% Result : Theorem 20.49s 3.26s
% Output : Refutation 20.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 33
% Syntax : Number of formulae : 195 ( 115 unt; 0 def)
% Number of atoms : 298 ( 64 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 176 ( 73 ~; 65 |; 2 &)
% ( 13 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 290 (; 286 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f172866,plain,
$false,
inference(subsumption_resolution,[],[f171894,f12479]) ).
fof(f12479,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(superposition,[],[f217,f11530]) ).
fof(f11530,plain,
! [X14,X13] : implies(X13,X14) = implies(X13,implies(X13,X14)),
inference(subsumption_resolution,[],[f11460,f217]) ).
fof(f11460,plain,
! [X14,X13] :
( implies(X13,X14) = implies(X13,implies(X13,X14))
| ~ is_a_theorem(implies(implies(X13,X14),implies(X13,implies(X13,X14)))) ),
inference(resolution,[],[f2822,f304]) ).
fof(f304,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(subsumption_resolution,[],[f206,f173]) ).
fof(f173,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_implies_2) ).
fof(f206,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f120]) ).
fof(f120,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[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.PL9YtiXPrR/Vampire---4.8_26882',implies_2) ).
fof(f2822,plain,
! [X6,X7] :
( ~ is_a_theorem(implies(X7,X6))
| X6 = X7
| ~ is_a_theorem(implies(X6,X7)) ),
inference(resolution,[],[f473,f478]) ).
fof(f478,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(subsumption_resolution,[],[f208,f164]) ).
fof(f164,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_equivalence_3) ).
fof(f208,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f110]) ).
fof(f110,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[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.PL9YtiXPrR/Vampire---4.8_26882',equivalence_3) ).
fof(f473,plain,
! [X10,X11,X8,X9] :
( ~ is_a_theorem(implies(X11,implies(X8,equiv(X9,X10))))
| X9 = X10
| ~ is_a_theorem(X8)
| ~ is_a_theorem(X11) ),
inference(resolution,[],[f233,f232]) ).
fof(f232,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(subsumption_resolution,[],[f210,f176]) ).
fof(f176,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_modus_ponens) ).
fof(f210,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f124]) ).
fof(f124,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[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.PL9YtiXPrR/Vampire---4.8_26882',modus_ponens) ).
fof(f233,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,equiv(X1,X2)))
| ~ is_a_theorem(X0)
| X1 = X2 ),
inference(resolution,[],[f232,f223]) ).
fof(f223,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(subsumption_resolution,[],[f209,f163]) ).
fof(f163,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',substitution_of_equivalents) ).
fof(f209,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f123]) ).
fof(f123,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',substitution_of_equivalents) ).
fof(f217,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(subsumption_resolution,[],[f199,f174]) ).
fof(f174,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_implies_1) ).
fof(f199,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f121]) ).
fof(f121,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',implies_1) ).
fof(f171894,plain,
~ is_a_theorem(implies(and(sK0,sK1),and(sK0,sK1))),
inference(backward_demodulation,[],[f228,f171547]) ).
fof(f171547,plain,
! [X2,X3] : and(X3,X2) = and(X2,X3),
inference(superposition,[],[f154006,f118504]) ).
fof(f118504,plain,
! [X698,X699] : and(X698,X699) = not(implies(X698,not(X699))),
inference(superposition,[],[f87505,f89089]) ).
fof(f89089,plain,
! [X8,X7] : implies(X8,not(X7)) = not(and(X8,X7)),
inference(forward_demodulation,[],[f88785,f12774]) ).
fof(f12774,plain,
! [X8] : and(X8,X8) = X8,
inference(subsumption_resolution,[],[f12767,f218]) ).
fof(f218,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(subsumption_resolution,[],[f200,f171]) ).
fof(f171,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_and_1) ).
fof(f200,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f118]) ).
fof(f118,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',and_1) ).
fof(f12767,plain,
! [X8] :
( and(X8,X8) = X8
| ~ is_a_theorem(implies(and(X8,X8),X8)) ),
inference(resolution,[],[f12481,f2822]) ).
fof(f12481,plain,
! [X4] : is_a_theorem(implies(X4,and(X4,X4))),
inference(superposition,[],[f229,f11530]) ).
fof(f229,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(subsumption_resolution,[],[f202,f169]) ).
fof(f169,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_and_3) ).
fof(f202,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f116]) ).
fof(f116,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',and_3) ).
fof(f88785,plain,
! [X8,X7] : implies(X8,and(not(X7),not(X7))) = not(and(X8,X7)),
inference(superposition,[],[f241,f87646]) ).
fof(f87646,plain,
! [X33] : implies(not(X33),X33) = X33,
inference(backward_demodulation,[],[f12801,f87505]) ).
fof(f12801,plain,
! [X33] : implies(not(X33),X33) = not(not(X33)),
inference(superposition,[],[f239,f12774]) ).
fof(f239,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(subsumption_resolution,[],[f188,f178]) ).
fof(f178,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_op_implies_and) ).
fof(f188,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,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.PL9YtiXPrR/Vampire---4.8_26882',op_implies_and) ).
fof(f241,plain,
! [X2,X3,X4] : implies(X4,and(X2,not(X3))) = not(and(X4,implies(X2,X3))),
inference(superposition,[],[f239,f239]) ).
fof(f87505,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f87444,f13598]) ).
fof(f13598,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| not(not(X0)) = X0 ),
inference(forward_demodulation,[],[f13570,f256]) ).
fof(f256,plain,
! [X2,X3] : implies(not(X2),X3) = or(X2,X3),
inference(superposition,[],[f249,f239]) ).
fof(f249,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(subsumption_resolution,[],[f191,f181]) ).
fof(f181,plain,
op_or,
inference(cnf_transformation,[],[f83]) ).
fof(f83,axiom,
op_or,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',s1_0_op_or) ).
fof(f191,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,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.PL9YtiXPrR/Vampire---4.8_26882',op_or) ).
fof(f13570,plain,
! [X0] :
( not(not(X0)) = X0
| ~ is_a_theorem(implies(not(not(X0)),X0)) ),
inference(resolution,[],[f13329,f2822]) ).
fof(f13329,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(superposition,[],[f215,f13016]) ).
fof(f13016,plain,
! [X285] : or(X285,X285) = not(not(X285)),
inference(superposition,[],[f249,f12774]) ).
fof(f215,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(subsumption_resolution,[],[f197,f168]) ).
fof(f168,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_or_1) ).
fof(f197,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',or_1) ).
fof(f87444,plain,
! [X92] : is_a_theorem(or(not(X92),X92)),
inference(forward_demodulation,[],[f87443,f11549]) ).
fof(f11549,plain,
! [X120,X121] : or(X120,X121) = or(X120,or(X120,X121)),
inference(subsumption_resolution,[],[f11501,f216]) ).
fof(f216,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(subsumption_resolution,[],[f198,f177]) ).
fof(f177,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_or_2) ).
fof(f198,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f114]) ).
fof(f114,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',or_2) ).
fof(f11501,plain,
! [X120,X121] :
( or(X120,X121) = or(X120,or(X120,X121))
| ~ is_a_theorem(implies(or(X120,X121),or(X120,or(X120,X121)))) ),
inference(resolution,[],[f2822,f337]) ).
fof(f337,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
inference(forward_demodulation,[],[f335,f256]) ).
fof(f335,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,implies(not(X0),X1)),implies(not(X0),X1))),
inference(superposition,[],[f304,f256]) ).
fof(f87443,plain,
! [X92] : is_a_theorem(or(not(X92),or(not(X92),X92))),
inference(forward_demodulation,[],[f87442,f256]) ).
fof(f87442,plain,
! [X92] : is_a_theorem(or(not(X92),implies(not(not(X92)),X92))),
inference(forward_demodulation,[],[f87290,f239]) ).
fof(f87290,plain,
! [X92] : is_a_theorem(or(not(X92),not(and(not(not(X92)),not(X92))))),
inference(superposition,[],[f1153,f85776]) ).
fof(f85776,plain,
! [X17] : not(X17) = or(not(X17),not(X17)),
inference(superposition,[],[f17202,f85636]) ).
fof(f85636,plain,
! [X0] : not(X0) = not(not(not(X0))),
inference(resolution,[],[f85345,f13598]) ).
fof(f85345,plain,
! [X33] : is_a_theorem(or(not(not(X33)),not(X33))),
inference(forward_demodulation,[],[f85344,f256]) ).
fof(f85344,plain,
! [X33] : is_a_theorem(implies(not(not(not(X33))),not(X33))),
inference(forward_demodulation,[],[f85343,f239]) ).
fof(f85343,plain,
! [X33] : is_a_theorem(not(and(not(not(not(X33))),not(not(X33))))),
inference(forward_demodulation,[],[f85342,f13016]) ).
fof(f85342,plain,
! [X33] : is_a_theorem(not(and(not(not(not(X33))),or(X33,X33)))),
inference(forward_demodulation,[],[f85272,f255]) ).
fof(f255,plain,
! [X6,X7,X5] : or(X7,and(not(X5),not(X6))) = not(and(not(X7),or(X5,X6))),
inference(superposition,[],[f249,f249]) ).
fof(f85272,plain,
! [X33] : is_a_theorem(or(not(not(X33)),and(not(X33),not(X33)))),
inference(superposition,[],[f85204,f12801]) ).
fof(f85204,plain,
! [X99,X100] : is_a_theorem(or(implies(X99,X100),and(X99,not(X100)))),
inference(forward_demodulation,[],[f85203,f11549]) ).
fof(f85203,plain,
! [X99,X100] : is_a_theorem(or(implies(X99,X100),or(implies(X99,X100),and(X99,not(X100))))),
inference(forward_demodulation,[],[f85202,f256]) ).
fof(f85202,plain,
! [X99,X100] : is_a_theorem(or(implies(X99,X100),implies(not(implies(X99,X100)),and(X99,not(X100))))),
inference(forward_demodulation,[],[f85099,f241]) ).
fof(f85099,plain,
! [X99,X100] : is_a_theorem(or(implies(X99,X100),not(and(not(implies(X99,X100)),implies(X99,X100))))),
inference(superposition,[],[f1153,f80398]) ).
fof(f80398,plain,
! [X213,X214] : implies(X213,X214) = or(implies(X213,X214),implies(X213,X214)),
inference(superposition,[],[f11549,f80085]) ).
fof(f80085,plain,
! [X0,X1] : implies(X0,X1) = or(implies(X0,X1),not(X0)),
inference(resolution,[],[f12494,f11454]) ).
fof(f11454,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(or(X0,X1),X0))
| or(X0,X1) = X0 ),
inference(resolution,[],[f2822,f215]) ).
fof(f12494,plain,
! [X26,X25] : is_a_theorem(implies(or(implies(X25,X26),not(X25)),implies(X25,X26))),
inference(superposition,[],[f280,f11530]) ).
fof(f280,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(forward_demodulation,[],[f279,f256]) ).
fof(f279,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(subsumption_resolution,[],[f205,f175]) ).
fof(f175,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_modus_tollens) ).
fof(f205,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f122]) ).
fof(f122,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[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.PL9YtiXPrR/Vampire---4.8_26882',modus_tollens) ).
fof(f17202,plain,
! [X3] : not(not(X3)) = or(X3,not(not(X3))),
inference(superposition,[],[f11549,f13016]) ).
fof(f1153,plain,
! [X2,X3] : is_a_theorem(or(X3,not(and(not(X2),or(X3,X2))))),
inference(forward_demodulation,[],[f1115,f256]) ).
fof(f1115,plain,
! [X2,X3] : is_a_theorem(implies(not(X3),not(and(not(X2),or(X3,X2))))),
inference(superposition,[],[f229,f259]) ).
fof(f259,plain,
! [X6,X7,X5] : implies(X7,and(not(X5),not(X6))) = not(and(X7,or(X5,X6))),
inference(superposition,[],[f239,f249]) ).
fof(f154006,plain,
! [X176,X177] : and(X176,X177) = not(implies(X177,not(X176))),
inference(superposition,[],[f87505,f135534]) ).
fof(f135534,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X0,X1)),
inference(superposition,[],[f121565,f87505]) ).
fof(f121565,plain,
! [X14,X15] : implies(X14,X15) = not(and(not(X15),X14)),
inference(superposition,[],[f121208,f87646]) ).
fof(f121208,plain,
! [X2,X3,X4] : not(and(not(X4),implies(X2,X3))) = implies(implies(X2,X3),X4),
inference(forward_demodulation,[],[f120817,f101077]) ).
fof(f101077,plain,
! [X10,X9] : implies(X9,X10) = or(X10,not(X9)),
inference(superposition,[],[f87771,f88600]) ).
fof(f88600,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(subsumption_resolution,[],[f88539,f87643]) ).
fof(f87643,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,X0),or(X0,X1))),
inference(backward_demodulation,[],[f294,f87505]) ).
fof(f294,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(not(X0))),or(X0,X1))),
inference(superposition,[],[f280,f256]) ).
fof(f88539,plain,
! [X0,X1] :
( or(X0,X1) = or(X1,X0)
| ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[],[f87643,f2822]) ).
fof(f87771,plain,
! [X29,X30] : implies(X29,X30) = or(not(X29),X30),
inference(superposition,[],[f256,f87505]) ).
fof(f120817,plain,
! [X2,X3,X4] : not(and(not(X4),implies(X2,X3))) = or(X4,not(implies(X2,X3))),
inference(backward_demodulation,[],[f254,f118948]) ).
fof(f118948,plain,
! [X14,X15] : and(X14,not(X15)) = not(implies(X14,X15)),
inference(forward_demodulation,[],[f118947,f85718]) ).
fof(f85718,plain,
! [X0] : not(X0) = implies(X0,not(X0)),
inference(backward_demodulation,[],[f49905,f85636]) ).
fof(f49905,plain,
! [X0] : not(not(not(X0))) = implies(X0,not(X0)),
inference(subsumption_resolution,[],[f49904,f13522]) ).
fof(f13522,plain,
! [X80] : is_a_theorem(or(not(not(X80)),implies(X80,not(X80)))),
inference(forward_demodulation,[],[f13379,f256]) ).
fof(f13379,plain,
! [X80] : is_a_theorem(implies(not(not(not(X80))),implies(X80,not(X80)))),
inference(superposition,[],[f280,f13016]) ).
fof(f49904,plain,
! [X0] :
( ~ is_a_theorem(or(not(not(X0)),implies(X0,not(X0))))
| not(not(not(X0))) = implies(X0,not(X0)) ),
inference(forward_demodulation,[],[f49858,f256]) ).
fof(f49858,plain,
! [X0] :
( not(not(not(X0))) = implies(X0,not(X0))
| ~ is_a_theorem(implies(not(not(not(X0))),implies(X0,not(X0)))) ),
inference(resolution,[],[f18718,f2822]) ).
fof(f18718,plain,
! [X3] : is_a_theorem(implies(implies(X3,not(X3)),not(not(not(X3))))),
inference(superposition,[],[f13476,f13016]) ).
fof(f13476,plain,
! [X21,X22] : is_a_theorem(implies(implies(X21,X22),or(not(X21),X22))),
inference(forward_demodulation,[],[f13475,f256]) ).
fof(f13475,plain,
! [X21,X22] : is_a_theorem(implies(implies(X21,X22),implies(not(not(X21)),X22))),
inference(forward_demodulation,[],[f13346,f11530]) ).
fof(f13346,plain,
! [X21,X22] : is_a_theorem(implies(implies(X21,X22),implies(implies(X21,X22),implies(not(not(X21)),X22)))),
inference(superposition,[],[f568,f13016]) ).
fof(f568,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))),
inference(subsumption_resolution,[],[f212,f167]) ).
fof(f167,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',hilbert_or_3) ).
fof(f212,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,plain,
( or_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(unused_predicate_definition_removal,[],[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.PL9YtiXPrR/Vampire---4.8_26882',or_3) ).
fof(f118947,plain,
! [X14,X15] : and(X14,not(X15)) = implies(implies(X14,X15),not(implies(X14,X15))),
inference(forward_demodulation,[],[f118717,f239]) ).
fof(f118717,plain,
! [X14,X15] : and(X14,not(X15)) = implies(not(and(X14,not(X15))),not(implies(X14,X15))),
inference(superposition,[],[f118262,f87646]) ).
fof(f118262,plain,
! [X2,X3,X4] : implies(X4,and(X2,not(X3))) = implies(X4,not(implies(X2,X3))),
inference(backward_demodulation,[],[f241,f89089]) ).
fof(f254,plain,
! [X2,X3,X4] : or(X4,and(X2,not(X3))) = not(and(not(X4),implies(X2,X3))),
inference(superposition,[],[f249,f239]) ).
fof(f228,plain,
~ is_a_theorem(implies(and(sK0,sK1),and(sK1,sK0))),
inference(resolution,[],[f225,f227]) ).
fof(f227,plain,
~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))),
inference(subsumption_resolution,[],[f193,f158]) ).
fof(f158,plain,
~ axiom_m1,
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
~ axiom_m1,
inference(flattening,[],[f89]) ).
fof(f89,negated_conjecture,
~ axiom_m1,
inference(negated_conjecture,[],[f88]) ).
fof(f88,conjecture,
axiom_m1,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',s1_0_axiom_m1) ).
fof(f193,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f135,f156]) ).
fof(f156,plain,
( ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
( axiom_m1
| ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> axiom_m1 ),
inference(unused_predicate_definition_removal,[],[f63]) ).
fof(f63,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',axiom_m1) ).
fof(f225,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f214,f224]) ).
fof(f224,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(subsumption_resolution,[],[f187,f180]) ).
fof(f180,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',s1_0_op_strict_implies) ).
fof(f187,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',op_strict_implies) ).
fof(f214,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(subsumption_resolution,[],[f196,f162]) ).
fof(f162,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',km5_necessitation) ).
fof(f196,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882',necessitation) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.33 % Computer : n007.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Aug 24 19:12:25 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.14/0.34 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.34 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.PL9YtiXPrR/Vampire---4.8_26882
% 0.14/0.34 % (26993)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (26998)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.20/0.40 % (26996)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.20/0.40 % (26999)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.20/0.40 % (27000)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.20/0.40 % (26995)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.20/0.40 % (26997)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.20/0.40 % (26994)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.20/0.40 % (26997)Refutation not found, incomplete strategy% (26997)------------------------------
% 0.20/0.40 % (26997)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.40 % (26997)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.40 % (26997)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.40
% 0.20/0.40 % (26997)Memory used [KB]: 5628
% 0.20/0.40 % (26997)Time elapsed: 0.003 s
% 0.20/0.40 % (26997)------------------------------
% 0.20/0.40 % (26997)------------------------------
% 0.20/0.46 % (27001)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_401 on Vampire---4 for (401ds/0Mi)
% 20.12/3.24 % (27001)First to succeed.
% 20.49/3.26 % (27001)Refutation found. Thanks to Tanya!
% 20.49/3.26 % SZS status Theorem for Vampire---4
% 20.49/3.26 % SZS output start Proof for Vampire---4
% See solution above
% 20.49/3.26 % (27001)------------------------------
% 20.49/3.26 % (27001)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 20.49/3.26 % (27001)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 20.49/3.26 % (27001)Termination reason: Refutation
% 20.49/3.26
% 20.49/3.26 % (27001)Memory used [KB]: 112322
% 20.49/3.26 % (27001)Time elapsed: 2.778 s
% 20.49/3.26 % (27001)------------------------------
% 20.49/3.26 % (27001)------------------------------
% 20.49/3.26 % (26993)Success in time 2.851 s
% 20.49/3.26 % Vampire---4.8 exiting
%------------------------------------------------------------------------------