TSTP Solution File: LCL457+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL457+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 : Tue Apr 30 13:42:27 EDT 2024
% Result : Theorem 10.65s 1.88s
% Output : Refutation 10.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 44
% Syntax : Number of formulae : 176 ( 82 unt; 0 def)
% Number of atoms : 287 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 187 ( 76 ~; 66 |; 2 &)
% ( 17 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 22 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 276 ( 270 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31593,plain,
$false,
inference(subsumption_resolution,[],[f31592,f21378]) ).
fof(f21378,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(X0,or(X1,X2)))),
inference(superposition,[],[f21329,f249]) ).
fof(f249,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f153,f151]) ).
fof(f151,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130]) ).
fof(f130,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,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/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f150,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129]) ).
fof(f129,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,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/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
fof(f128,plain,
op_equiv,
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_equiv) ).
fof(f127,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f126,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f125,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f124,plain,
op_and,
inference(cnf_transformation,[],[f51]) ).
fof(f51,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f123,plain,
op_implies_or,
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f122,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f121,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f120,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f119,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f118,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f117,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f116,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f115,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f114,plain,
equivalence_1,
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f113,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f112,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f111,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f110,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f109,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f108,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f107,plain,
~ r4,
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
~ r4,
inference(flattening,[],[f54]) ).
fof(f54,negated_conjecture,
~ r4,
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
r4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r4) ).
fof(f153,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132]) ).
fof(f132,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,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/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f152,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131]) ).
fof(f131,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,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/sandbox/benchmark/theBenchmark.p',op_and) ).
fof(f21329,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,or(X2,X0)))),
inference(resolution,[],[f20591,f386]) ).
fof(f386,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f316,f168]) ).
fof(f168,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139,f160,f140,f161,f141,f162,f142,f163,f143,f164,f144,f165,f145,f166,f146,f167,f147]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f101]) ).
fof(f101,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,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/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f167,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139,f160,f140,f161,f141,f162,f142,f163,f143,f164,f144,f165,f145,f166,f146]) ).
fof(f146,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,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/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f166,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139,f160,f140,f161,f141,f162,f142,f163,f143,f164,f144,f165,f145]) ).
fof(f145,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,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/sandbox/benchmark/theBenchmark.p',equivalence_3) ).
fof(f165,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139,f160,f140,f161,f141,f162,f142,f163,f143,f164,f144]) ).
fof(f144,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,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/sandbox/benchmark/theBenchmark.p',implies_2) ).
fof(f164,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139,f160,f140,f161,f141,f162,f142,f163,f143]) ).
fof(f143,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,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/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
fof(f163,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139,f160,f140,f161,f141,f162,f142]) ).
fof(f142,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
( equivalence_1
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f13,axiom,
( equivalence_1
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_1) ).
fof(f162,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139,f160,f140,f161,f141]) ).
fof(f141,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
( equivalence_2
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
fof(f161,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139,f160,f140]) ).
fof(f140,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,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/sandbox/benchmark/theBenchmark.p',and_3) ).
fof(f160,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139]) ).
fof(f139,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
fof(f159,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138]) ).
fof(f138,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,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/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f158,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137]) ).
fof(f137,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,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/sandbox/benchmark/theBenchmark.p',implies_1) ).
fof(f157,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136]) ).
fof(f136,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,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/sandbox/benchmark/theBenchmark.p',or_2) ).
fof(f156,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135]) ).
fof(f135,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,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/sandbox/benchmark/theBenchmark.p',or_1) ).
fof(f155,plain,
~ is_a_theorem(implies(or(sK0,or(sK1,sK2)),or(sK1,or(sK0,sK2)))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134]) ).
fof(f134,plain,
( r4
| ~ is_a_theorem(implies(or(sK0,or(sK1,sK2)),or(sK1,or(sK0,sK2)))) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
( r4
| ~ is_a_theorem(implies(or(sK0,or(sK1,sK2)),or(sK1,or(sK0,sK2)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f88,f105]) ).
fof(f105,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
=> ~ is_a_theorem(implies(or(sK0,or(sK1,sK2)),or(sK1,or(sK0,sK2)))) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
( r4
| ? [X0,X1,X2] : ~ is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
=> r4 ),
inference(unused_predicate_definition_removal,[],[f66]) ).
fof(f66,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/sandbox/benchmark/theBenchmark.p',r4) ).
fof(f154,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133]) ).
fof(f133,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,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/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f316,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(forward_demodulation,[],[f164,f249]) ).
fof(f20591,plain,
! [X2,X0,X1] : is_a_theorem(or(implies(X0,or(X1,X2)),not(X2))),
inference(forward_demodulation,[],[f20585,f249]) ).
fof(f20585,plain,
! [X2,X0,X1] : is_a_theorem(implies(not(implies(X0,or(X1,X2))),not(X2))),
inference(superposition,[],[f20473,f256]) ).
fof(f256,plain,
! [X2,X0,X1] : and(X2,and(not(X0),not(X1))) = not(implies(X2,or(X0,X1))),
inference(superposition,[],[f200,f153]) ).
fof(f200,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[],[f152,f150]) ).
fof(f20473,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,X2)),X2)),
inference(resolution,[],[f12353,f160]) ).
fof(f12353,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X2,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1752,f160]) ).
fof(f1752,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f601,f168]) ).
fof(f601,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f169,f168]) ).
fof(f169,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139,f160,f140,f161,f141,f162,f142,f163,f143,f164,f144,f165,f145,f166,f146,f167,f147,f168,f148]) ).
fof(f148,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[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/sandbox/benchmark/theBenchmark.p',implies_3) ).
fof(f31592,plain,
~ is_a_theorem(implies(sK2,or(sK1,or(sK0,sK2)))),
inference(subsumption_resolution,[],[f31585,f156]) ).
fof(f31585,plain,
( ~ is_a_theorem(implies(sK1,or(sK1,or(sK0,sK2))))
| ~ is_a_theorem(implies(sK2,or(sK1,or(sK0,sK2)))) ),
inference(resolution,[],[f31549,f6965]) ).
fof(f6965,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,X2),X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(resolution,[],[f658,f168]) ).
fof(f658,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),X1)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(resolution,[],[f170,f168]) ).
fof(f170,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))),
inference(global_subsumption,[],[f107,f108,f109,f110,f111,f112,f113,f114,f115,f116,f117,f118,f119,f120,f121,f122,f123,f124,f125,f126,f127,f128,f129,f150,f130,f151,f131,f152,f132,f153,f133,f154,f134,f155,f135,f156,f136,f157,f137,f158,f138,f159,f139,f160,f140,f161,f141,f162,f142,f163,f143,f164,f144,f165,f145,f166,f146,f167,f147,f168,f148,f169,f149]) ).
fof(f149,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,[],[f104]) ).
fof(f104,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,[],[f71]) ).
fof(f71,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/sandbox/benchmark/theBenchmark.p',or_3) ).
fof(f31549,plain,
~ is_a_theorem(implies(or(sK1,sK2),or(sK1,or(sK0,sK2)))),
inference(subsumption_resolution,[],[f31508,f17336]) ).
fof(f17336,plain,
! [X2,X0,X1] : is_a_theorem(implies(X1,or(X0,or(X1,X2)))),
inference(superposition,[],[f17277,f249]) ).
fof(f17277,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,or(X0,X2)))),
inference(resolution,[],[f16684,f386]) ).
fof(f16684,plain,
! [X2,X0,X1] : is_a_theorem(or(implies(X0,or(X1,X2)),not(X1))),
inference(forward_demodulation,[],[f16677,f249]) ).
fof(f16677,plain,
! [X2,X0,X1] : is_a_theorem(implies(not(implies(X0,or(X1,X2))),not(X1))),
inference(superposition,[],[f16522,f256]) ).
fof(f16522,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,X2)),X1)),
inference(resolution,[],[f12352,f160]) ).
fof(f12352,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1752,f159]) ).
fof(f31508,plain,
( ~ is_a_theorem(implies(sK0,or(sK1,or(sK0,sK2))))
| ~ is_a_theorem(implies(or(sK1,sK2),or(sK1,or(sK0,sK2)))) ),
inference(resolution,[],[f6965,f155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL457+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 23:10:34 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (8275)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (8280)WARNING: value z3 for option sas not known
% 0.14/0.39 % (8278)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (8279)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (8280)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 theBenchmark for (569ds/0Mi)
% 0.14/0.39 % (8281)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (8282)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 theBenchmark for (531ds/0Mi)
% 0.14/0.39 % (8284)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 theBenchmark for (497ds/0Mi)
% 0.14/0.39 % (8283)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 theBenchmark for (522ds/0Mi)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [3]
% 0.21/0.40 TRYING [2]
% 0.21/0.41 TRYING [4]
% 0.21/0.41 TRYING [3]
% 0.21/0.48 TRYING [4]
% 0.21/0.50 TRYING [5]
% 2.39/0.71 TRYING [5]
% 3.12/0.80 TRYING [6]
% 7.63/1.48 TRYING [1]
% 7.63/1.49 TRYING [2]
% 7.63/1.49 TRYING [3]
% 7.63/1.50 TRYING [4]
% 8.23/1.55 TRYING [5]
% 10.65/1.87 % (8280)First to succeed.
% 10.65/1.88 % (8280)Refutation found. Thanks to Tanya!
% 10.65/1.88 % SZS status Theorem for theBenchmark
% 10.65/1.88 % SZS output start Proof for theBenchmark
% See solution above
% 10.65/1.88 % (8280)------------------------------
% 10.65/1.88 % (8280)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 10.65/1.88 % (8280)Termination reason: Refutation
% 10.65/1.88
% 10.65/1.88 % (8280)Memory used [KB]: 16404
% 10.65/1.88 % (8280)Time elapsed: 1.500 s
% 10.65/1.88 % (8280)Instructions burned: 5756 (million)
% 10.65/1.88 % (8280)------------------------------
% 10.65/1.88 % (8280)------------------------------
% 10.65/1.88 % (8275)Success in time 1.491 s
%------------------------------------------------------------------------------