TSTP Solution File: LCL502+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL502+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 : 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 : Sun May 5 07:46:13 EDT 2024
% Result : Theorem 171.50s 24.83s
% Output : Refutation 171.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 22
% Syntax : Number of formulae : 195 ( 79 unt; 0 def)
% Number of atoms : 349 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 290 ( 136 ~; 129 |; 2 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 343 ( 339 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f198277,plain,
$false,
inference(resolution,[],[f179230,f127]) ).
fof(f127,plain,
~ is_a_theorem(implies(or(sK1,not(sK0)),implies(sK0,sK1))),
inference(forward_demodulation,[],[f101,f115]) ).
fof(f115,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f99,f98]) ).
fof(f98,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89]) ).
fof(f89,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,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/benchmark/theBenchmark.p',op_implies_and) ).
fof(f88,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f87,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_or) ).
fof(f86,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_implies_and) ).
fof(f85,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_equiv) ).
fof(f84,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f83,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f82,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_modus_ponens) ).
fof(f81,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f80,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f78,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f77,plain,
~ modus_tollens,
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
~ modus_tollens,
inference(flattening,[],[f44]) ).
fof(f44,negated_conjecture,
~ modus_tollens,
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f99,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90]) ).
fof(f90,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,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/benchmark/theBenchmark.p',op_or) ).
fof(f101,plain,
~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92]) ).
fof(f92,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f68,f75]) ).
fof(f75,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
=> ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( modus_tollens
| ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
=> modus_tollens ),
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/benchmark/theBenchmark.p',modus_tollens) ).
fof(f100,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91]) ).
fof(f91,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,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/benchmark/theBenchmark.p',op_equiv) ).
fof(f179230,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(superposition,[],[f67647,f176204]) ).
fof(f176204,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(superposition,[],[f115,f175249]) ).
fof(f175249,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f175239,f104]) ).
fof(f104,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92,f101,f93,f102,f94,f103,f95]) ).
fof(f95,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,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/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f103,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92,f101,f93,f102,f94]) ).
fof(f94,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[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/benchmark/theBenchmark.p',kn2) ).
fof(f102,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92,f101,f93]) ).
fof(f93,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[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/benchmark/theBenchmark.p',kn1) ).
fof(f175239,plain,
! [X0] : is_a_theorem(equiv(X0,not(not(X0)))),
inference(subsumption_resolution,[],[f175237,f42274]) ).
fof(f42274,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f42176,f218]) ).
fof(f218,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(resolution,[],[f215,f103]) ).
fof(f215,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(not(X1),not(X1)),X0))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f198,f122]) ).
fof(f122,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f102,f115]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f188,f105]) ).
fof(f105,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92,f101,f93,f102,f94,f103,f95,f104,f96]) ).
fof(f96,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,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/benchmark/theBenchmark.p',modus_ponens) ).
fof(f188,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),or(X1,X2)))
| ~ is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f180,f105]) ).
fof(f180,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f179,f115]) ).
fof(f179,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f175,f118]) ).
fof(f118,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(forward_demodulation,[],[f111,f98]) ).
fof(f111,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2))),
inference(superposition,[],[f99,f98]) ).
fof(f175,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,not(X0)),or(X0,X1)))),
inference(superposition,[],[f159,f99]) ).
fof(f159,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(forward_demodulation,[],[f106,f115]) ).
fof(f106,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f98,f90,f99,f91,f100,f92,f101,f93,f102,f94,f103,f95,f104,f96,f105,f97]) ).
fof(f97,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,plain,
( kn3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(unused_predicate_definition_removal,[],[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/benchmark/theBenchmark.p',kn3) ).
fof(f42176,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f42124,f192]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(and(X1,X2)))
| is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f181,f123]) ).
fof(f123,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f105,f115]) ).
fof(f181,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,X1),implies(X1,X2)))
| ~ is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f178,f105]) ).
fof(f178,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f174,f115]) ).
fof(f174,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,X0),implies(X0,X1)))),
inference(superposition,[],[f159,f98]) ).
fof(f42124,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f33219,f102]) ).
fof(f33219,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,and(X0,X2)))
| is_a_theorem(not(and(not(X0),X1))) ),
inference(resolution,[],[f2314,f103]) ).
fof(f2314,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(not(and(not(X2),X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f358,f105]) ).
fof(f358,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),not(and(not(X1),X2))))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(superposition,[],[f170,f118]) ).
fof(f170,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,X1),not(and(X1,X2))))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f159,f105]) ).
fof(f175237,plain,
! [X0] :
( is_a_theorem(equiv(X0,not(not(X0))))
| ~ is_a_theorem(implies(X0,not(not(X0)))) ),
inference(superposition,[],[f173921,f129]) ).
fof(f129,plain,
! [X0,X1] : equiv(X1,not(X0)) = and(implies(X1,not(X0)),or(X0,X1)),
inference(superposition,[],[f100,f115]) ).
fof(f173921,plain,
! [X0,X1] :
( is_a_theorem(and(X0,or(not(X1),X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f173799,f54773]) ).
fof(f54773,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(or(not(X1),X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f54728,f1074]) ).
fof(f1074,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1066,f105]) ).
fof(f1066,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1065,f115]) ).
fof(f1065,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1052,f118]) ).
fof(f1052,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(and(not(X0),not(X0)),X1)) ),
inference(resolution,[],[f237,f122]) ).
fof(f237,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X2,X1)) ),
inference(forward_demodulation,[],[f231,f115]) ).
fof(f231,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X2,X1))
| ~ is_a_theorem(implies(not(X0),X2)) ),
inference(resolution,[],[f223,f198]) ).
fof(f223,plain,
! [X0,X1] :
( is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f218,f198]) ).
fof(f54728,plain,
! [X0,X1] : is_a_theorem(or(or(not(X0),X0),X1)),
inference(resolution,[],[f54421,f314]) ).
fof(f314,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f264,f99]) ).
fof(f264,plain,
! [X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f232,f103]) ).
fof(f232,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(not(X0))
| ~ is_a_theorem(not(X1)) ),
inference(resolution,[],[f223,f123]) ).
fof(f54421,plain,
! [X0] : is_a_theorem(not(not(or(not(X0),X0)))),
inference(subsumption_resolution,[],[f54396,f25453]) ).
fof(f25453,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(resolution,[],[f24539,f20554]) ).
fof(f20554,plain,
! [X0,X1] : is_a_theorem(or(not(X0),or(X0,X1))),
inference(superposition,[],[f20472,f115]) ).
fof(f20472,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(resolution,[],[f233,f103]) ).
fof(f233,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(and(X0,not(X1)),X2))
| is_a_theorem(or(X2,implies(X0,X1))) ),
inference(superposition,[],[f223,f98]) ).
fof(f24539,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,or(X0,X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f24412,f21344]) ).
fof(f21344,plain,
! [X2,X0,X1] :
( is_a_theorem(or(or(X0,X1),X2))
| ~ is_a_theorem(or(X1,X2)) ),
inference(resolution,[],[f20526,f188]) ).
fof(f20526,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X1,X2),X0))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f20472,f198]) ).
fof(f24412,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(duplicate_literal_removal,[],[f24358]) ).
fof(f24358,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[],[f24313,f19685]) ).
fof(f19685,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(X0)
| ~ is_a_theorem(or(X1,X1)) ),
inference(resolution,[],[f19648,f105]) ).
fof(f19648,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(or(X1,not(X0))) ),
inference(resolution,[],[f192,f557]) ).
fof(f557,plain,
! [X0] : is_a_theorem(not(and(not(X0),or(X0,X0)))),
inference(superposition,[],[f102,f117]) ).
fof(f117,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1))),
inference(superposition,[],[f98,f99]) ).
fof(f24313,plain,
! [X0] :
( is_a_theorem(or(X0,not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[],[f21422,f140]) ).
fof(f140,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f137,f105]) ).
fof(f137,plain,
! [X0,X1] : is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f133,f115]) ).
fof(f133,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(superposition,[],[f103,f100]) ).
fof(f21422,plain,
! [X0] :
( is_a_theorem(equiv(not(X0),not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[],[f21339,f19685]) ).
fof(f21339,plain,
! [X0] : is_a_theorem(or(equiv(X0,X0),X0)),
inference(resolution,[],[f20526,f131]) ).
fof(f131,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[],[f102,f100]) ).
fof(f54396,plain,
! [X0] :
( is_a_theorem(not(not(or(not(X0),X0))))
| ~ is_a_theorem(or(X0,not(X0))) ),
inference(resolution,[],[f42469,f24840]) ).
fof(f24840,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),or(not(X0),X0))),
inference(resolution,[],[f24522,f190]) ).
fof(f190,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(X0)),implies(or(X0,X1),or(X1,X2)))),
inference(superposition,[],[f180,f115]) ).
fof(f24522,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f24412,f20527]) ).
fof(f20527,plain,
! [X2,X0,X1] :
( is_a_theorem(or(implies(X0,X2),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f20472,f237]) ).
fof(f42469,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f42409,f810]) ).
fof(f810,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(not(not(X0)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f268,f223]) ).
fof(f268,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(not(not(X0)))
| ~ is_a_theorem(not(X1)) ),
inference(superposition,[],[f232,f115]) ).
fof(f42409,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f42274,f105]) ).
fof(f173799,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f136286,f53027]) ).
fof(f53027,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,implies(X1,X0)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f52498,f24412]) ).
fof(f52498,plain,
! [X2,X0,X1] :
( is_a_theorem(or(implies(X0,X1),X2))
| ~ is_a_theorem(or(X1,X2)) ),
inference(resolution,[],[f48886,f181]) ).
fof(f48886,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(and(X0,X1),X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f48814,f19677]) ).
fof(f19677,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,not(X0)))
| ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X2)) ),
inference(forward_demodulation,[],[f19662,f115]) ).
fof(f19662,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(or(X2,not(X0))) ),
inference(superposition,[],[f192,f99]) ).
fof(f48814,plain,
! [X0,X1] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(resolution,[],[f42169,f218]) ).
fof(f42169,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(forward_demodulation,[],[f42168,f115]) ).
fof(f42168,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(not(X1),X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(forward_demodulation,[],[f42154,f98]) ).
fof(f42154,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(not(and(not(X1),not(X0)))) ),
inference(superposition,[],[f33219,f115]) ).
fof(f136286,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,X1),implies(X1,X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f69730,f178]) ).
fof(f69730,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X2,X0),X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f68426,f3903]) ).
fof(f3903,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f1952,f1066]) ).
fof(f1952,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X0,X2),X1))
| is_a_theorem(X1)
| ~ is_a_theorem(not(not(X0))) ),
inference(resolution,[],[f1896,f1074]) ).
fof(f1896,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X2,or(X0,X1)))
| ~ is_a_theorem(not(not(X0))) ),
inference(superposition,[],[f1814,f99]) ).
fof(f1814,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X1,not(and(X0,X2))))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f1792,f1121]) ).
fof(f1121,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1069,f218]) ).
fof(f1069,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X2,X1))
| ~ is_a_theorem(not(X0)) ),
inference(forward_demodulation,[],[f1057,f115]) ).
fof(f1057,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(not(X0),X1))
| is_a_theorem(or(X2,X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f237,f443]) ).
fof(f443,plain,
! [X0,X1] :
( is_a_theorem(or(not(X0),X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f431,f314]) ).
fof(f431,plain,
! [X0] :
( is_a_theorem(not(not(not(X0))))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f336,f313]) ).
fof(f313,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f264,f98]) ).
fof(f336,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,not(X0)))
| is_a_theorem(not(not(not(X0)))) ),
inference(resolution,[],[f270,f223]) ).
fof(f270,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(not(not(X0))) ),
inference(superposition,[],[f258,f99]) ).
fof(f258,plain,
! [X0] :
( ~ is_a_theorem(not(and(X0,X0)))
| is_a_theorem(not(X0)) ),
inference(resolution,[],[f232,f102]) ).
fof(f1792,plain,
! [X0,X1] :
( is_a_theorem(not(not(not(and(X0,X1)))))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f1233,f103]) ).
fof(f1233,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(not(not(not(X0)))) ),
inference(resolution,[],[f1229,f223]) ).
fof(f1229,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X0))
| is_a_theorem(not(not(X0)))
| ~ is_a_theorem(not(X1)) ),
inference(forward_demodulation,[],[f1220,f115]) ).
fof(f1220,plain,
! [X0,X1] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(implies(not(X1),X0))
| ~ is_a_theorem(not(X1)) ),
inference(resolution,[],[f810,f431]) ).
fof(f68426,plain,
! [X0,X1] :
( is_a_theorem(not(not(or(X0,X1))))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f68351,f42469]) ).
fof(f68351,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,X0))),
inference(resolution,[],[f68273,f42176]) ).
fof(f68273,plain,
! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X1))),
inference(resolution,[],[f67647,f20578]) ).
fof(f20578,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X1,X2),X0))
| is_a_theorem(or(X0,not(X1))) ),
inference(resolution,[],[f20554,f198]) ).
fof(f67647,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_demodulation,[],[f67646,f115]) ).
fof(f67646,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),implies(not(X1),X0))),
inference(forward_demodulation,[],[f67545,f98]) ).
fof(f67545,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),not(and(not(X1),not(X0))))),
inference(resolution,[],[f66516,f282]) ).
fof(f282,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,not(X0)),implies(or(X0,X1),not(and(not(X1),X2))))),
inference(superposition,[],[f159,f119]) ).
fof(f119,plain,
! [X2,X0,X1] : implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2),
inference(forward_demodulation,[],[f112,f98]) ).
fof(f112,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),X2) = not(and(or(X0,X1),not(X2))),
inference(superposition,[],[f99,f99]) ).
fof(f66516,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X1,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f66495,f1074]) ).
fof(f66495,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X0),X1)),
inference(resolution,[],[f66411,f314]) ).
fof(f66411,plain,
! [X0] : is_a_theorem(not(not(implies(X0,X0)))),
inference(resolution,[],[f54446,f133]) ).
fof(f54446,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(not(not(X0))) ),
inference(resolution,[],[f54417,f810]) ).
fof(f54417,plain,
! [X0] : is_a_theorem(not(not(equiv(X0,X0)))),
inference(subsumption_resolution,[],[f54340,f42234]) ).
fof(f42234,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f42176,f25453]) ).
fof(f54340,plain,
! [X0] :
( is_a_theorem(not(not(equiv(X0,X0))))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[],[f42469,f131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LCL502+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 13:47:01 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (23109)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (23123)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (23124)WARNING: value z3 for option sas not known
% 0.13/0.38 % (23128)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)
% 0.13/0.38 % (23126)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)
% 0.13/0.38 % (23124)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)
% 0.13/0.38 % (23122)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 % (23127)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)
% 0.13/0.38 % (23125)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.39 TRYING [3]
% 0.13/0.39 TRYING [3]
% 0.21/0.41 TRYING [4]
% 0.21/0.43 TRYING [4]
% 0.21/0.50 TRYING [5]
% 5.23/1.13 TRYING [5]
% 7.87/1.47 TRYING [1]
% 7.87/1.47 TRYING [2]
% 7.87/1.47 TRYING [3]
% 7.87/1.48 TRYING [4]
% 8.33/1.54 TRYING [5]
% 9.44/1.71 TRYING [6]
% 16.66/2.77 TRYING [6]
% 171.38/24.80 % (23124)First to succeed.
% 171.38/24.81 % (23124)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23109"
% 171.50/24.83 % (23124)Refutation found. Thanks to Tanya!
% 171.50/24.83 % SZS status Theorem for theBenchmark
% 171.50/24.83 % SZS output start Proof for theBenchmark
% See solution above
% 171.50/24.84 % (23124)------------------------------
% 171.50/24.84 % (23124)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 171.50/24.84 % (23124)Termination reason: Refutation
% 171.50/24.84
% 171.50/24.84 % (23124)Memory used [KB]: 232917
% 171.50/24.84 % (23124)Time elapsed: 24.425 s
% 171.50/24.84 % (23124)Instructions burned: 89106 (million)
% 171.50/24.84 % (23109)Success in time 24.318 s
%------------------------------------------------------------------------------