TSTP Solution File: LCL519+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL519+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 : n022.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 13:42:38 EDT 2024
% Result : Theorem 2.28s 0.70s
% Output : Refutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 24
% Syntax : Number of formulae : 155 ( 80 unt; 0 def)
% Number of atoms : 250 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 168 ( 73 ~; 67 |; 2 &)
% ( 10 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 255 ( 251 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12745,plain,
$false,
inference(resolution,[],[f12709,f105]) ).
fof(f105,plain,
~ is_a_theorem(implies(sK1,or(sK0,sK1))),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f100,f90,f101,f91,f102,f92,f103,f93,f104,f94]) ).
fof(f94,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f68,f75]) ).
fof(f75,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1)))
=> ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( r2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
=> r2 ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f53,plain,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
( r2
<=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
fof(f104,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,f100,f90,f101,f91,f102,f92,f103,f93]) ).
fof(f93,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/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f103,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,f100,f90,f101,f91,f102,f92]) ).
fof(f92,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/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f102,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(global_subsumption,[],[f77,f78,f79,f80,f81,f82,f83,f84,f85,f86,f87,f88,f89,f100,f90,f101,f91]) ).
fof(f91,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,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(f101,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,f100,f90]) ).
fof(f90,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,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(f100,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),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) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,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(f88,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_equiv) ).
fof(f87,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_equiv) ).
fof(f86,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_or) ).
fof(f85,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_implies_and) ).
fof(f84,plain,
op_and,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f83,plain,
op_implies_or,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f82,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f80,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f78,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f77,plain,
~ r2,
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
~ r2,
inference(flattening,[],[f44]) ).
fof(f44,negated_conjecture,
~ r2,
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
fof(f12709,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,X0))),
inference(resolution,[],[f12652,f9771]) ).
fof(f9771,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f9157,f109]) ).
fof(f109,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,f100,f90,f101,f91,f102,f92,f103,f93,f104,f94,f105,f95,f106,f96,f107,f97,f108,f98]) ).
fof(f98,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/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f108,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,f100,f90,f101,f91,f102,f92,f103,f93,f104,f94,f105,f95,f106,f96,f107,f97]) ).
fof(f97,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/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f107,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,f100,f90,f101,f91,f102,f92,f103,f93,f104,f94,f105,f95,f106,f96]) ).
fof(f96,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,[],[f59]) ).
fof(f59,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/sandbox/benchmark/theBenchmark.p',kn2) ).
fof(f106,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,f100,f90,f101,f91,f102,f92,f103,f93,f104,f94,f105,f95]) ).
fof(f95,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,[],[f60]) ).
fof(f60,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/sandbox/benchmark/theBenchmark.p',kn1) ).
fof(f9157,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(forward_demodulation,[],[f9135,f395]) ).
fof(f395,plain,
! [X2,X0,X1] : implies(or(X0,not(X1)),X2) = or(and(not(X0),X1),X2),
inference(superposition,[],[f120,f127]) ).
fof(f127,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f103,f101]) ).
fof(f120,plain,
! [X2,X0,X1] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[],[f100,f116]) ).
fof(f116,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[],[f102,f100]) ).
fof(f9135,plain,
! [X0,X1] : is_a_theorem(or(and(not(X1),X0),implies(X0,X1))),
inference(superposition,[],[f4756,f101]) ).
fof(f4756,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),not(and(X1,X0)))),
inference(resolution,[],[f4225,f169]) ).
fof(f169,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(forward_demodulation,[],[f110,f127]) ).
fof(f110,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,f100,f90,f101,f91,f102,f92,f103,f93,f104,f94,f105,f95,f106,f96,f107,f97,f108,f98,f109,f99]) ).
fof(f99,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,[],[f58]) ).
fof(f58,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/sandbox/benchmark/theBenchmark.p',kn3) ).
fof(f4225,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X1,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f4197,f158]) ).
fof(f158,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f139,f100]) ).
fof(f139,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f109,f127]) ).
fof(f4197,plain,
! [X0] : is_a_theorem(not(not(implies(X0,X0)))),
inference(resolution,[],[f3291,f211]) ).
fof(f211,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),not(not(implies(X0,X1))))),
inference(superposition,[],[f195,f104]) ).
fof(f195,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),not(not(X0)))),
inference(superposition,[],[f107,f184]) ).
fof(f184,plain,
! [X0,X1] : and(X0,X1) = and(not(not(X0)),X1),
inference(forward_demodulation,[],[f174,f116]) ).
fof(f174,plain,
! [X0,X1] : not(implies(X0,not(X1))) = and(not(not(X0)),X1),
inference(superposition,[],[f140,f100]) ).
fof(f140,plain,
! [X0,X1] : and(not(X0),X1) = not(or(X0,not(X1))),
inference(superposition,[],[f116,f127]) ).
fof(f3291,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f3263,f158]) ).
fof(f3263,plain,
! [X0] : is_a_theorem(not(not(equiv(X0,X0)))),
inference(resolution,[],[f3251,f2228]) ).
fof(f2228,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(not(not(X0))) ),
inference(resolution,[],[f2191,f568]) ).
fof(f568,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f438,f109]) ).
fof(f438,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,not(not(X1))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f271,f101]) ).
fof(f271,plain,
! [X0,X1] :
( ~ is_a_theorem(not(and(X0,X1)))
| is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[],[f257,f116]) ).
fof(f257,plain,
! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(X0) ),
inference(resolution,[],[f192,f112]) ).
fof(f112,plain,
! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X0) ),
inference(resolution,[],[f109,f107]) ).
fof(f192,plain,
! [X0] :
( is_a_theorem(and(X0,not(not(X0))))
| ~ is_a_theorem(not(not(X0))) ),
inference(superposition,[],[f111,f184]) ).
fof(f111,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f109,f106]) ).
fof(f2191,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(forward_demodulation,[],[f2175,f100]) ).
fof(f2175,plain,
! [X0] : is_a_theorem(or(not(or(X0,X0)),X0)),
inference(resolution,[],[f2165,f1955]) ).
fof(f1955,plain,
! [X0,X1] :
( ~ is_a_theorem(or(or(X1,X1),X0))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f1954,f127]) ).
fof(f1954,plain,
! [X0,X1] :
( ~ is_a_theorem(or(implies(not(X1),X1),X0))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f1924,f115]) ).
fof(f115,plain,
! [X2,X0,X1] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2),
inference(superposition,[],[f100,f101]) ).
fof(f1924,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(and(not(X1),not(X1)),X0)) ),
inference(resolution,[],[f1601,f138]) ).
fof(f138,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f106,f127]) ).
fof(f1601,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f1381,f109]) ).
fof(f1381,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X0),or(X0,X1)))
| ~ is_a_theorem(or(X1,X2)) ),
inference(forward_demodulation,[],[f1377,f132]) ).
fof(f132,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(forward_demodulation,[],[f121,f101]) ).
fof(f121,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2))),
inference(superposition,[],[f103,f101]) ).
fof(f1377,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X2,not(X0)),or(X0,X1)))
| ~ is_a_theorem(or(X1,X2)) ),
inference(superposition,[],[f712,f127]) ).
fof(f712,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,X1),implies(X1,X2)))
| ~ is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f254,f109]) ).
fof(f254,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f251,f127]) ).
fof(f251,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,X0),implies(X0,X1)))),
inference(superposition,[],[f169,f101]) ).
fof(f2165,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[],[f2140,f127]) ).
fof(f2140,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(forward_demodulation,[],[f2124,f100]) ).
fof(f2124,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(resolution,[],[f1955,f352]) ).
fof(f352,plain,
! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X0))),
inference(superposition,[],[f330,f127]) ).
fof(f330,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[],[f107,f115]) ).
fof(f3251,plain,
! [X0,X1] : is_a_theorem(or(equiv(X0,X0),X1)),
inference(subsumption_resolution,[],[f3246,f2140]) ).
fof(f3246,plain,
! [X0,X1] :
( is_a_theorem(or(equiv(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[],[f2421,f104]) ).
fof(f2421,plain,
! [X0,X1] :
( is_a_theorem(or(and(X0,X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f2375,f659]) ).
fof(f659,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(X0,X0),X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f634,f158]) ).
fof(f634,plain,
! [X0] :
( is_a_theorem(not(not(and(X0,X0))))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f568,f106]) ).
fof(f2375,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(forward_demodulation,[],[f2343,f100]) ).
fof(f2343,plain,
! [X0,X1] : is_a_theorem(or(not(X0),or(X0,X1))),
inference(resolution,[],[f2190,f352]) ).
fof(f2190,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X0))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f2172,f127]) ).
fof(f2172,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(not(X1),X0)) ),
inference(resolution,[],[f2165,f1601]) ).
fof(f12652,plain,
! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X1))),
inference(superposition,[],[f12594,f131]) ).
fof(f131,plain,
! [X2,X0,X1] : implies(and(not(X0),not(X1)),X2) = or(or(X0,X1),X2),
inference(superposition,[],[f100,f103]) ).
fof(f12594,plain,
! [X0,X1] : is_a_theorem(implies(and(not(X0),X1),X1)),
inference(forward_demodulation,[],[f12555,f606]) ).
fof(f606,plain,
! [X2,X0,X1] : or(or(X0,not(X1)),X2) = implies(and(not(X0),X1),X2),
inference(superposition,[],[f134,f127]) ).
fof(f134,plain,
! [X2,X0,X1] : or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(forward_demodulation,[],[f123,f101]) ).
fof(f123,plain,
! [X2,X0,X1] : or(implies(X0,not(X1)),X2) = not(and(and(X0,X1),not(X2))),
inference(superposition,[],[f103,f116]) ).
fof(f12555,plain,
! [X0,X1] : is_a_theorem(or(or(X0,not(X1)),X1)),
inference(resolution,[],[f2396,f9351]) ).
fof(f9351,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,X0),or(X0,not(X1)))),
inference(forward_demodulation,[],[f9337,f132]) ).
fof(f9337,plain,
! [X0,X1] : is_a_theorem(or(and(X1,not(X0)),or(X0,not(X1)))),
inference(superposition,[],[f6533,f127]) ).
fof(f6533,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))),
inference(resolution,[],[f713,f4225]) ).
fof(f713,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),implies(X2,not(X0))))),
inference(superposition,[],[f254,f100]) ).
fof(f2396,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X1,X2),X0))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f2330,f1601]) ).
fof(f2330,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(resolution,[],[f2190,f330]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL519+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n022.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 22:49:14 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (28420)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.38 % (28424)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.38 TRYING [1]
% 0.23/0.38 % (28423)WARNING: value z3 for option sas not known
% 0.23/0.38 TRYING [2]
% 0.23/0.39 % (28425)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)
% 0.23/0.39 % (28426)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)
% 0.23/0.39 % (28422)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.39 % (28421)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.39 % (28427)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)
% 0.23/0.39 % (28423)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)
% 0.23/0.39 TRYING [3]
% 0.23/0.39 TRYING [1]
% 0.23/0.39 TRYING [2]
% 0.23/0.40 TRYING [4]
% 0.23/0.40 TRYING [3]
% 0.23/0.43 TRYING [4]
% 0.23/0.48 TRYING [5]
% 2.28/0.70 % (28423)First to succeed.
% 2.28/0.70 % (28423)Refutation found. Thanks to Tanya!
% 2.28/0.70 % SZS status Theorem for theBenchmark
% 2.28/0.70 % SZS output start Proof for theBenchmark
% See solution above
% 2.28/0.71 % (28423)------------------------------
% 2.28/0.71 % (28423)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.28/0.71 % (28423)Termination reason: Refutation
% 2.28/0.71
% 2.28/0.71 % (28423)Memory used [KB]: 5952
% 2.28/0.71 % (28423)Time elapsed: 0.320 s
% 2.28/0.71 % (28423)Instructions burned: 969 (million)
% 2.28/0.71 % (28423)------------------------------
% 2.28/0.71 % (28423)------------------------------
% 2.28/0.71 % (28420)Success in time 0.326 s
%------------------------------------------------------------------------------