TSTP Solution File: LCL507+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL507+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 : n002.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 07:46:14 EDT 2024
% Result : Theorem 33.01s 5.09s
% Output : Refutation 33.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 22
% Syntax : Number of formulae : 152 ( 65 unt; 0 def)
% Number of atoms : 269 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 215 ( 98 ~; 92 |; 2 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 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 : 255 ( 251 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f71942,plain,
$false,
inference(resolution,[],[f71852,f101]) ).
fof(f101,plain,
~ is_a_theorem(implies(and(sK0,sK1),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,
( and_2
| ~ is_a_theorem(implies(and(sK0,sK1),sK1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( and_2
| ~ is_a_theorem(implies(and(sK0,sK1),sK1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f68,f75]) ).
fof(f75,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X1))
=> ~ is_a_theorem(implies(and(sK0,sK1),sK1)) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( and_2
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X1)) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
=> and_2 ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).
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(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(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,
~ and_2,
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
~ and_2,
inference(flattening,[],[f44]) ).
fof(f44,negated_conjecture,
~ and_2,
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f71852,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(resolution,[],[f71722,f42055]) ).
fof(f42055,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f42003,f191]) ).
fof(f191,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,[],[f180,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(f115,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f99,f98]) ).
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(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(f180,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,X1),implies(X1,X2)))
| ~ is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f177,f105]) ).
fof(f177,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f173,f115]) ).
fof(f173,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,X0),implies(X0,X1)))),
inference(superposition,[],[f168,f98]) ).
fof(f168,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(f42003,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f33104,f102]) ).
fof(f33104,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,and(X0,X2)))
| is_a_theorem(not(and(not(X0),X1))) ),
inference(resolution,[],[f2356,f103]) ).
fof(f2356,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,[],[f169,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(f169,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,X1),not(and(X1,X2))))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f168,f105]) ).
fof(f71722,plain,
! [X0,X1] : is_a_theorem(or(X0,not(and(X1,X0)))),
inference(resolution,[],[f71577,f25361]) ).
fof(f25361,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f24756,f19556]) ).
fof(f19556,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,[],[f19541,f115]) ).
fof(f19541,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,[],[f191,f99]) ).
fof(f24756,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(resolution,[],[f24418,f20433]) ).
fof(f20433,plain,
! [X0,X1] : is_a_theorem(or(not(X0),or(X0,X1))),
inference(superposition,[],[f20351,f115]) ).
fof(f20351,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(resolution,[],[f232,f103]) ).
fof(f232,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(and(X0,not(X1)),X2))
| is_a_theorem(or(X2,implies(X0,X1))) ),
inference(superposition,[],[f222,f98]) ).
fof(f222,plain,
! [X0,X1] :
( is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f217,f197]) ).
fof(f197,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f187,f105]) ).
fof(f187,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),or(X1,X2)))
| ~ is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f179,f105]) ).
fof(f179,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f178,f115]) ).
fof(f178,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f174,f118]) ).
fof(f174,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,not(X0)),or(X0,X1)))),
inference(superposition,[],[f168,f99]) ).
fof(f217,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(resolution,[],[f214,f103]) ).
fof(f214,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(not(X1),not(X1)),X0))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f197,f122]) ).
fof(f122,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f102,f115]) ).
fof(f24418,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,or(X0,X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f24291,f21223]) ).
fof(f21223,plain,
! [X2,X0,X1] :
( is_a_theorem(or(or(X0,X1),X2))
| ~ is_a_theorem(or(X1,X2)) ),
inference(resolution,[],[f20405,f187]) ).
fof(f20405,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X1,X2),X0))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f20351,f197]) ).
fof(f24291,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(duplicate_literal_removal,[],[f24237]) ).
fof(f24237,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[],[f24192,f19564]) ).
fof(f19564,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(X0)
| ~ is_a_theorem(or(X1,X1)) ),
inference(resolution,[],[f19527,f105]) ).
fof(f19527,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(or(X1,not(X0))) ),
inference(resolution,[],[f191,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(f24192,plain,
! [X0] :
( is_a_theorem(or(X0,not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[],[f21301,f139]) ).
fof(f139,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f136,f105]) ).
fof(f136,plain,
! [X0,X1] : is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f132,f115]) ).
fof(f132,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(superposition,[],[f103,f100]) ).
fof(f21301,plain,
! [X0] :
( is_a_theorem(equiv(not(X0),not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[],[f21218,f19564]) ).
fof(f21218,plain,
! [X0] : is_a_theorem(or(equiv(X0,X0),X0)),
inference(resolution,[],[f20405,f130]) ).
fof(f130,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[],[f102,f100]) ).
fof(f71577,plain,
! [X0,X1] : is_a_theorem(or(not(and(X0,X1)),X1)),
inference(resolution,[],[f67432,f48764]) ).
fof(f48764,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(and(X0,X1),X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f48692,f19556]) ).
fof(f48692,plain,
! [X0,X1] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(resolution,[],[f42048,f217]) ).
fof(f42048,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(forward_demodulation,[],[f42047,f115]) ).
fof(f42047,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(not(X1),X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(forward_demodulation,[],[f42033,f98]) ).
fof(f42033,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(not(and(not(X1),not(X0)))) ),
inference(superposition,[],[f33104,f115]) ).
fof(f67432,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),not(and(X1,X0)))),
inference(resolution,[],[f66398,f168]) ).
fof(f66398,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X1,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f66377,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,[],[f236,f122]) ).
fof(f236,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,[],[f230,f115]) ).
fof(f230,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,[],[f222,f197]) ).
fof(f66377,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X0),X1)),
inference(resolution,[],[f66293,f276]) ).
fof(f276,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f263,f99]) ).
fof(f263,plain,
! [X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f231,f103]) ).
fof(f231,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(not(X0))
| ~ is_a_theorem(not(X1)) ),
inference(resolution,[],[f222,f123]) ).
fof(f66293,plain,
! [X0] : is_a_theorem(not(not(implies(X0,X0)))),
inference(resolution,[],[f54328,f132]) ).
fof(f54328,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(not(not(X0))) ),
inference(resolution,[],[f54299,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,[],[f267,f222]) ).
fof(f267,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(not(not(X0)))
| ~ is_a_theorem(not(X1)) ),
inference(superposition,[],[f231,f115]) ).
fof(f54299,plain,
! [X0] : is_a_theorem(not(not(equiv(X0,X0)))),
inference(subsumption_resolution,[],[f54222,f42113]) ).
fof(f42113,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f42055,f24756]) ).
fof(f54222,plain,
! [X0] :
( is_a_theorem(not(not(equiv(X0,X0))))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[],[f42348,f130]) ).
fof(f42348,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f42288,f810]) ).
fof(f42288,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f42153,f105]) ).
fof(f42153,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f42055,f217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : LCL507+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n002.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 14:05:12 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (22821)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33 % (22824)WARNING: value z3 for option sas not known
% 0.10/0.33 % (22822)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.33 % (22827)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)
% 0.10/0.33 % (22828)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)
% 0.10/0.33 % (22825)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.33 % (22824)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)
% 0.10/0.33 % (22826)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)
% 0.10/0.33 % (22823)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [2]
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [3]
% 0.10/0.34 TRYING [2]
% 0.10/0.34 TRYING [3]
% 0.10/0.35 TRYING [4]
% 0.10/0.37 TRYING [4]
% 0.17/0.41 TRYING [5]
% 2.28/0.65 TRYING [5]
% 7.53/1.43 TRYING [1]
% 7.53/1.43 TRYING [2]
% 7.53/1.44 TRYING [3]
% 7.99/1.45 TRYING [4]
% 8.45/1.53 TRYING [5]
% 9.62/1.70 TRYING [6]
% 20.95/3.42 TRYING [6]
% 33.01/5.08 % (22824)First to succeed.
% 33.01/5.08 % (22824)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22821"
% 33.01/5.09 % (22824)Refutation found. Thanks to Tanya!
% 33.01/5.09 % SZS status Theorem for theBenchmark
% 33.01/5.09 % SZS output start Proof for theBenchmark
% See solution above
% 33.01/5.09 % (22824)------------------------------
% 33.01/5.09 % (22824)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 33.01/5.09 % (22824)Termination reason: Refutation
% 33.01/5.09
% 33.01/5.09 % (22824)Memory used [KB]: 41660
% 33.01/5.09 % (22824)Time elapsed: 4.746 s
% 33.01/5.09 % (22824)Instructions burned: 10678 (million)
% 33.01/5.09 % (22821)Success in time 4.715 s
%------------------------------------------------------------------------------