TSTP Solution File: LCL498+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL498+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 : n004.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 13:42:35 EDT 2024
% Result : Theorem 64.55s 9.60s
% Output : Refutation 64.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 26
% Syntax : Number of formulae : 154 ( 61 unt; 0 def)
% Number of atoms : 270 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 205 ( 89 ~; 83 |; 2 &)
% ( 14 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 256 ( 254 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96773,plain,
$false,
inference(resolution,[],[f96612,f113]) ).
fof(f113,plain,
~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98,f110,f99,f111,f100,f112,f101]) ).
fof(f101,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f73,f82]) ).
fof(f82,plain,
( ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0))
=> ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
( cn3
| ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,plain,
( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
=> cn3 ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f53,plain,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
( cn3
<=> ! [X3] : is_a_theorem(implies(implies(not(X3),X3),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3) ).
fof(f112,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98,f110,f99,f111,f100]) ).
fof(f100,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,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(f111,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98,f110,f99]) ).
fof(f99,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,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(f110,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98]) ).
fof(f98,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,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/sandbox2/benchmark/theBenchmark.p',op_and) ).
fof(f109,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97]) ).
fof(f97,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,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/sandbox2/benchmark/theBenchmark.p',op_implies_or) ).
fof(f96,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).
fof(f95,plain,
op_equiv,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_op_equiv) ).
fof(f94,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
fof(f93,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f92,plain,
op_or,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_op_or) ).
fof(f91,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
fof(f90,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f89,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(f88,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
fof(f87,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r5) ).
fof(f86,plain,
r4,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r4) ).
fof(f85,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f84,plain,
~ cn3,
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
~ cn3,
inference(flattening,[],[f46]) ).
fof(f46,negated_conjecture,
~ cn3,
inference(negated_conjecture,[],[f45]) ).
fof(f45,conjecture,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
fof(f96612,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(resolution,[],[f55819,f1025]) ).
fof(f1025,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1023,f109]) ).
fof(f1023,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,implies(X0,X1)))
| is_a_theorem(or(not(X0),X1)) ),
inference(superposition,[],[f853,f109]) ).
fof(f853,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X1,X0)))
| is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f649,f125]) ).
fof(f125,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f118,f114]) ).
fof(f114,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98,f110,f99,f111,f100,f112,f101,f113,f102]) ).
fof(f102,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f54]) ).
fof(f54,plain,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
( r1
<=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).
fof(f118,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98,f110,f99,f111,f100,f112,f101,f113,f102,f114,f103,f115,f104,f116,f105,f117,f106]) ).
fof(f106,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,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(f117,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98,f110,f99,f111,f100,f112,f101,f113,f102,f114,f103,f115,f104,f116,f105]) ).
fof(f105,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,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(f116,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98,f110,f99,f111,f100,f112,f101,f113,f102,f114,f103,f115,f104]) ).
fof(f104,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f56,plain,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
( r3
<=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3) ).
fof(f115,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98,f110,f99,f111,f100,f112,f101,f113,f102,f114,f103]) ).
fof(f103,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f55,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/sandbox2/benchmark/theBenchmark.p',r2) ).
fof(f649,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X1,or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f509,f248]) ).
fof(f248,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X1,or(X0,X2)))
| is_a_theorem(or(X0,or(X1,X2))) ),
inference(resolution,[],[f120,f118]) ).
fof(f120,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98,f110,f99,f111,f100,f112,f101,f113,f102,f114,f103,f115,f104,f116,f105,f117,f106,f118,f107,f119,f108]) ).
fof(f108,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
( r4
=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f58,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/sandbox2/benchmark/theBenchmark.p',r4) ).
fof(f119,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))),
inference(global_subsumption,[],[f84,f85,f86,f87,f88,f89,f90,f91,f92,f93,f94,f95,f96,f97,f109,f98,f110,f99,f111,f100,f112,f101,f113,f102,f114,f103,f115,f104,f116,f105,f117,f106,f118,f107]) ).
fof(f107,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f57,plain,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
( r5
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
fof(f509,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,or(X1,X2)))
| ~ is_a_theorem(or(X2,X1)) ),
inference(resolution,[],[f460,f116]) ).
fof(f460,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X2,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f424,f118]) ).
fof(f424,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,or(X1,X2)))
| ~ is_a_theorem(implies(X0,X2)) ),
inference(forward_demodulation,[],[f423,f109]) ).
fof(f423,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,or(X1,X2)))
| ~ is_a_theorem(or(not(X0),X2)) ),
inference(superposition,[],[f367,f109]) ).
fof(f367,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,or(X1,X2)))
| ~ is_a_theorem(or(X0,X2)) ),
inference(resolution,[],[f248,f127]) ).
fof(f127,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f118,f115]) ).
fof(f55819,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(implies(not(X0),X1),X1))),
inference(resolution,[],[f7892,f7829]) ).
fof(f7829,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[],[f5862,f415]) ).
fof(f415,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(forward_demodulation,[],[f411,f109]) ).
fof(f411,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,or(not(X0),X2)))),
inference(superposition,[],[f253,f109]) ).
fof(f253,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,implies(X0,X1)),implies(X0,or(X2,X1)))),
inference(forward_demodulation,[],[f249,f109]) ).
fof(f249,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,implies(X0,X1)),or(not(X0),or(X2,X1)))),
inference(superposition,[],[f120,f109]) ).
fof(f5862,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X0),X1))
| is_a_theorem(X1) ),
inference(superposition,[],[f2736,f4516]) ).
fof(f4516,plain,
! [X0] : implies(X0,X0) = equiv(X0,X0),
inference(subsumption_resolution,[],[f4498,f2323]) ).
fof(f2323,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f2154,f115]) ).
fof(f2154,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f372,f1025]) ).
fof(f372,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,or(X1,X2))) ),
inference(forward_demodulation,[],[f370,f109]) ).
fof(f370,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| is_a_theorem(or(X1,or(not(X0),X2))) ),
inference(superposition,[],[f248,f109]) ).
fof(f4498,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,X0))
| implies(X0,X0) = equiv(X0,X0) ),
inference(resolution,[],[f4447,f220]) ).
fof(f220,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[],[f217,f112]) ).
fof(f217,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(forward_demodulation,[],[f216,f134]) ).
fof(f134,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[],[f110,f109]) ).
fof(f216,plain,
! [X0] : is_a_theorem(implies(X0,not(implies(X0,not(X0))))),
inference(forward_demodulation,[],[f210,f109]) ).
fof(f210,plain,
! [X0] : is_a_theorem(implies(X0,not(or(not(X0),not(X0))))),
inference(resolution,[],[f180,f114]) ).
fof(f180,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[],[f137,f109]) ).
fof(f137,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f126,f109]) ).
fof(f126,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X0))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f118,f116]) ).
fof(f4447,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| X0 = X1 ),
inference(resolution,[],[f4078,f117]) ).
fof(f4078,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X0)) ),
inference(superposition,[],[f3185,f112]) ).
fof(f3185,plain,
! [X2,X0,X1] :
( is_a_theorem(and(implies(X0,X1),X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(resolution,[],[f2673,f2058]) ).
fof(f2058,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X1,X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f2041,f172]) ).
fof(f172,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f124,f118]) ).
fof(f124,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(superposition,[],[f116,f109]) ).
fof(f2041,plain,
! [X0,X1] :
( is_a_theorem(or(and(X0,X1),not(X0)))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f2016,f118]) ).
fof(f2016,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(and(X1,X0),not(X1)))),
inference(resolution,[],[f371,f289]) ).
fof(f289,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))),
inference(forward_demodulation,[],[f264,f109]) ).
fof(f264,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),or(not(X1),not(X0)))),
inference(superposition,[],[f123,f156]) ).
fof(f156,plain,
! [X2,X0,X1] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[],[f109,f134]) ).
fof(f123,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[],[f116,f109]) ).
fof(f371,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,implies(X0,X1)))
| is_a_theorem(implies(X0,or(X2,X1))) ),
inference(forward_demodulation,[],[f369,f109]) ).
fof(f369,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,implies(X0,X1)))
| is_a_theorem(or(not(X0),or(X2,X1))) ),
inference(superposition,[],[f248,f109]) ).
fof(f2673,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X1,X2),X0))
| is_a_theorem(X0)
| ~ is_a_theorem(X2) ),
inference(resolution,[],[f2624,f516]) ).
fof(f516,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,implies(X1,X2)))
| ~ is_a_theorem(X2) ),
inference(resolution,[],[f460,f122]) ).
fof(f122,plain,
! [X0,X1] : is_a_theorem(implies(X1,implies(X0,X1))),
inference(superposition,[],[f115,f109]) ).
fof(f2624,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X0))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f2321,f118]) ).
fof(f2321,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),X0))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f2154,f228]) ).
fof(f228,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X0,X2)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f119,f118]) ).
fof(f2736,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(subsumption_resolution,[],[f2676,f2323]) ).
fof(f2676,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(equiv(X1,X1),X0))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(resolution,[],[f2624,f526]) ).
fof(f526,plain,
! [X0,X1] :
( is_a_theorem(or(X0,equiv(X1,X1)))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(resolution,[],[f460,f220]) ).
fof(f7892,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f7831,f313]) ).
fof(f313,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X2,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f228,f118]) ).
fof(f7831,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(resolution,[],[f5862,f123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL498+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 29 22:56:33 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % (5806)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.35 % (5809)WARNING: value z3 for option sas not known
% 0.17/0.35 % (5811)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)
% 0.17/0.35 % (5808)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.35 % (5807)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.35 % (5812)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)
% 0.17/0.35 % (5810)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.35 % (5809)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)
% 0.17/0.35 % (5813)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)
% 0.17/0.36 TRYING [1]
% 0.17/0.36 TRYING [2]
% 0.17/0.36 TRYING [1]
% 0.17/0.36 TRYING [3]
% 0.17/0.36 TRYING [2]
% 0.17/0.37 TRYING [3]
% 0.17/0.37 TRYING [4]
% 0.17/0.39 TRYING [4]
% 0.17/0.41 TRYING [5]
% 0.17/0.48 TRYING [5]
% 0.17/0.54 TRYING [6]
% 4.24/0.95 TRYING [6]
% 4.81/1.04 TRYING [7]
% 7.24/1.45 TRYING [1]
% 7.24/1.45 TRYING [2]
% 7.24/1.46 TRYING [3]
% 7.93/1.47 TRYING [4]
% 8.17/1.51 TRYING [5]
% 9.45/1.69 TRYING [6]
% 14.35/2.45 TRYING [7]
% 18.97/3.05 TRYING [8]
% 34.76/5.35 TRYING [8]
% 55.96/8.41 TRYING [7]
% 59.76/8.88 TRYING [9]
% 64.55/9.58 % (5809)First to succeed.
% 64.55/9.60 % (5809)Refutation found. Thanks to Tanya!
% 64.55/9.60 % SZS status Theorem for theBenchmark
% 64.55/9.60 % SZS output start Proof for theBenchmark
% See solution above
% 64.55/9.60 % (5809)------------------------------
% 64.55/9.60 % (5809)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 64.55/9.60 % (5809)Termination reason: Refutation
% 64.55/9.60
% 64.55/9.60 % (5809)Memory used [KB]: 45864
% 64.55/9.60 % (5809)Time elapsed: 9.225 s
% 64.55/9.60 % (5809)Instructions burned: 29138 (million)
% 64.55/9.60 % (5809)------------------------------
% 64.55/9.60 % (5809)------------------------------
% 64.55/9.60 % (5806)Success in time 9.223 s
%------------------------------------------------------------------------------