%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL507+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:52:38 AM UTC 2026
% Result : Theorem 8.24s 2.11s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 18
% Syntax : Number of formulae : 143 ( 63 unt; 0 def)
% Number of atoms : 250 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 197 ( 90 ~; 86 |; 2 &)
% ( 6 <=>; 13 =>; 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 : 246 ( 244 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
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(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
fof(f18,axiom,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn3) ).
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(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(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(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',use_substitution_of_equivalents) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f44,negated_conjecture,
~ and_2,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ and_2,
inference(flattening,[],[f44]) ).
fof(f46,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,[],[f18]) ).
fof(f47,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f48,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
=> and_2 ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f50,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f51,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f54,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f51]) ).
fof(f55,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f50]) ).
fof(f57,plain,
( and_2
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X1)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f58,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(ennf_transformation,[],[f48]) ).
fof(f59,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f47]) ).
fof(f60,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(ennf_transformation,[],[f46]) ).
fof(f61,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f62,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,plain,
( and_2
| ~ is_a_theorem(implies(and(sK0,sK1),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f57]) ).
fof(f65,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f55]) ).
fof(f66,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f56]) ).
fof(f67,plain,
( and_2
| ~ is_a_theorem(implies(and(sK0,sK1),sK1)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f68,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f69,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f78,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f81,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f82,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
~ and_2,
inference(cnf_transformation,[],[f45]) ).
fof(f86,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[],[f73,f84]) ).
fof(f87,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[],[f72,f83]) ).
fof(f88,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[],[f71,f82]) ).
fof(f89,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(forward_subsumption_resolution,[],[f70,f80]) ).
fof(f90,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[],[f69,f79]) ).
fof(f91,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[],[f68,f78]) ).
fof(f92,plain,
~ is_a_theorem(implies(and(sK0,sK1),sK1)),
inference(forward_subsumption_resolution,[],[f67,f85]) ).
fof(f93,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f66,f81]) ).
fof(f94,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[],[f65,f77]) ).
fof(f95,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_demodulation,[],[f88,f87]) ).
fof(f97,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X0),implies(implies(X0,X1),not(and(not(X1),X2))))),
inference(superposition,[],[f89,f87]) ).
fof(f98,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),implies(not(and(X2,X0)),implies(X0,X1)))),
inference(superposition,[],[f89,f87]) ).
fof(f99,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X1),X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f98,f95]) ).
fof(f100,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,X0),implies(X0,X1)))),
inference(forward_demodulation,[],[f99,f95]) ).
fof(f101,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[],[f95,f87]) ).
fof(f102,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X0),or(and(X0,X1),not(and(X1,X2))))),
inference(superposition,[],[f89,f95]) ).
fof(f103,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f91,f95]) ).
fof(f107,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f94,f91]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(not(and(X1,X2)),not(and(X2,X0)))) ),
inference(resolution,[],[f94,f89]) ).
fof(f110,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0))
| is_a_theorem(X1) ),
inference(superposition,[],[f94,f95]) ).
fof(f111,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f109,f95]) ).
fof(f113,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),or(and(X2,not(X0)),or(X0,X1)))),
inference(superposition,[],[f100,f95]) ).
fof(f114,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(forward_demodulation,[],[f113,f101]) ).
fof(f115,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f114,f94]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f115,f94]) ).
fof(f139,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),not(and(not(X2),X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f97,f94]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(not(and(not(X2),X0))) ),
inference(resolution,[],[f139,f94]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(not(and(not(X1),X0))) ),
inference(resolution,[],[f148,f90]) ).
fof(f164,plain,
! [X0] : is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[],[f159,f91]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(not(and(not(X1),not(X0)))) ),
inference(superposition,[],[f159,f95]) ).
fof(f168,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(not(X1),X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(forward_demodulation,[],[f167,f87]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(forward_demodulation,[],[f168,f95]) ).
fof(f171,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[],[f164,f87]) ).
fof(f172,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f171,f95]) ).
fof(f173,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f172,f119]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(not(X0),X2))
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[],[f173,f119]) ).
fof(f177,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,[],[f175,f95]) ).
fof(f183,plain,
! [X0,X1] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(resolution,[],[f169,f172]) ).
fof(f188,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[],[f183,f87]) ).
fof(f191,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| is_a_theorem(or(X2,X0)) ),
inference(resolution,[],[f188,f119]) ).
fof(f201,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(and(not(X0),not(X0)),X1)) ),
inference(resolution,[],[f103,f177]) ).
fof(f205,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f201,f101]) ).
fof(f206,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f205,f95]) ).
fof(f208,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(resolution,[],[f206,f94]) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(and(X0,X1)))
| is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f110,f111]) ).
fof(f228,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f110,f188]) ).
fof(f245,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(and(X0,X1))) ),
inference(resolution,[],[f223,f164]) ).
fof(f248,plain,
! [X0,X1] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X1)) ),
inference(resolution,[],[f245,f228]) ).
fof(f253,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(superposition,[],[f245,f95]) ).
fof(f254,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f253,f87]) ).
fof(f256,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,X1),and(X2,X0)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(resolution,[],[f254,f111]) ).
fof(f257,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[],[f254,f172]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(X2,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X2)) ),
inference(resolution,[],[f256,f94]) ).
fof(f268,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f257,f94]) ).
fof(f272,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f263,f107]) ).
fof(f315,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f248,f87]) ).
fof(f316,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f315,f268]) ).
fof(f320,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f316,f272]) ).
fof(f325,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f316,f191]) ).
fof(f329,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[],[f325,f177]) ).
fof(f341,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[],[f320,f86]) ).
fof(f345,plain,
! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(resolution,[],[f341,f257]) ).
fof(f351,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,and(X0,X1)))
| is_a_theorem(equiv(X0,and(X0,X1))) ),
inference(resolution,[],[f341,f90]) ).
fof(f359,plain,
! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(forward_demodulation,[],[f345,f95]) ).
fof(f362,plain,
! [X0] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[],[f359,f172]) ).
fof(f444,plain,
! [X0] : is_a_theorem(equiv(X0,and(X0,X0))),
inference(resolution,[],[f351,f91]) ).
fof(f589,plain,
! [X0] : not(not(X0)) = X0,
inference(resolution,[],[f93,f362]) ).
fof(f591,plain,
! [X0] : and(X0,X0) = X0,
inference(resolution,[],[f93,f444]) ).
fof(f601,plain,
! [X0,X1] : implies(X1,not(X0)) = not(and(X1,X0)),
inference(superposition,[],[f87,f589]) ).
fof(f602,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(superposition,[],[f95,f589]) ).
fof(f607,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[],[f172,f589]) ).
fof(f642,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,X0),or(X0,implies(X0,X1)))),
inference(superposition,[],[f100,f591]) ).
fof(f701,plain,
! [X0] : not(X0) = implies(X0,not(X0)),
inference(superposition,[],[f601,f591]) ).
fof(f772,plain,
! [X2,X0,X1] : implies(and(X0,X1),X2) = or(implies(X0,not(X1)),X2),
inference(superposition,[],[f602,f601]) ).
fof(f1004,plain,
! [X0] : is_a_theorem(implies(or(not(X0),X0),or(X0,not(X0)))),
inference(superposition,[],[f642,f701]) ).
fof(f1007,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),or(X0,not(X0)))),
inference(forward_demodulation,[],[f1004,f602]) ).
fof(f1020,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),or(not(X0),not(not(X0))))),
inference(superposition,[],[f1007,f95]) ).
fof(f1030,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,not(not(X0))))),
inference(forward_demodulation,[],[f1020,f602]) ).
fof(f1039,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),implies(X0,X0))),
inference(forward_demodulation,[],[f1030,f589]) ).
fof(f1045,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,not(X0)))
| is_a_theorem(or(X1,implies(X0,X0))) ),
inference(resolution,[],[f1039,f329]) ).
fof(f1063,plain,
! [X0,X1] : is_a_theorem(or(X1,implies(X0,X0))),
inference(forward_subsumption_resolution,[],[f1045,f607]) ).
fof(f1073,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X0),X1))
| is_a_theorem(X1) ),
inference(resolution,[],[f1063,f208]) ).
fof(f1129,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),not(and(X1,X0)))),
inference(resolution,[],[f1073,f102]) ).
fof(f1147,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))),
inference(forward_demodulation,[],[f1129,f601]) ).
fof(f1181,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(and(X0,X1),X2))
| is_a_theorem(or(implies(X1,not(X0)),X2)) ),
inference(resolution,[],[f1147,f177]) ).
fof(f1196,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(and(X0,X1),X2))
| is_a_theorem(implies(and(X1,X0),X2)) ),
inference(forward_demodulation,[],[f1181,f772]) ).
fof(f1199,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(resolution,[],[f1196,f90]) ).
fof(f1218,plain,
$false,
inference(resolution,[],[f1199,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL507+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 % Computer : n016.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8046.5625MB
% 0.11/0.42 % OS : Linux 6.8.0-71-generic
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Sun Sep 27 15:58:48 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.45 Running first-order theorem proving
% 0.11/0.45 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.24/2.11 % (2810053)Detected formulas, will run a generic FOF schedule.
% 8.24/2.11 % (2810061)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3529763109:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.24/2.11 % (2810061)Refutation not found, incomplete strategy
% 8.24/2.11 % (2810061)------------------------------
% 8.24/2.11 % (2810061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810061)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810061)Termination reason: Refutation not found, incomplete strategy
% 8.24/2.11 % (2810061)Time elapsed: 0.0000 s
% 8.24/2.11 % (2810061)Peak memory usage: 87 MB
% 8.24/2.11 % (2810062)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1956236977:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.24/2.11 % (2810064)dis-21_1_sil=8000:lcm=predicate:random_seed=1642512986:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 8.24/2.11 % (2810063)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2774551745:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.24/2.11 % (2810058)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=753750336:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.24/2.11 % (2810060)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4002647180:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.24/2.11 % (2810059)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3786218620:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.24/2.11 % (2810062)Refutation not found, incomplete strategy
% 8.24/2.11 % (2810062)------------------------------
% 8.24/2.11 % (2810062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810062)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810062)Termination reason: Refutation not found, incomplete strategy
% 8.24/2.11 % (2810062)Time elapsed: 0.001 s
% 8.24/2.11 % (2810062)Peak memory usage: 86 MB
% 8.24/2.11 % (2810064)Refutation not found, incomplete strategy
% 8.24/2.11 % (2810064)------------------------------
% 8.24/2.11 % (2810064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810064)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810064)Termination reason: Refutation not found, incomplete strategy
% 8.24/2.11 % (2810064)Time elapsed: 0.002 s
% 8.24/2.11 % (2810064)Peak memory usage: 88 MB
% 8.24/2.11 % (2810064)Instructions burned: 1 (million)
% 8.24/2.11 % (2810063)Instruction limit reached!
% 8.24/2.11 % (2810063)------------------------------
% 8.24/2.11 % (2810063)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810063)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810063)Termination reason: Instruction limit
% 8.24/2.11 % (2810063)Termination phase: Saturation
% 8.24/2.11 % (2810063)Time elapsed: 0.091 s
% 8.24/2.11 % (2810063)Peak memory usage: 90 MB
% 8.24/2.11 % (2810063)Instructions burned: 140 (million)
% 8.24/2.11 % (2810061)------------------------------
% 8.24/2.11 % (2810061)------------------------------
% 8.24/2.11 % (2810073)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1788640692:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.24/2.11 % (2810073)Refutation not found, incomplete strategy
% 8.24/2.11 % (2810073)------------------------------
% 8.24/2.11 % (2810073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810073)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810073)Termination reason: Refutation not found, incomplete strategy
% 8.24/2.11 % (2810073)Time elapsed: 0.001 s
% 8.24/2.11 % (2810073)Peak memory usage: 87 MB
% 8.24/2.11 % (2810072)lrs+10_1_sil=8000:sp=occurrence:random_seed=561065782:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.24/2.11 % (2810072)Refutation not found, incomplete strategy
% 8.24/2.11 % (2810072)------------------------------
% 8.24/2.11 % (2810072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810072)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810072)Termination reason: Refutation not found, incomplete strategy
% 8.24/2.11 % (2810072)Time elapsed: 0.001 s
% 8.24/2.11 % (2810072)Peak memory usage: 87 MB
% 8.24/2.11 % (2810064)------------------------------
% 8.24/2.11 % (2810064)------------------------------
% 8.24/2.11 % (2810062)------------------------------
% 8.24/2.11 % (2810062)------------------------------
% 8.24/2.11 % (2810073)------------------------------
% 8.24/2.11 % (2810073)------------------------------
% 8.24/2.11 % (2810076)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2974047755:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 8.24/2.11 % (2810077)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3528107434:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 8.24/2.11 % (2810076)Refutation not found, incomplete strategy
% 8.24/2.11 % (2810076)------------------------------
% 8.24/2.11 % (2810076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810076)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810076)Termination reason: Refutation not found, incomplete strategy
% 8.24/2.11 % (2810076)Time elapsed: 0.001 s
% 8.24/2.11 % (2810076)Peak memory usage: 87 MB
% 8.24/2.11 % (2810072)------------------------------
% 8.24/2.11 % (2810072)------------------------------
% 8.24/2.11 % (2810078)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2968043946:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 8.24/2.11 % (2810078)Refutation not found, incomplete strategy
% 8.24/2.11 % (2810078)------------------------------
% 8.24/2.11 % (2810078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810078)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810078)Termination reason: Refutation not found, incomplete strategy
% 8.24/2.11 % (2810078)Time elapsed: 0.0000 s
% 8.24/2.11 % (2810078)Peak memory usage: 87 MB
% 8.24/2.11 % (2810060)Refutation not found, incomplete strategy
% 8.24/2.11 % (2810060)------------------------------
% 8.24/2.11 % (2810060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810060)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810060)Termination reason: Refutation not found, incomplete strategy
% 8.24/2.11 % (2810060)Time elapsed: 0.561 s
% 8.24/2.11 % (2810060)Peak memory usage: 125 MB
% 8.24/2.11 % (2810060)Instructions burned: 826 (million)
% 8.24/2.11 % (2810077)Instruction limit reached!
% 8.24/2.11 % (2810077)------------------------------
% 8.24/2.11 % (2810077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810077)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810077)Termination reason: Instruction limit
% 8.24/2.11 % (2810077)Termination phase: Saturation
% 8.24/2.11 % (2810077)Time elapsed: 0.164 s
% 8.24/2.11 % (2810077)Peak memory usage: 92 MB
% 8.24/2.11 % (2810077)Instructions burned: 249 (million)
% 8.24/2.11 % (2810081)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2112860849:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 8.24/2.11 % (2810076)------------------------------
% 8.24/2.11 % (2810076)------------------------------
% 8.24/2.11 % (2810078)------------------------------
% 8.24/2.11 % (2810078)------------------------------
% 8.24/2.11 % (2810083)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1812138524:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 8.24/2.11 % (2810083)Refutation not found, incomplete strategy
% 8.24/2.11 % (2810083)------------------------------
% 8.24/2.11 % (2810083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810083)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810083)Termination reason: Refutation not found, incomplete strategy
% 8.24/2.11 % (2810083)Time elapsed: 0.001 s
% 8.24/2.11 % (2810083)Peak memory usage: 88 MB
% 8.24/2.11 % (2810058)First to succeed.
% 8.24/2.11 % (2810058)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2810053"
% 8.24/2.11 % (2810060)------------------------------
% 8.24/2.11 % (2810060)------------------------------
% 8.24/2.11 % (2810086)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=379049124:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 8.24/2.11 % (2810086)Refutation not found, incomplete strategy
% 8.24/2.11 % (2810086)------------------------------
% 8.24/2.11 % (2810086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810086)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810086)Termination reason: Refutation not found, incomplete strategy
% 8.24/2.11 % (2810086)Time elapsed: 0.0000 s
% 8.24/2.11 % (2810086)Peak memory usage: 87 MB
% 8.24/2.11 % (2810085)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2329638785:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 8.24/2.11 % (2810085)Instruction limit reached!
% 8.24/2.11 % (2810085)------------------------------
% 8.24/2.11 % (2810085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.11 % (2810085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.11 % (2810085)CaDiCaL version: 2.1.3
% 8.24/2.11 % (2810085)Termination reason: Instruction limit
% 8.24/2.11 % (2810085)Termination phase: Saturation
% 8.24/2.11 % (2810085)Time elapsed: 0.069 s
% 8.24/2.11 % (2810085)Peak memory usage: 89 MB
% 8.24/2.11 % (2810085)Instructions burned: 128 (million)
% 8.24/2.11 % (2810086)------------------------------
% 8.24/2.11 % (2810086)------------------------------
% 8.24/2.11 % (2810090)lrs+10_1_sil=8000:sp=occurrence:random_seed=1874605519:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 8.24/2.11 % (2810083)------------------------------
% 8.24/2.11 % (2810083)------------------------------
% 8.24/2.11 % (2810058)Refutation found. Thanks to Tanya!
% 8.24/2.11 % SZS status Theorem for theBenchmark
% 8.24/2.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/2.30 % (2810058)------------------------------
% 0.17/2.30 % (2810058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.30 % (2810058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.30 % (2810058)CaDiCaL version: 2.1.3
% 0.17/2.30 % (2810058)Termination reason: Refutation
% 0.17/2.30 % (2810058)Time elapsed: 0.777 s
% 0.17/2.30 % (2810058)Peak memory usage: 128 MB
% 0.17/2.30 % (2810058)Instructions burned: 1137 (million)
% 0.17/2.30 % (2810058)------------------------------
% 0.17/2.30 % (2810058)------------------------------
% 0.17/2.30 % (2810053)Success in time 1.219 s
% 0.17/2.30 % Vampire exiting
%------------------------------------------------------------------------------