%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL539+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 11:58:53 AM UTC 2026
% Result : Theorem 0.15s 0.51s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 37
% Syntax : Number of formulae : 154 ( 50 unt; 19 def)
% Number of atoms : 365 ( 24 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 380 ( 169 ~; 166 |; 4 &)
% ( 26 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 29 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 107 !; 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/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_3) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
fof(f53,axiom,
( substitution_strict_equiv
<=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',substitution_strict_equiv) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(f76,axiom,
( op_strict_equiv
=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_equiv) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_axiom_M) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f89,conjecture,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f90,negated_conjecture,
~ substitution_strict_equiv,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ substitution_strict_equiv,
inference(flattening,[],[f90]) ).
fof(f94,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f96,plain,
( ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 )
=> substitution_strict_equiv ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f98,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f105,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f106,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f111,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f112,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(f117,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f112]) ).
fof(f118,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f111]) ).
fof(f124,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f106]) ).
fof(f125,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f105]) ).
fof(f132,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f98]) ).
fof(f137,plain,
( substitution_strict_equiv
| ? [X0,X1] :
( X0 != X1
& is_a_theorem(strict_equiv(X0,X1)) ) ),
inference(ennf_transformation,[],[f96]) ).
fof(f139,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f94]) ).
fof(f143,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f144,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f76]) ).
fof(f145,plain,
( substitution_strict_equiv
| ( sK0 != sK1
& is_a_theorem(strict_equiv(sK0,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f137]) ).
fof(f146,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f118]) ).
fof(f147,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f119]) ).
fof(f152,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f153,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f160,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f132]) ).
fof(f167,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f172,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f173,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f180,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f181,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f183,plain,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(sK0,sK1)) ),
inference(cnf_transformation,[],[f145]) ).
fof(f184,plain,
( substitution_strict_equiv
| sK0 != sK1 ),
inference(cnf_transformation,[],[f145]) ).
fof(f186,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f139]) ).
fof(f190,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f143]) ).
fof(f191,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f144]) ).
fof(f195,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f200,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f202,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f88]) ).
fof(f203,plain,
~ substitution_strict_equiv,
inference(cnf_transformation,[],[f91]) ).
fof(f205,definition,
( spl2_1
<=> op_strict_equiv ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f209,definition,
( spl2_2
<=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f210,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f211,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f191,f209,f205]) ).
fof(f213,definition,
( spl2_3
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f217,definition,
( spl2_4
<=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f218,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f219,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f190,f217,f213]) ).
fof(f245,definition,
( spl2_11
<=> axiom_M ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f249,definition,
( spl2_12
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f250,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( ~ spl2_11
| spl2_12 ),
inference(avatar_split_clause,[],[f186,f249,f245]) ).
fof(f261,definition,
( spl2_15
<=> is_a_theorem(strict_equiv(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f263,plain,
( is_a_theorem(strict_equiv(sK0,sK1))
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f265,definition,
( spl2_16
<=> substitution_strict_equiv ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f268,plain,
( spl2_15
| spl2_16 ),
inference(avatar_split_clause,[],[f183,f265,f261]) ).
fof(f270,definition,
( spl2_17
<=> sK0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f272,plain,
( sK0 != sK1
| spl2_17 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,plain,
( ~ spl2_17
| spl2_16 ),
inference(avatar_split_clause,[],[f184,f265,f270]) ).
fof(f307,definition,
( spl2_26
<=> equivalence_3 ),
introduced(definition,[new_symbols(definition,[spl2_26])],[avatar_definition]) ).
fof(f311,definition,
( spl2_27
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl2_27])],[avatar_definition]) ).
fof(f312,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f313,plain,
( ~ spl2_26
| spl2_27 ),
inference(avatar_split_clause,[],[f160,f311,f307]) ).
fof(f363,definition,
( spl2_40
<=> and_2 ),
introduced(definition,[new_symbols(definition,[spl2_40])],[avatar_definition]) ).
fof(f367,definition,
( spl2_41
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
introduced(definition,[new_symbols(definition,[spl2_41])],[avatar_definition]) ).
fof(f368,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ spl2_41 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f369,plain,
( ~ spl2_40
| spl2_41 ),
inference(avatar_split_clause,[],[f153,f367,f363]) ).
fof(f371,definition,
( spl2_42
<=> and_1 ),
introduced(definition,[new_symbols(definition,[spl2_42])],[avatar_definition]) ).
fof(f375,definition,
( spl2_43
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_43])],[avatar_definition]) ).
fof(f376,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_43 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f377,plain,
( ~ spl2_42
| spl2_43 ),
inference(avatar_split_clause,[],[f152,f375,f371]) ).
fof(f411,definition,
( spl2_52
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[spl2_52])],[avatar_definition]) ).
fof(f415,definition,
( spl2_53
<=> ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_53])],[avatar_definition]) ).
fof(f416,plain,
( ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 )
| ~ spl2_53 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f417,plain,
( ~ spl2_52
| spl2_53 ),
inference(avatar_split_clause,[],[f147,f415,f411]) ).
fof(f419,definition,
( spl2_54
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl2_54])],[avatar_definition]) ).
fof(f423,definition,
( spl2_55
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_55])],[avatar_definition]) ).
fof(f424,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl2_55 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f425,plain,
( ~ spl2_54
| spl2_55 ),
inference(avatar_split_clause,[],[f146,f423,f419]) ).
fof(f426,plain,
~ spl2_16,
inference(avatar_split_clause,[],[f203,f265]) ).
fof(f430,plain,
spl2_54,
inference(avatar_split_clause,[],[f167,f419]) ).
fof(f435,plain,
spl2_42,
inference(avatar_split_clause,[],[f172,f371]) ).
fof(f436,plain,
spl2_40,
inference(avatar_split_clause,[],[f173,f363]) ).
fof(f443,plain,
spl2_26,
inference(avatar_split_clause,[],[f180,f307]) ).
fof(f444,plain,
spl2_52,
inference(avatar_split_clause,[],[f181,f411]) ).
fof(f448,plain,
spl2_11,
inference(avatar_split_clause,[],[f195,f245]) ).
fof(f451,plain,
spl2_3,
inference(avatar_split_clause,[],[f200,f213]) ).
fof(f452,plain,
spl2_1,
inference(avatar_split_clause,[],[f202,f205]) ).
fof(f464,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X1) )
| ~ spl2_41
| ~ spl2_55 ),
inference(resolution,[],[f424,f368]) ).
fof(f465,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X0) )
| ~ spl2_43
| ~ spl2_55 ),
inference(resolution,[],[f424,f376]) ).
fof(f466,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) )
| ~ spl2_12
| ~ spl2_55 ),
inference(resolution,[],[f424,f250]) ).
fof(f473,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_4
| ~ spl2_12
| ~ spl2_55 ),
inference(superposition,[],[f466,f218]) ).
fof(f504,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X1,X0)) )
| ~ spl2_2
| ~ spl2_41
| ~ spl2_55 ),
inference(superposition,[],[f464,f210]) ).
fof(f506,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) )
| ~ spl2_2
| ~ spl2_43
| ~ spl2_55 ),
inference(superposition,[],[f465,f210]) ).
fof(f523,plain,
( ! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl2_27
| ~ spl2_55 ),
inference(resolution,[],[f312,f424]) ).
fof(f706,plain,
( is_a_theorem(strict_implies(sK1,sK0))
| ~ spl2_2
| ~ spl2_15
| ~ spl2_41
| ~ spl2_55 ),
inference(resolution,[],[f504,f263]) ).
fof(f728,plain,
( is_a_theorem(implies(sK1,sK0))
| ~ spl2_2
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| ~ spl2_41
| ~ spl2_55 ),
inference(resolution,[],[f706,f473]) ).
fof(f897,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) )
| ~ spl2_27
| ~ spl2_55 ),
inference(resolution,[],[f523,f424]) ).
fof(f943,plain,
( is_a_theorem(strict_implies(sK0,sK1))
| ~ spl2_2
| ~ spl2_15
| ~ spl2_43
| ~ spl2_55 ),
inference(resolution,[],[f506,f263]) ).
fof(f1016,plain,
( is_a_theorem(implies(sK0,sK1))
| ~ spl2_2
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| ~ spl2_43
| ~ spl2_55 ),
inference(resolution,[],[f943,f473]) ).
fof(f2800,plain,
( ~ is_a_theorem(implies(sK0,sK1))
| is_a_theorem(equiv(sK0,sK1))
| ~ spl2_2
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| ~ spl2_27
| ~ spl2_41
| ~ spl2_55 ),
inference(resolution,[],[f897,f728]) ).
fof(f2804,plain,
( is_a_theorem(equiv(sK0,sK1))
| ~ spl2_2
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| ~ spl2_27
| ~ spl2_41
| ~ spl2_43
| ~ spl2_55 ),
inference(forward_subsumption_resolution,[],[f2800,f1016]) ).
fof(f2830,plain,
( sK0 = sK1
| ~ spl2_2
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| ~ spl2_27
| ~ spl2_41
| ~ spl2_43
| ~ spl2_53
| ~ spl2_55 ),
inference(resolution,[],[f2804,f416]) ).
fof(f2831,plain,
( $false
| ~ spl2_2
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| spl2_17
| ~ spl2_27
| ~ spl2_41
| ~ spl2_43
| ~ spl2_53
| ~ spl2_55 ),
inference(forward_subsumption_resolution,[],[f2830,f272]) ).
fof(f2832,plain,
( ~ spl2_2
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| spl2_17
| ~ spl2_27
| ~ spl2_41
| ~ spl2_43
| ~ spl2_53
| ~ spl2_55 ),
inference(avatar_contradiction_clause,[],[f2831]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f211]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f219]) ).
cnf(s6,plain,
( ~ spl2_11
| spl2_12 ),
inference(sat_conversion,[],[f251]) ).
cnf(s8,plain,
( spl2_15
| spl2_16 ),
inference(sat_conversion,[],[f268]) ).
cnf(s9,plain,
( spl2_16
| ~ spl2_17 ),
inference(sat_conversion,[],[f273]) ).
cnf(s14,plain,
( ~ spl2_26
| spl2_27 ),
inference(sat_conversion,[],[f313]) ).
cnf(s21,plain,
( ~ spl2_40
| spl2_41 ),
inference(sat_conversion,[],[f369]) ).
cnf(s22,plain,
( ~ spl2_42
| spl2_43 ),
inference(sat_conversion,[],[f377]) ).
cnf(s27,plain,
( ~ spl2_52
| spl2_53 ),
inference(sat_conversion,[],[f417]) ).
cnf(s28,plain,
( ~ spl2_54
| spl2_55 ),
inference(sat_conversion,[],[f425]) ).
cnf(s29,plain,
~ spl2_16,
inference(sat_conversion,[],[f426]) ).
cnf(s33,plain,
spl2_54,
inference(sat_conversion,[],[f430]) ).
cnf(s38,plain,
spl2_42,
inference(sat_conversion,[],[f435]) ).
cnf(s39,plain,
spl2_40,
inference(sat_conversion,[],[f436]) ).
cnf(s46,plain,
spl2_26,
inference(sat_conversion,[],[f443]) ).
cnf(s47,plain,
spl2_52,
inference(sat_conversion,[],[f444]) ).
cnf(s51,plain,
spl2_11,
inference(sat_conversion,[],[f448]) ).
cnf(s56,plain,
spl2_3,
inference(sat_conversion,[],[f451]) ).
cnf(s58,plain,
spl2_1,
inference(sat_conversion,[],[f452]) ).
cnf(s70,plain,
( ~ spl2_2
| ~ spl2_4
| ~ spl2_12
| ~ spl2_15
| spl2_17
| ~ spl2_27
| ~ spl2_41
| ~ spl2_43
| ~ spl2_53
| ~ spl2_55 ),
inference(sat_conversion,[],[f2832]) ).
cnf(s71,plain,
spl2_55,
inference(rat,[],[s28,s33]) ).
cnf(s72,plain,
spl2_53,
inference(rat,[],[s27,s47]) ).
cnf(s77,plain,
spl2_43,
inference(rat,[],[s22,s38]) ).
cnf(s78,plain,
spl2_41,
inference(rat,[],[s21,s39]) ).
cnf(s85,plain,
spl2_27,
inference(rat,[],[s14,s46]) ).
cnf(s90,plain,
~ spl2_17,
inference(rat,[],[s9,s29]) ).
cnf(s91,plain,
spl2_15,
inference(rat,[],[s8,s29]) ).
cnf(s93,plain,
spl2_12,
inference(rat,[],[s6,s51]) ).
cnf(s97,plain,
spl2_4,
inference(rat,[],[s2,s56]) ).
cnf(s98,plain,
~ spl2_2,
inference(rat,[],[s70,s71,s72,s77,s78,s85,s90,s91,s93,s97]) ).
cnf(s99,plain,
$false,
inference(rat,[],[s1,s98,s58]) ).
fof(f2833,plain,
$false,
inference(avatar_sat_refutation,[],[s99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL539+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:58:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.51 % (4170410)Will run a generic schedule for satisfiability detection.
% 0.15/0.51 % (4170419)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3521780783:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.51 % (4170416)% WARNING: option uhcvi not known.
% 0.15/0.51 % (4170415)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3849360786_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.51 % (4170416)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2346576098:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.51 % (4170417)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2589540414:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.51 % (4170418)dis+10_1_sil=32000:sp=arity:random_seed=1509571619:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.51 % (4170420)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3764185207:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.51 % (4170421)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2168605564:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.51 % TRYING [1]
% 0.15/0.51 % TRYING [2]
% 0.15/0.51 % TRYING [3]
% 0.15/0.51 % TRYING [4]
% 0.15/0.51 % (4170419)Instruction limit reached!
% 0.15/0.51 % (4170419)------------------------------
% 0.15/0.51 % (4170419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.51 % (4170419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.51 % (4170419)CaDiCaL version: 2.1.3
% 0.15/0.51 % (4170419)Termination reason: Instruction limit
% 0.15/0.51 % (4170419)Termination phase: Saturation
% 0.15/0.51 % (4170419)Time elapsed: 0.043 s
% 0.15/0.51 % (4170419)Peak memory usage: 13 MB
% 0.15/0.51 % (4170419)Instructions burned: 118 (million)
% 0.15/0.51 % (4170429)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=274635453:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.15/0.51 % TRYING [1]
% 0.15/0.51 % TRYING [2]
% 0.15/0.51 % TRYING [3]
% 0.15/0.51 % TRYING [4]
% 0.15/0.51 % (4170418) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4170410-4170418"...
% 0.15/0.51 % (4170418)...printing done.
% 0.15/0.51 % (4170418)Refutation found. Thanks to Tanya!
% 0.15/0.51 % SZS status Theorem for theBenchmark
% 0.15/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.51 % (4170418)------------------------------
% 0.15/0.51 % (4170418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.51 % (4170418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.51 % (4170418)CaDiCaL version: 2.1.3
% 0.15/0.51 % (4170418)Termination reason: Refutation
% 0.15/0.51 % (4170418)Time elapsed: 0.059 s
% 0.15/0.51 % (4170418)Peak memory usage: 14 MB
% 0.15/0.51 % (4170418)Instructions burned: 89 (million)
% 0.15/0.51 % (4170410)Success in time 0.099 s
% 0.15/0.51 % Vampire exiting
%------------------------------------------------------------------------------