%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 11:58:43 AM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 44
% Syntax : Number of formulae : 180 ( 59 unt; 22 def)
% Number of atoms : 430 ( 20 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 458 ( 208 ~; 202 |; 2 &)
% ( 31 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 36 ( 34 usr; 34 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 145 ( 0 sgn 144 !; 1 ?)
% 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/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/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_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/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_3) ).
fof(f21,axiom,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_2) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
fof(f53,conjecture,
cn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn3) ).
fof(f54,negated_conjecture,
~ cn3,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ cn3,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0))
=> cn3 ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f57,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(f61,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f63,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f64,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f67,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f69,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f70,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f71,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(f75,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f71]) ).
fof(f76,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f70]) ).
fof(f78,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f69]) ).
fof(f80,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f67]) ).
fof(f83,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f64]) ).
fof(f84,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f63]) ).
fof(f86,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f61]) ).
fof(f90,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f57]) ).
fof(f91,plain,
( cn3
| ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(ennf_transformation,[],[f56]) ).
fof(f92,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f93,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f95,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f91]) ).
fof(f96,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f76]) ).
fof(f97,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f77]) ).
fof(f98,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f78]) ).
fof(f100,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f80]) ).
fof(f103,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f104,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f84]) ).
fof(f106,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f86]) ).
fof(f110,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f90]) ).
fof(f111,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f112,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f92]) ).
fof(f113,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f93]) ).
fof(f115,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f116,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f118,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f119,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f121,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f124,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f125,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f127,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f131,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f132,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f135,plain,
~ cn3,
inference(cnf_transformation,[],[f55]) ).
fof(f145,definition,
( spl1_3
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f149,definition,
( spl1_4
<=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f150,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f151,plain,
( ~ spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f113,f149,f145]) ).
fof(f153,definition,
( spl1_5
<=> op_or ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f157,definition,
( spl1_6
<=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f158,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( ~ spl1_5
| spl1_6 ),
inference(avatar_split_clause,[],[f112,f157,f153]) ).
fof(f161,definition,
( spl1_7
<=> is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f163,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| spl1_7 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f165,definition,
( spl1_8
<=> cn3 ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f168,plain,
( ~ spl1_7
| spl1_8 ),
inference(avatar_split_clause,[],[f111,f165,f161]) ).
fof(f170,definition,
( spl1_9
<=> equivalence_3 ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f174,definition,
( spl1_10
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f175,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f176,plain,
( ~ spl1_9
| spl1_10 ),
inference(avatar_split_clause,[],[f110,f174,f170]) ).
fof(f202,definition,
( spl1_17
<=> or_2 ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f206,definition,
( spl1_18
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_18])],[avatar_definition]) ).
fof(f207,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ spl1_18 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f208,plain,
( ~ spl1_17
| spl1_18 ),
inference(avatar_split_clause,[],[f106,f206,f202]) ).
fof(f218,definition,
( spl1_21
<=> and_3 ),
introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition]) ).
fof(f222,definition,
( spl1_22
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl1_22])],[avatar_definition]) ).
fof(f223,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( ~ spl1_21
| spl1_22 ),
inference(avatar_split_clause,[],[f104,f222,f218]) ).
fof(f226,definition,
( spl1_23
<=> and_2 ),
introduced(definition,[new_symbols(definition,[spl1_23])],[avatar_definition]) ).
fof(f230,definition,
( spl1_24
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
introduced(definition,[new_symbols(definition,[spl1_24])],[avatar_definition]) ).
fof(f231,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ spl1_24 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f232,plain,
( ~ spl1_23
| spl1_24 ),
inference(avatar_split_clause,[],[f103,f230,f226]) ).
fof(f250,definition,
( spl1_29
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[spl1_29])],[avatar_definition]) ).
fof(f254,definition,
( spl1_30
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_30])],[avatar_definition]) ).
fof(f255,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl1_30 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( ~ spl1_29
| spl1_30 ),
inference(avatar_split_clause,[],[f100,f254,f250]) ).
fof(f266,definition,
( spl1_33
<=> modus_tollens ),
introduced(definition,[new_symbols(definition,[spl1_33])],[avatar_definition]) ).
fof(f270,definition,
( spl1_34
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_34])],[avatar_definition]) ).
fof(f271,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ spl1_34 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f272,plain,
( ~ spl1_33
| spl1_34 ),
inference(avatar_split_clause,[],[f98,f270,f266]) ).
fof(f274,definition,
( spl1_35
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[spl1_35])],[avatar_definition]) ).
fof(f278,definition,
( spl1_36
<=> ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_36])],[avatar_definition]) ).
fof(f279,plain,
( ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 )
| ~ spl1_36 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f280,plain,
( ~ spl1_35
| spl1_36 ),
inference(avatar_split_clause,[],[f97,f278,f274]) ).
fof(f282,definition,
( spl1_37
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl1_37])],[avatar_definition]) ).
fof(f286,definition,
( spl1_38
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_38])],[avatar_definition]) ).
fof(f287,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl1_38 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f288,plain,
( ~ spl1_37
| spl1_38 ),
inference(avatar_split_clause,[],[f96,f286,f282]) ).
fof(f289,plain,
~ spl1_8,
inference(avatar_split_clause,[],[f135,f165]) ).
fof(f290,plain,
spl1_5,
inference(avatar_split_clause,[],[f115,f153]) ).
fof(f291,plain,
spl1_3,
inference(avatar_split_clause,[],[f116,f145]) ).
fof(f293,plain,
spl1_37,
inference(avatar_split_clause,[],[f118,f282]) ).
fof(f294,plain,
spl1_33,
inference(avatar_split_clause,[],[f119,f266]) ).
fof(f296,plain,
spl1_29,
inference(avatar_split_clause,[],[f121,f250]) ).
fof(f299,plain,
spl1_23,
inference(avatar_split_clause,[],[f124,f226]) ).
fof(f300,plain,
spl1_21,
inference(avatar_split_clause,[],[f125,f218]) ).
fof(f302,plain,
spl1_17,
inference(avatar_split_clause,[],[f127,f202]) ).
fof(f306,plain,
spl1_9,
inference(avatar_split_clause,[],[f131,f170]) ).
fof(f307,plain,
spl1_35,
inference(avatar_split_clause,[],[f132,f274]) ).
fof(f317,plain,
( ! [X0,X1] : or(X0,X1) = implies(not(X0),X1)
| ~ spl1_4
| ~ spl1_6 ),
inference(forward_demodulation,[],[f158,f150]) ).
fof(f326,plain,
( ! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X0))))
| ~ spl1_4
| ~ spl1_6
| ~ spl1_18 ),
inference(superposition,[],[f207,f317]) ).
fof(f328,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| ~ spl1_4
| ~ spl1_6
| spl1_7 ),
inference(superposition,[],[f163,f317]) ).
fof(f332,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl1_30
| ~ spl1_38 ),
inference(resolution,[],[f255,f287]) ).
fof(f337,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1)))
| ~ spl1_4
| ~ spl1_6
| ~ spl1_34 ),
inference(forward_demodulation,[],[f271,f317]) ).
fof(f340,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X1,not(not(X0))),or(X0,X1)))
| ~ spl1_4
| ~ spl1_6
| ~ spl1_34 ),
inference(superposition,[],[f337,f317]) ).
fof(f350,plain,
( ! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl1_10
| ~ spl1_38 ),
inference(resolution,[],[f175,f287]) ).
fof(f404,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ spl1_22
| ~ spl1_30
| ~ spl1_38 ),
inference(resolution,[],[f332,f223]) ).
fof(f418,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(X0,not(not(X1))))
| is_a_theorem(or(X1,X0)) )
| ~ spl1_4
| ~ spl1_6
| ~ spl1_34
| ~ spl1_38 ),
inference(resolution,[],[f340,f287]) ).
fof(f460,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) )
| ~ spl1_10
| ~ spl1_38 ),
inference(resolution,[],[f350,f287]) ).
fof(f883,plain,
( ! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) )
| ~ spl1_10
| ~ spl1_22
| ~ spl1_30
| ~ spl1_38 ),
inference(resolution,[],[f460,f404]) ).
fof(f894,plain,
( ! [X0] : is_a_theorem(equiv(and(X0,X0),X0))
| ~ spl1_10
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_38 ),
inference(forward_subsumption_resolution,[],[f883,f231]) ).
fof(f912,plain,
( ! [X0] : and(X0,X0) = X0
| ~ spl1_10
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_36
| ~ spl1_38 ),
inference(resolution,[],[f894,f279]) ).
fof(f968,plain,
( ! [X0] : implies(not(X0),X0) = not(not(X0))
| ~ spl1_4
| ~ spl1_10
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_36
| ~ spl1_38 ),
inference(superposition,[],[f150,f912]) ).
fof(f991,plain,
( ! [X0] : or(X0,X0) = not(not(X0))
| ~ spl1_4
| ~ spl1_6
| ~ spl1_10
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_36
| ~ spl1_38 ),
inference(forward_demodulation,[],[f968,f317]) ).
fof(f1104,plain,
( ! [X0] : is_a_theorem(or(X0,not(not(not(X0)))))
| ~ spl1_4
| ~ spl1_6
| ~ spl1_10
| ~ spl1_18
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_36
| ~ spl1_38 ),
inference(superposition,[],[f326,f991]) ).
fof(f1112,plain,
( ~ is_a_theorem(implies(not(not(sK0)),sK0))
| ~ spl1_4
| ~ spl1_6
| spl1_7
| ~ spl1_10
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_36
| ~ spl1_38 ),
inference(superposition,[],[f328,f991]) ).
fof(f1113,plain,
( ~ is_a_theorem(or(not(sK0),sK0))
| ~ spl1_4
| ~ spl1_6
| spl1_7
| ~ spl1_10
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_36
| ~ spl1_38 ),
inference(forward_demodulation,[],[f1112,f317]) ).
fof(f1211,plain,
( ! [X0] : is_a_theorem(or(not(X0),X0))
| ~ spl1_4
| ~ spl1_6
| ~ spl1_10
| ~ spl1_18
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_34
| ~ spl1_36
| ~ spl1_38 ),
inference(resolution,[],[f1104,f418]) ).
fof(f1219,plain,
( $false
| ~ spl1_4
| ~ spl1_6
| spl1_7
| ~ spl1_10
| ~ spl1_18
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_34
| ~ spl1_36
| ~ spl1_38 ),
inference(resolution,[],[f1211,f1113]) ).
fof(f1224,plain,
( ~ spl1_4
| ~ spl1_6
| spl1_7
| ~ spl1_10
| ~ spl1_18
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_34
| ~ spl1_36
| ~ spl1_38 ),
inference(avatar_contradiction_clause,[],[f1219]) ).
cnf(s2,plain,
( ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f151]) ).
cnf(s3,plain,
( ~ spl1_5
| spl1_6 ),
inference(sat_conversion,[],[f159]) ).
cnf(s4,plain,
( ~ spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f168]) ).
cnf(s5,plain,
( ~ spl1_9
| spl1_10 ),
inference(sat_conversion,[],[f176]) ).
cnf(s9,plain,
( ~ spl1_17
| spl1_18 ),
inference(sat_conversion,[],[f208]) ).
cnf(s11,plain,
( ~ spl1_21
| spl1_22 ),
inference(sat_conversion,[],[f224]) ).
cnf(s12,plain,
( ~ spl1_23
| spl1_24 ),
inference(sat_conversion,[],[f232]) ).
cnf(s15,plain,
( ~ spl1_29
| spl1_30 ),
inference(sat_conversion,[],[f256]) ).
cnf(s17,plain,
( ~ spl1_33
| spl1_34 ),
inference(sat_conversion,[],[f272]) ).
cnf(s18,plain,
( ~ spl1_35
| spl1_36 ),
inference(sat_conversion,[],[f280]) ).
cnf(s19,plain,
( ~ spl1_37
| spl1_38 ),
inference(sat_conversion,[],[f288]) ).
cnf(s20,plain,
~ spl1_8,
inference(sat_conversion,[],[f289]) ).
cnf(s21,plain,
spl1_5,
inference(sat_conversion,[],[f290]) ).
cnf(s22,plain,
spl1_3,
inference(sat_conversion,[],[f291]) ).
cnf(s24,plain,
spl1_37,
inference(sat_conversion,[],[f293]) ).
cnf(s25,plain,
spl1_33,
inference(sat_conversion,[],[f294]) ).
cnf(s27,plain,
spl1_29,
inference(sat_conversion,[],[f296]) ).
cnf(s30,plain,
spl1_23,
inference(sat_conversion,[],[f299]) ).
cnf(s31,plain,
spl1_21,
inference(sat_conversion,[],[f300]) ).
cnf(s33,plain,
spl1_17,
inference(sat_conversion,[],[f302]) ).
cnf(s37,plain,
spl1_9,
inference(sat_conversion,[],[f306]) ).
cnf(s38,plain,
spl1_35,
inference(sat_conversion,[],[f307]) ).
cnf(s43,plain,
( ~ spl1_4
| ~ spl1_6
| spl1_7
| ~ spl1_10
| ~ spl1_18
| ~ spl1_22
| ~ spl1_24
| ~ spl1_30
| ~ spl1_34
| ~ spl1_36
| ~ spl1_38 ),
inference(sat_conversion,[],[f1224]) ).
cnf(s44,plain,
spl1_38,
inference(rat,[],[s19,s24]) ).
cnf(s45,plain,
spl1_36,
inference(rat,[],[s18,s38]) ).
cnf(s46,plain,
spl1_34,
inference(rat,[],[s17,s25]) ).
cnf(s48,plain,
spl1_30,
inference(rat,[],[s15,s27]) ).
cnf(s51,plain,
spl1_24,
inference(rat,[],[s12,s30]) ).
cnf(s52,plain,
spl1_22,
inference(rat,[],[s11,s31]) ).
cnf(s54,plain,
spl1_18,
inference(rat,[],[s9,s33]) ).
cnf(s58,plain,
spl1_10,
inference(rat,[],[s5,s37]) ).
cnf(s59,plain,
~ spl1_7,
inference(rat,[],[s4,s20]) ).
cnf(s60,plain,
spl1_6,
inference(rat,[],[s3,s21]) ).
cnf(s61,plain,
~ spl1_4,
inference(rat,[],[s43,s44,s45,s46,s48,s51,s52,s54,s58,s59,s60]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s2,s61,s22]) ).
fof(f1225,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 15:45:00 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 Running first-order model finding
% 0.12/0.38 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 % (2200954)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (2200959)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4288398222_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.45 % TRYING [1]
% 0.12/0.45 % TRYING [2]
% 0.12/0.45 % TRYING [3]
% 0.12/0.45 % (2200960)% WARNING: option uhcvi not known.
% 0.12/0.45 % (2200961)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4079386606:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.45 % (2200960)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2061727363:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.45 % (2200962)dis+10_1_sil=32000:sp=arity:random_seed=1504808296:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.45 % TRYING [4]
% 0.12/0.45 % (2200963)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1458507711:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.45 % (2200964)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1676952524:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.45 % (2200965)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3560021129:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.45 % (2200962) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2200954-2200962"...
% 0.12/0.45 % TRYING [5]
% 0.12/0.45 % (2200962)...printing done.
% 0.12/0.45 % (2200962)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (2200962)------------------------------
% 0.12/0.46 % (2200962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (2200962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (2200962)CaDiCaL version: 2.1.3
% 0.12/0.46 % (2200962)Termination reason: Refutation
% 0.12/0.46 % (2200962)Time elapsed: 0.027 s
% 0.12/0.46 % (2200962)Peak memory usage: 13 MB
% 0.12/0.46 % (2200962)Instructions burned: 39 (million)
% 0.12/0.46 % (2200954)Success in time 0.061 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------