%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL537+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 11:58:53 AM UTC 2026
% Result : Theorem 3.94s 1.21s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 60
% Syntax : Number of formulae : 267 ( 90 unt; 30 def)
% Number of atoms : 685 ( 42 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 780 ( 362 ~; 355 |; 2 &)
% ( 42 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 48 ( 46 usr; 46 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 204 ( 0 sgn 203 !; 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(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_1) ).
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(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(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
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(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
fof(f56,axiom,
( axiom_4
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_4) ).
fof(f57,axiom,
( axiom_B
<=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_B) ).
fof(f58,axiom,
( axiom_5
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_5) ).
fof(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
fof(f77,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_op_possibly) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_M) ).
fof(f81,axiom,
axiom_4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_4) ).
fof(f82,axiom,
axiom_B,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_axiom_B) ).
fof(f83,conjecture,
axiom_5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(f84,negated_conjecture,
~ axiom_5,
inference(negated_conjecture,[status(cth)],[f83]) ).
fof(f85,plain,
~ axiom_5,
inference(flattening,[],[f84]) ).
fof(f86,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
=> axiom_5 ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f87,plain,
( axiom_B
=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f88,plain,
( axiom_4
=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f89,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f92,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(f97,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f98,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f99,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f102,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f104,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f105,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f106,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(f112,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f106]) ).
fof(f113,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f105]) ).
fof(f115,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f104]) ).
fof(f117,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f102]) ).
fof(f120,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f99]) ).
fof(f121,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f98]) ).
fof(f122,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f97]) ).
fof(f127,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f92]) ).
fof(f128,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f129,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f133,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f89]) ).
fof(f134,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(ennf_transformation,[],[f88]) ).
fof(f135,plain,
( ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(ennf_transformation,[],[f87]) ).
fof(f136,plain,
( axiom_5
| ? [X0] : ~ is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f86]) ).
fof(f137,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f73]) ).
fof(f138,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f139,plain,
! [X0,X1] :
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f114]) ).
fof(f140,plain,
! [X0,X1] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f115]) ).
fof(f142,plain,
! [X0,X1] :
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f117]) ).
fof(f145,plain,
! [X0,X1] :
( ~ and_2
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f146,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f121]) ).
fof(f147,plain,
! [X0,X1] :
( ~ or_1
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(cnf_transformation,[],[f122]) ).
fof(f152,plain,
! [X0,X1] :
( ~ equivalence_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(cnf_transformation,[],[f127]) ).
fof(f153,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f128]) ).
fof(f154,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f129]) ).
fof(f156,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f157,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f159,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f160,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f162,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f165,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f166,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f167,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f172,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f173,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f176,plain,
! [X0] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f177,plain,
! [X0] :
( ~ axiom_4
| is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(cnf_transformation,[],[f134]) ).
fof(f178,plain,
! [X0] :
( ~ axiom_B
| is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(cnf_transformation,[],[f135]) ).
fof(f179,plain,
( ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0))))
| axiom_5 ),
inference(cnf_transformation,[],[f136]) ).
fof(f180,plain,
! [X0] :
( ~ op_possibly
| possibly(X0) = not(necessarily(not(X0))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f181,plain,
op_possibly,
inference(cnf_transformation,[],[f77]) ).
fof(f184,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f185,plain,
axiom_4,
inference(cnf_transformation,[],[f81]) ).
fof(f186,plain,
axiom_B,
inference(cnf_transformation,[],[f82]) ).
fof(f187,plain,
~ axiom_5,
inference(cnf_transformation,[],[f85]) ).
fof(f188,plain,
! [X0,X1] :
( substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(consistent_polarity_flipping,[],[f139]) ).
fof(f189,plain,
! [X0,X1] :
( modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(consistent_polarity_flipping,[],[f140]) ).
fof(f190,plain,
! [X0,X1] :
( implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(consistent_polarity_flipping,[],[f142]) ).
fof(f192,plain,
! [X0,X1] :
( and_2
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(consistent_polarity_flipping,[],[f145]) ).
fof(f195,plain,
! [X0,X1] :
( equivalence_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(consistent_polarity_flipping,[],[f152]) ).
fof(f196,plain,
! [X0,X1] :
( op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(consistent_polarity_flipping,[],[f153]) ).
fof(f197,plain,
! [X0,X1] :
( op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(consistent_polarity_flipping,[],[f154]) ).
fof(f198,plain,
~ op_or,
inference(consistent_polarity_flipping,[],[f156]) ).
fof(f199,plain,
~ op_implies_and,
inference(consistent_polarity_flipping,[],[f157]) ).
fof(f200,plain,
~ modus_tollens,
inference(consistent_polarity_flipping,[],[f160]) ).
fof(f201,plain,
~ implies_2,
inference(consistent_polarity_flipping,[],[f162]) ).
fof(f203,plain,
~ and_2,
inference(consistent_polarity_flipping,[],[f165]) ).
fof(f206,plain,
~ equivalence_3,
inference(consistent_polarity_flipping,[],[f172]) ).
fof(f207,plain,
~ substitution_of_equivalents,
inference(consistent_polarity_flipping,[],[f173]) ).
fof(f208,plain,
! [X0] :
( axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(consistent_polarity_flipping,[],[f176]) ).
fof(f209,plain,
! [X0] :
( axiom_B
| is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(consistent_polarity_flipping,[],[f178]) ).
fof(f210,plain,
( ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0))))
| ~ axiom_5 ),
inference(consistent_polarity_flipping,[],[f179]) ).
fof(f211,plain,
! [X0] :
( op_possibly
| possibly(X0) = not(necessarily(not(X0))) ),
inference(consistent_polarity_flipping,[],[f180]) ).
fof(f212,plain,
~ op_possibly,
inference(consistent_polarity_flipping,[],[f181]) ).
fof(f213,plain,
~ axiom_M,
inference(consistent_polarity_flipping,[],[f184]) ).
fof(f214,plain,
~ axiom_B,
inference(consistent_polarity_flipping,[],[f186]) ).
fof(f215,plain,
axiom_5,
inference(consistent_polarity_flipping,[],[f187]) ).
fof(f217,definition,
( spl1_1
<=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f218,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f220,definition,
( spl1_2
<=> op_possibly ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f223,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f211,f220,f217]) ).
fof(f225,definition,
( spl1_3
<=> axiom_5 ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f229,definition,
( spl1_4
<=> is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0)))) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f231,plain,
( ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0))))
| spl1_4 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f232,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f210,f229,f225]) ).
fof(f234,definition,
( spl1_5
<=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f235,plain,
( ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f237,definition,
( spl1_6
<=> axiom_B ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f240,plain,
( spl1_5
| spl1_6 ),
inference(avatar_split_clause,[],[f209,f237,f234]) ).
fof(f242,definition,
( spl1_7
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f243,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,definition,
( spl1_8
<=> axiom_4 ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f248,plain,
( spl1_7
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f177,f245,f242]) ).
fof(f250,definition,
( spl1_9
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f251,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,definition,
( spl1_10
<=> axiom_M ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f256,plain,
( spl1_9
| spl1_10 ),
inference(avatar_split_clause,[],[f208,f253,f250]) ).
fof(f282,definition,
( spl1_17
<=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f283,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f285,definition,
( spl1_18
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[spl1_18])],[avatar_definition]) ).
fof(f288,plain,
( spl1_17
| spl1_18 ),
inference(avatar_split_clause,[],[f197,f285,f282]) ).
fof(f290,definition,
( spl1_19
<=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition]) ).
fof(f291,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f293,definition,
( spl1_20
<=> op_or ),
introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition]) ).
fof(f296,plain,
( spl1_19
| spl1_20 ),
inference(avatar_split_clause,[],[f196,f293,f290]) ).
fof(f298,definition,
( spl1_21
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition]) ).
fof(f299,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ spl1_21 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f301,definition,
( spl1_22
<=> equivalence_3 ),
introduced(definition,[new_symbols(definition,[spl1_22])],[avatar_definition]) ).
fof(f304,plain,
( spl1_21
| spl1_22 ),
inference(avatar_split_clause,[],[f195,f301,f298]) ).
fof(f338,definition,
( spl1_31
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_31])],[avatar_definition]) ).
fof(f339,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ spl1_31 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f341,definition,
( spl1_32
<=> or_1 ),
introduced(definition,[new_symbols(definition,[spl1_32])],[avatar_definition]) ).
fof(f344,plain,
( spl1_31
| ~ spl1_32 ),
inference(avatar_split_clause,[],[f147,f341,f338]) ).
fof(f346,definition,
( spl1_33
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl1_33])],[avatar_definition]) ).
fof(f347,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl1_33 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f349,definition,
( spl1_34
<=> and_3 ),
introduced(definition,[new_symbols(definition,[spl1_34])],[avatar_definition]) ).
fof(f352,plain,
( spl1_33
| ~ spl1_34 ),
inference(avatar_split_clause,[],[f146,f349,f346]) ).
fof(f354,definition,
( spl1_35
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
introduced(definition,[new_symbols(definition,[spl1_35])],[avatar_definition]) ).
fof(f355,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ spl1_35 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f357,definition,
( spl1_36
<=> and_2 ),
introduced(definition,[new_symbols(definition,[spl1_36])],[avatar_definition]) ).
fof(f360,plain,
( spl1_35
| spl1_36 ),
inference(avatar_split_clause,[],[f192,f357,f354]) ).
fof(f378,definition,
( spl1_41
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_41])],[avatar_definition]) ).
fof(f379,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl1_41 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f381,definition,
( spl1_42
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[spl1_42])],[avatar_definition]) ).
fof(f384,plain,
( spl1_41
| spl1_42 ),
inference(avatar_split_clause,[],[f190,f381,f378]) ).
fof(f394,definition,
( spl1_45
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[spl1_45])],[avatar_definition]) ).
fof(f395,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ spl1_45 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f397,definition,
( spl1_46
<=> modus_tollens ),
introduced(definition,[new_symbols(definition,[spl1_46])],[avatar_definition]) ).
fof(f400,plain,
( spl1_45
| spl1_46 ),
inference(avatar_split_clause,[],[f189,f397,f394]) ).
fof(f402,definition,
( spl1_47
<=> ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[spl1_47])],[avatar_definition]) ).
fof(f403,plain,
( ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 )
| ~ spl1_47 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f405,definition,
( spl1_48
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[spl1_48])],[avatar_definition]) ).
fof(f408,plain,
( spl1_47
| spl1_48 ),
inference(avatar_split_clause,[],[f188,f405,f402]) ).
fof(f410,definition,
( spl1_49
<=> ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_49])],[avatar_definition]) ).
fof(f411,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ spl1_49 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f413,definition,
( spl1_50
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl1_50])],[avatar_definition]) ).
fof(f416,plain,
( spl1_49
| ~ spl1_50 ),
inference(avatar_split_clause,[],[f138,f413,f410]) ).
fof(f417,plain,
spl1_3,
inference(avatar_split_clause,[],[f215,f225]) ).
fof(f419,plain,
spl1_50,
inference(avatar_split_clause,[],[f159,f413]) ).
fof(f422,plain,
spl1_34,
inference(avatar_split_clause,[],[f166,f349]) ).
fof(f423,plain,
spl1_32,
inference(avatar_split_clause,[],[f167,f341]) ).
fof(f428,plain,
spl1_8,
inference(avatar_split_clause,[],[f185,f245]) ).
fof(f429,plain,
~ spl1_20,
inference(avatar_split_clause,[],[f198,f293]) ).
fof(f430,plain,
~ spl1_18,
inference(avatar_split_clause,[],[f199,f285]) ).
fof(f431,plain,
~ spl1_46,
inference(avatar_split_clause,[],[f200,f397]) ).
fof(f432,plain,
~ spl1_42,
inference(avatar_split_clause,[],[f201,f381]) ).
fof(f434,plain,
~ spl1_36,
inference(avatar_split_clause,[],[f203,f357]) ).
fof(f437,plain,
~ spl1_22,
inference(avatar_split_clause,[],[f206,f301]) ).
fof(f438,plain,
~ spl1_48,
inference(avatar_split_clause,[],[f207,f405]) ).
fof(f439,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f212,f220]) ).
fof(f440,plain,
~ spl1_10,
inference(avatar_split_clause,[],[f213,f253]) ).
fof(f441,plain,
~ spl1_6,
inference(avatar_split_clause,[],[f214,f237]) ).
fof(f462,plain,
( ! [X0,X1] : or(X1,necessarily(not(X0))) = not(and(not(X1),possibly(X0)))
| ~ spl1_1
| ~ spl1_19 ),
inference(superposition,[],[f291,f218]) ).
fof(f465,plain,
( ! [X0,X1] : or(X0,X1) = implies(not(X0),X1)
| ~ spl1_17
| ~ spl1_19 ),
inference(superposition,[],[f291,f283]) ).
fof(f472,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl1_41
| ~ spl1_49 ),
inference(resolution,[],[f379,f411]) ).
fof(f473,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(not(X1),not(X0))) )
| ~ spl1_45
| ~ spl1_49 ),
inference(resolution,[],[f395,f411]) ).
fof(f485,plain,
( ! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),equiv(X1,X0)))
| ~ is_a_theorem(implies(X1,X0)) )
| ~ spl1_21
| ~ spl1_49 ),
inference(resolution,[],[f299,f411]) ).
fof(f523,plain,
( ! [X0,X1] : is_a_theorem(or(X0,or(not(X0),X1)))
| ~ spl1_17
| ~ spl1_19
| ~ spl1_31 ),
inference(superposition,[],[f339,f465]) ).
fof(f566,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ spl1_33
| ~ spl1_41
| ~ spl1_49 ),
inference(resolution,[],[f472,f347]) ).
fof(f576,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl1_17
| ~ spl1_19
| ~ spl1_45
| ~ spl1_49 ),
inference(forward_demodulation,[],[f473,f465]) ).
fof(f583,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,or(X0,X1)))
| is_a_theorem(implies(and(not(X0),not(X1)),X2)) )
| ~ spl1_17
| ~ spl1_19
| ~ spl1_45
| ~ spl1_49 ),
inference(superposition,[],[f576,f291]) ).
fof(f628,plain,
( ! [X0,X1] : possibly(and(not(X0),possibly(X1))) = not(necessarily(or(X0,necessarily(not(X1)))))
| ~ spl1_1
| ~ spl1_19 ),
inference(superposition,[],[f218,f462]) ).
fof(f746,plain,
( ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0)) )
| ~ spl1_21
| ~ spl1_49 ),
inference(resolution,[],[f485,f411]) ).
fof(f2233,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| X0 = X1 )
| ~ spl1_21
| ~ spl1_47
| ~ spl1_49 ),
inference(resolution,[],[f746,f403]) ).
fof(f3130,plain,
( ! [X0,X1] : is_a_theorem(implies(and(not(not(X0)),not(X1)),X0))
| ~ spl1_17
| ~ spl1_19
| ~ spl1_31
| ~ spl1_45
| ~ spl1_49 ),
inference(resolution,[],[f583,f523]) ).
fof(f38836,plain,
( ! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| and(X0,X0) = X0 )
| ~ spl1_21
| ~ spl1_33
| ~ spl1_41
| ~ spl1_47
| ~ spl1_49 ),
inference(resolution,[],[f2233,f566]) ).
fof(f38980,plain,
( ! [X0] :
( ~ is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0)))
| necessarily(X0) = necessarily(necessarily(X0)) )
| ~ spl1_7
| ~ spl1_21
| ~ spl1_47
| ~ spl1_49 ),
inference(resolution,[],[f2233,f243]) ).
fof(f39012,plain,
( ! [X0] : necessarily(X0) = necessarily(necessarily(X0))
| ~ spl1_7
| ~ spl1_9
| ~ spl1_21
| ~ spl1_47
| ~ spl1_49 ),
inference(forward_subsumption_resolution,[],[f38980,f251]) ).
fof(f39057,plain,
( ! [X0] : and(X0,X0) = X0
| ~ spl1_21
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_47
| ~ spl1_49 ),
inference(forward_subsumption_resolution,[],[f38836,f355]) ).
fof(f39247,plain,
( ! [X0] : or(X0,X0) = not(not(X0))
| ~ spl1_19
| ~ spl1_21
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_47
| ~ spl1_49 ),
inference(superposition,[],[f291,f39057]) ).
fof(f39279,plain,
( ! [X0] : is_a_theorem(implies(not(not(X0)),X0))
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(superposition,[],[f3130,f39057]) ).
fof(f39291,plain,
( ! [X0] : is_a_theorem(or(not(X0),X0))
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(forward_demodulation,[],[f39279,f465]) ).
fof(f39475,plain,
( ! [X0] : is_a_theorem(implies(X0,not(not(X0))))
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(resolution,[],[f39291,f576]) ).
fof(f40249,plain,
( ! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| not(not(X0)) = X0 )
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(resolution,[],[f39475,f2233]) ).
fof(f40292,plain,
( ! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| not(not(X0)) = X0 )
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(forward_demodulation,[],[f40249,f465]) ).
fof(f40294,plain,
( ! [X0] : not(not(X0)) = X0
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(forward_subsumption_resolution,[],[f40292,f39291]) ).
fof(f45550,plain,
( ! [X0] : or(X0,X0) = X0
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(forward_demodulation,[],[f39247,f40294]) ).
fof(f45824,plain,
( ! [X0] : possibly(and(not(necessarily(not(X0))),possibly(X0))) = not(necessarily(necessarily(not(X0))))
| ~ spl1_1
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(superposition,[],[f628,f45550]) ).
fof(f45906,plain,
( ! [X0] : not(necessarily(not(X0))) = possibly(and(not(necessarily(not(X0))),possibly(X0)))
| ~ spl1_1
| ~ spl1_7
| ~ spl1_9
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(forward_demodulation,[],[f45824,f39012]) ).
fof(f45998,plain,
( ! [X0] : possibly(X0) = possibly(and(possibly(X0),possibly(X0)))
| ~ spl1_1
| ~ spl1_7
| ~ spl1_9
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(forward_demodulation,[],[f45906,f218]) ).
fof(f46064,plain,
( ! [X0] : possibly(X0) = possibly(possibly(X0))
| ~ spl1_1
| ~ spl1_7
| ~ spl1_9
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(forward_demodulation,[],[f45998,f39057]) ).
fof(f46406,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ spl1_1
| ~ spl1_5
| ~ spl1_7
| ~ spl1_9
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(superposition,[],[f235,f46064]) ).
fof(f55610,plain,
( $false
| ~ spl1_1
| spl1_4
| ~ spl1_5
| ~ spl1_7
| ~ spl1_9
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(backward_subsumption_resolution,[],[f231,f46406]) ).
fof(f55638,plain,
( ~ spl1_1
| spl1_4
| ~ spl1_5
| ~ spl1_7
| ~ spl1_9
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(avatar_contradiction_clause,[],[f55610]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f223]) ).
cnf(s2,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f232]) ).
cnf(s3,plain,
( spl1_5
| spl1_6 ),
inference(sat_conversion,[],[f240]) ).
cnf(s4,plain,
( spl1_7
| ~ spl1_8 ),
inference(sat_conversion,[],[f248]) ).
cnf(s5,plain,
( spl1_9
| spl1_10 ),
inference(sat_conversion,[],[f256]) ).
cnf(s9,plain,
( spl1_17
| spl1_18 ),
inference(sat_conversion,[],[f288]) ).
cnf(s10,plain,
( spl1_19
| spl1_20 ),
inference(sat_conversion,[],[f296]) ).
cnf(s11,plain,
( spl1_21
| spl1_22 ),
inference(sat_conversion,[],[f304]) ).
cnf(s16,plain,
( spl1_31
| ~ spl1_32 ),
inference(sat_conversion,[],[f344]) ).
cnf(s17,plain,
( spl1_33
| ~ spl1_34 ),
inference(sat_conversion,[],[f352]) ).
cnf(s18,plain,
( spl1_35
| spl1_36 ),
inference(sat_conversion,[],[f360]) ).
cnf(s21,plain,
( spl1_41
| spl1_42 ),
inference(sat_conversion,[],[f384]) ).
cnf(s23,plain,
( spl1_45
| spl1_46 ),
inference(sat_conversion,[],[f400]) ).
cnf(s24,plain,
( spl1_47
| spl1_48 ),
inference(sat_conversion,[],[f408]) ).
cnf(s25,plain,
( spl1_49
| ~ spl1_50 ),
inference(sat_conversion,[],[f416]) ).
cnf(s26,plain,
spl1_3,
inference(sat_conversion,[],[f417]) ).
cnf(s28,plain,
spl1_50,
inference(sat_conversion,[],[f419]) ).
cnf(s31,plain,
spl1_34,
inference(sat_conversion,[],[f422]) ).
cnf(s32,plain,
spl1_32,
inference(sat_conversion,[],[f423]) ).
cnf(s37,plain,
spl1_8,
inference(sat_conversion,[],[f428]) ).
cnf(s38,plain,
~ spl1_20,
inference(sat_conversion,[],[f429]) ).
cnf(s39,plain,
~ spl1_18,
inference(sat_conversion,[],[f430]) ).
cnf(s40,plain,
~ spl1_46,
inference(sat_conversion,[],[f431]) ).
cnf(s41,plain,
~ spl1_42,
inference(sat_conversion,[],[f432]) ).
cnf(s43,plain,
~ spl1_36,
inference(sat_conversion,[],[f434]) ).
cnf(s46,plain,
~ spl1_22,
inference(sat_conversion,[],[f437]) ).
cnf(s47,plain,
~ spl1_48,
inference(sat_conversion,[],[f438]) ).
cnf(s48,plain,
~ spl1_2,
inference(sat_conversion,[],[f439]) ).
cnf(s49,plain,
~ spl1_10,
inference(sat_conversion,[],[f440]) ).
cnf(s50,plain,
~ spl1_6,
inference(sat_conversion,[],[f441]) ).
cnf(s98,plain,
( ~ spl1_1
| spl1_4
| ~ spl1_5
| ~ spl1_7
| ~ spl1_9
| ~ spl1_17
| ~ spl1_19
| ~ spl1_21
| ~ spl1_31
| ~ spl1_33
| ~ spl1_35
| ~ spl1_41
| ~ spl1_45
| ~ spl1_47
| ~ spl1_49 ),
inference(sat_conversion,[],[f55638]) ).
cnf(s99,plain,
spl1_49,
inference(rat,[],[s25,s28]) ).
cnf(s100,plain,
spl1_47,
inference(rat,[],[s24,s47]) ).
cnf(s101,plain,
spl1_45,
inference(rat,[],[s23,s40]) ).
cnf(s103,plain,
spl1_41,
inference(rat,[],[s21,s41]) ).
cnf(s106,plain,
spl1_35,
inference(rat,[],[s18,s43]) ).
cnf(s107,plain,
spl1_33,
inference(rat,[],[s17,s31]) ).
cnf(s108,plain,
spl1_31,
inference(rat,[],[s16,s32]) ).
cnf(s113,plain,
spl1_21,
inference(rat,[],[s11,s46]) ).
cnf(s114,plain,
spl1_19,
inference(rat,[],[s10,s38]) ).
cnf(s115,plain,
spl1_17,
inference(rat,[],[s9,s39]) ).
cnf(s120,plain,
spl1_9,
inference(rat,[],[s5,s49]) ).
cnf(s121,plain,
spl1_7,
inference(rat,[],[s4,s37]) ).
cnf(s122,plain,
spl1_5,
inference(rat,[],[s3,s50]) ).
cnf(s124,plain,
~ spl1_4,
inference(rat,[],[s2,s26]) ).
cnf(s125,plain,
~ spl1_1,
inference(rat,[],[s98,s99,s100,s101,s103,s106,s107,s108,s113,s114,s115,s120,s121,s122,s124]) ).
cnf(s134,plain,
$false,
inference(rat,[],[s1,s48,s125]) ).
fof(f55655,plain,
$false,
inference(avatar_sat_refutation,[],[s134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL537+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:57:45 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 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
% 3.94/1.20 % (2215079)Will run a generic schedule for satisfiability detection.
% 3.94/1.20 % (2215085)% WARNING: option uhcvi not known.
% 3.94/1.20 % (2215088)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2829846945:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.94/1.20 % (2215090)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1620259624:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.94/1.20 % (2215084)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=532836563_2999 on theBenchmark for (2999ds/0Mi)
% 3.94/1.20 % (2215085)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2136887675:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.94/1.20 % (2215087)dis+10_1_sil=32000:sp=arity:random_seed=2716454037:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.94/1.20 % (2215086)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2633100423:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.94/1.20 % (2215089)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2635385203:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.94/1.20 % TRYING [1]
% 3.94/1.20 % TRYING [2]
% 3.94/1.20 % TRYING [3]
% 3.94/1.20 % TRYING [4]
% 3.94/1.20 % (2215087)Instruction limit reached!
% 3.94/1.20 % (2215087)------------------------------
% 3.94/1.20 % (2215087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.20 % (2215087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.20 % (2215087)CaDiCaL version: 2.1.3
% 3.94/1.20 % (2215087)Termination reason: Instruction limit
% 3.94/1.20 % (2215087)Termination phase: Saturation
% 3.94/1.20 % (2215087)Time elapsed: 0.067 s
% 3.94/1.20 % (2215087)Peak memory usage: 13 MB
% 3.94/1.20 % (2215087)Instructions burned: 104 (million)
% 3.94/1.20 % (2215088)Instruction limit reached!
% 3.94/1.20 % (2215088)------------------------------
% 3.94/1.20 % (2215088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.20 % (2215088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.20 % (2215088)CaDiCaL version: 2.1.3
% 3.94/1.20 % (2215088)Termination reason: Instruction limit
% 3.94/1.20 % (2215088)Termination phase: Saturation
% 3.94/1.20 % (2215088)Time elapsed: 0.075 s
% 3.94/1.20 % (2215088)Peak memory usage: 13 MB
% 3.94/1.20 % (2215088)Instructions burned: 117 (million)
% 3.94/1.20 % (2215089)Instruction limit reached!
% 3.94/1.20 % (2215089)------------------------------
% 3.94/1.20 % (2215089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.20 % (2215089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.20 % (2215089)CaDiCaL version: 2.1.3
% 3.94/1.20 % (2215089)Termination reason: Instruction limit
% 3.94/1.20 % (2215089)Termination phase: Saturation
% 3.94/1.20 % (2215089)Time elapsed: 0.084 s
% 3.94/1.20 % (2215089)Peak memory usage: 14 MB
% 3.94/1.20 % (2215089)Instructions burned: 132 (million)
% 3.94/1.20 % (2215098)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1109950442:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.94/1.20 % TRYING [1]
% 3.94/1.20 % TRYING [2]
% 3.94/1.20 % TRYING [3]
% 3.94/1.20 % (2215099)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2353907262:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 3.94/1.20 % TRYING [5]
% 3.94/1.20 % (2215100)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3108702196:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.94/1.20 % TRYING [4]
% 3.94/1.20 % (2215090)Instruction limit reached!
% 3.94/1.20 % (2215090)------------------------------
% 3.94/1.20 % (2215090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.20 % (2215090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.20 % (2215090)CaDiCaL version: 2.1.3
% 3.94/1.20 % (2215090)Termination reason: Instruction limit
% 3.94/1.20 % (2215090)Termination phase: Saturation
% 3.94/1.20 % (2215090)Time elapsed: 0.113 s
% 3.94/1.20 % (2215090)Peak memory usage: 14 MB
% 3.94/1.20 % (2215090)Instructions burned: 160 (million)
% 3.94/1.20 % (2215104)ott-21_1_sil=16000:fs=off:random_seed=3801731732:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.94/1.20 % (2215099)Instruction limit reached!
% 3.94/1.20 % (2215099)------------------------------
% 3.94/1.20 % (2215099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.20 % (2215099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.20 % (2215099)CaDiCaL version: 2.1.3
% 3.94/1.20 % (2215099)Termination reason: Instruction limit
% 3.94/1.20 % (2215099)Termination phase: Saturation
% 3.94/1.20 % (2215099)Time elapsed: 0.090 s
% 3.94/1.20 % (2215099)Peak memory usage: 14 MB
% 3.94/1.20 % (2215099)Instructions burned: 132 (million)
% 3.94/1.20 % (2215106)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1739871201:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 3.94/1.20 % TRYING [5]
% 3.94/1.20 % (2215104)Instruction limit reached!
% 3.94/1.20 % (2215104)------------------------------
% 3.94/1.20 % (2215104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.20 % (2215104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.20 % (2215104)CaDiCaL version: 2.1.3
% 3.94/1.20 % (2215104)Termination reason: Instruction limit
% 3.94/1.20 % (2215104)Termination phase: Saturation
% 3.94/1.20 % (2215104)Time elapsed: 0.099 s
% 3.94/1.20 % (2215104)Peak memory usage: 13 MB
% 3.94/1.20 % (2215104)Instructions burned: 181 (million)
% 3.94/1.21 % (2215108)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2749890183:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 3.94/1.21 % TRYING [1]
% 3.94/1.21 % TRYING [2]
% 3.94/1.21 % TRYING [3]
% 3.94/1.21 % TRYING [4]
% 3.94/1.21 % (2215098)Instruction limit reached!
% 3.94/1.21 % (2215098)------------------------------
% 3.94/1.21 % (2215098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.21 % (2215098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.21 % (2215098)CaDiCaL version: 2.1.3
% 3.94/1.21 % (2215098)Termination reason: Instruction limit
% 3.94/1.21 % (2215098)Termination phase: Finite model building SAT solving
% 3.94/1.21 % (2215098)Time elapsed: 0.403 s
% 3.94/1.21 % (2215098)Peak memory usage: 23 MB
% 3.94/1.21 % (2215098)Instructions burned: 714 (million)
% 3.94/1.21 % TRYING [6]
% 3.94/1.21 % (2215100)Instruction limit reached!
% 3.94/1.21 % (2215100)------------------------------
% 3.94/1.21 % (2215100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.21 % (2215100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.21 % (2215100)CaDiCaL version: 2.1.3
% 3.94/1.21 % (2215100)Termination reason: Instruction limit
% 3.94/1.21 % (2215100)Termination phase: Saturation
% 3.94/1.21 % (2215100)Time elapsed: 0.398 s
% 3.94/1.21 % (2215100)Peak memory usage: 20 MB
% 3.94/1.21 % (2215100)Instructions burned: 685 (million)
% 3.94/1.21 % (2215110)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=947988937:i=1179_2994 on theBenchmark for (2994ds/1179Mi)
% 3.94/1.21 % (2215111)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3241427800:i=889:ins=1_2994 on theBenchmark for (2994ds/889Mi)
% 3.94/1.21 % (2215106)Instruction limit reached!
% 3.94/1.21 % (2215106)------------------------------
% 3.94/1.21 % (2215106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.21 % (2215106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.21 % (2215106)CaDiCaL version: 2.1.3
% 3.94/1.21 % (2215106)Termination reason: Instruction limit
% 3.94/1.21 % (2215106)Termination phase: Saturation
% 3.94/1.21 % (2215106)Time elapsed: 0.320 s
% 3.94/1.21 % (2215106)Peak memory usage: 14 MB
% 3.94/1.21 % (2215106)Instructions burned: 478 (million)
% 3.94/1.21 % (2215114)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2415200711:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 3.94/1.21 % (2215108)Instruction limit reached!
% 3.94/1.21 % (2215108)------------------------------
% 3.94/1.21 % (2215108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.21 % (2215108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.21 % (2215108)CaDiCaL version: 2.1.3
% 3.94/1.21 % (2215108)Termination reason: Instruction limit
% 3.94/1.21 % (2215108)Termination phase: Finite model building SAT solving
% 3.94/1.21 % (2215108)Time elapsed: 0.333 s
% 3.94/1.21 % (2215108)Peak memory usage: 22 MB
% 3.94/1.21 % (2215108)Instructions burned: 867 (million)
% 3.94/1.21 % (2215116)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3895634889:i=879:kws=inv_precedence:fsr=off_2993 on theBenchmark for (2993ds/879Mi)
% 3.94/1.21 % TRYING [14]
% 3.94/1.21 % (2215085) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2215079-2215085"...
% 3.94/1.21 % (2215085)...printing done.
% 3.94/1.21 % (2215085)Refutation found. Thanks to Tanya!
% 3.94/1.21 % SZS status Theorem for theBenchmark
% 3.94/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.21 % (2215085)------------------------------
% 3.94/1.21 % (2215085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.94/1.21 % (2215085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.21 % (2215085)CaDiCaL version: 2.1.3
% 3.94/1.21 % (2215085)Termination reason: Refutation
% 3.94/1.21 % (2215085)Time elapsed: 0.767 s
% 3.94/1.21 % (2215085)Peak memory usage: 44 MB
% 3.94/1.21 % (2215085)Instructions burned: 2539 (million)
% 3.94/1.21 % (2215079)Success in time 0.805 s
% 3.94/1.21 % Vampire exiting
%------------------------------------------------------------------------------