%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL526+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 : n006.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 11:58:52 AM UTC 2026
% Result : Theorem 0.17s 0.54s
% Output : Refutation 0.17s
% 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+2.ax',km5_axiom_M) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f87,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f88,conjecture,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f89,negated_conjecture,
~ substitution_strict_equiv,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ substitution_strict_equiv,
inference(flattening,[],[f89]) ).
fof(f92,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f94,plain,
( ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 )
=> substitution_strict_equiv ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f96,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(f103,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f104,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f109,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f110,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(f115,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f110]) ).
fof(f116,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f109]) ).
fof(f122,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f104]) ).
fof(f123,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f103]) ).
fof(f130,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f96]) ).
fof(f135,plain,
( substitution_strict_equiv
| ? [X0,X1] :
( X0 != X1
& is_a_theorem(strict_equiv(X0,X1)) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f137,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f92]) ).
fof(f140,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f141,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f76]) ).
fof(f142,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)],[f135]) ).
fof(f143,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens ),
inference(cnf_transformation,[],[f116]) ).
fof(f144,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f117]) ).
fof(f149,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f122]) ).
fof(f150,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f123]) ).
fof(f157,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f130]) ).
fof(f164,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f169,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f170,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f177,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f178,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f180,plain,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(sK0,sK1)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f181,plain,
( substitution_strict_equiv
| sK0 != sK1 ),
inference(cnf_transformation,[],[f142]) ).
fof(f183,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f137]) ).
fof(f186,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f140]) ).
fof(f187,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f141]) ).
fof(f191,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f195,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f197,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f87]) ).
fof(f198,plain,
~ substitution_strict_equiv,
inference(cnf_transformation,[],[f90]) ).
fof(f200,definition,
( spl2_1
<=> op_strict_equiv ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f204,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(f205,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f206,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f187,f204,f200]) ).
fof(f208,definition,
( spl2_3
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f212,definition,
( spl2_4
<=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f213,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f214,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f186,f212,f208]) ).
fof(f232,definition,
( spl2_9
<=> axiom_M ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f236,definition,
( spl2_10
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f237,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( ~ spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f183,f236,f232]) ).
fof(f248,definition,
( spl2_13
<=> is_a_theorem(strict_equiv(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f250,plain,
( is_a_theorem(strict_equiv(sK0,sK1))
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f252,definition,
( spl2_14
<=> substitution_strict_equiv ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
fof(f255,plain,
( spl2_13
| spl2_14 ),
inference(avatar_split_clause,[],[f180,f252,f248]) ).
fof(f257,definition,
( spl2_15
<=> sK0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f259,plain,
( sK0 != sK1
| spl2_15 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f260,plain,
( ~ spl2_15
| spl2_14 ),
inference(avatar_split_clause,[],[f181,f252,f257]) ).
fof(f294,definition,
( spl2_24
<=> equivalence_3 ),
introduced(definition,[new_symbols(definition,[spl2_24])],[avatar_definition]) ).
fof(f298,definition,
( spl2_25
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[spl2_25])],[avatar_definition]) ).
fof(f299,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ spl2_25 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f300,plain,
( ~ spl2_24
| spl2_25 ),
inference(avatar_split_clause,[],[f157,f298,f294]) ).
fof(f350,definition,
( spl2_38
<=> and_2 ),
introduced(definition,[new_symbols(definition,[spl2_38])],[avatar_definition]) ).
fof(f354,definition,
( spl2_39
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
introduced(definition,[new_symbols(definition,[spl2_39])],[avatar_definition]) ).
fof(f355,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ spl2_39 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f356,plain,
( ~ spl2_38
| spl2_39 ),
inference(avatar_split_clause,[],[f150,f354,f350]) ).
fof(f358,definition,
( spl2_40
<=> and_1 ),
introduced(definition,[new_symbols(definition,[spl2_40])],[avatar_definition]) ).
fof(f362,definition,
( spl2_41
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[spl2_41])],[avatar_definition]) ).
fof(f363,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_41 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f364,plain,
( ~ spl2_40
| spl2_41 ),
inference(avatar_split_clause,[],[f149,f362,f358]) ).
fof(f398,definition,
( spl2_50
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[spl2_50])],[avatar_definition]) ).
fof(f402,definition,
( spl2_51
<=> ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_51])],[avatar_definition]) ).
fof(f403,plain,
( ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 )
| ~ spl2_51 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f404,plain,
( ~ spl2_50
| spl2_51 ),
inference(avatar_split_clause,[],[f144,f402,f398]) ).
fof(f406,definition,
( spl2_52
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl2_52])],[avatar_definition]) ).
fof(f410,definition,
( spl2_53
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl2_53])],[avatar_definition]) ).
fof(f411,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl2_53 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f412,plain,
( ~ spl2_52
| spl2_53 ),
inference(avatar_split_clause,[],[f143,f410,f406]) ).
fof(f413,plain,
~ spl2_14,
inference(avatar_split_clause,[],[f198,f252]) ).
fof(f417,plain,
spl2_52,
inference(avatar_split_clause,[],[f164,f406]) ).
fof(f422,plain,
spl2_40,
inference(avatar_split_clause,[],[f169,f358]) ).
fof(f423,plain,
spl2_38,
inference(avatar_split_clause,[],[f170,f350]) ).
fof(f430,plain,
spl2_24,
inference(avatar_split_clause,[],[f177,f294]) ).
fof(f431,plain,
spl2_50,
inference(avatar_split_clause,[],[f178,f398]) ).
fof(f435,plain,
spl2_9,
inference(avatar_split_clause,[],[f191,f232]) ).
fof(f437,plain,
spl2_3,
inference(avatar_split_clause,[],[f195,f208]) ).
fof(f438,plain,
spl2_1,
inference(avatar_split_clause,[],[f197,f200]) ).
fof(f448,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X1) )
| ~ spl2_39
| ~ spl2_53 ),
inference(resolution,[],[f411,f355]) ).
fof(f449,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X0) )
| ~ spl2_41
| ~ spl2_53 ),
inference(resolution,[],[f411,f363]) ).
fof(f450,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) )
| ~ spl2_10
| ~ spl2_53 ),
inference(resolution,[],[f411,f237]) ).
fof(f453,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_4
| ~ spl2_10
| ~ spl2_53 ),
inference(superposition,[],[f450,f213]) ).
fof(f486,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) )
| ~ spl2_2
| ~ spl2_41
| ~ spl2_53 ),
inference(superposition,[],[f449,f205]) ).
fof(f487,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X1,X0)) )
| ~ spl2_2
| ~ spl2_39
| ~ spl2_53 ),
inference(superposition,[],[f448,f205]) ).
fof(f523,plain,
( ! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl2_25
| ~ spl2_53 ),
inference(resolution,[],[f299,f411]) ).
fof(f570,plain,
( is_a_theorem(strict_implies(sK0,sK1))
| ~ spl2_2
| ~ spl2_13
| ~ spl2_41
| ~ spl2_53 ),
inference(resolution,[],[f486,f250]) ).
fof(f583,plain,
( is_a_theorem(implies(sK0,sK1))
| ~ spl2_2
| ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| ~ spl2_41
| ~ spl2_53 ),
inference(resolution,[],[f570,f453]) ).
fof(f880,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(equiv(X0,X1)) )
| ~ spl2_25
| ~ spl2_53 ),
inference(resolution,[],[f523,f411]) ).
fof(f884,plain,
( is_a_theorem(strict_implies(sK1,sK0))
| ~ spl2_2
| ~ spl2_13
| ~ spl2_39
| ~ spl2_53 ),
inference(resolution,[],[f487,f250]) ).
fof(f898,plain,
( is_a_theorem(implies(sK1,sK0))
| ~ spl2_2
| ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| ~ spl2_39
| ~ spl2_53 ),
inference(resolution,[],[f884,f453]) ).
fof(f3579,plain,
( ~ is_a_theorem(implies(sK0,sK1))
| is_a_theorem(equiv(sK0,sK1))
| ~ spl2_2
| ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| ~ spl2_25
| ~ spl2_39
| ~ spl2_53 ),
inference(resolution,[],[f880,f898]) ).
fof(f3583,plain,
( is_a_theorem(equiv(sK0,sK1))
| ~ spl2_2
| ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| ~ spl2_25
| ~ spl2_39
| ~ spl2_41
| ~ spl2_53 ),
inference(forward_subsumption_resolution,[],[f3579,f583]) ).
fof(f3606,plain,
( sK0 = sK1
| ~ spl2_2
| ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| ~ spl2_25
| ~ spl2_39
| ~ spl2_41
| ~ spl2_51
| ~ spl2_53 ),
inference(resolution,[],[f3583,f403]) ).
fof(f3607,plain,
( $false
| ~ spl2_2
| ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| spl2_15
| ~ spl2_25
| ~ spl2_39
| ~ spl2_41
| ~ spl2_51
| ~ spl2_53 ),
inference(forward_subsumption_resolution,[],[f3606,f259]) ).
fof(f3608,plain,
( ~ spl2_2
| ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| spl2_15
| ~ spl2_25
| ~ spl2_39
| ~ spl2_41
| ~ spl2_51
| ~ spl2_53 ),
inference(avatar_contradiction_clause,[],[f3607]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f206]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f214]) ).
cnf(s5,plain,
( ~ spl2_9
| spl2_10 ),
inference(sat_conversion,[],[f238]) ).
cnf(s7,plain,
( spl2_13
| spl2_14 ),
inference(sat_conversion,[],[f255]) ).
cnf(s8,plain,
( spl2_14
| ~ spl2_15 ),
inference(sat_conversion,[],[f260]) ).
cnf(s13,plain,
( ~ spl2_24
| spl2_25 ),
inference(sat_conversion,[],[f300]) ).
cnf(s20,plain,
( ~ spl2_38
| spl2_39 ),
inference(sat_conversion,[],[f356]) ).
cnf(s21,plain,
( ~ spl2_40
| spl2_41 ),
inference(sat_conversion,[],[f364]) ).
cnf(s26,plain,
( ~ spl2_50
| spl2_51 ),
inference(sat_conversion,[],[f404]) ).
cnf(s27,plain,
( ~ spl2_52
| spl2_53 ),
inference(sat_conversion,[],[f412]) ).
cnf(s28,plain,
~ spl2_14,
inference(sat_conversion,[],[f413]) ).
cnf(s32,plain,
spl2_52,
inference(sat_conversion,[],[f417]) ).
cnf(s37,plain,
spl2_40,
inference(sat_conversion,[],[f422]) ).
cnf(s38,plain,
spl2_38,
inference(sat_conversion,[],[f423]) ).
cnf(s45,plain,
spl2_24,
inference(sat_conversion,[],[f430]) ).
cnf(s46,plain,
spl2_50,
inference(sat_conversion,[],[f431]) ).
cnf(s50,plain,
spl2_9,
inference(sat_conversion,[],[f435]) ).
cnf(s54,plain,
spl2_3,
inference(sat_conversion,[],[f437]) ).
cnf(s56,plain,
spl2_1,
inference(sat_conversion,[],[f438]) ).
cnf(s88,plain,
( ~ spl2_2
| ~ spl2_4
| ~ spl2_10
| ~ spl2_13
| spl2_15
| ~ spl2_25
| ~ spl2_39
| ~ spl2_41
| ~ spl2_51
| ~ spl2_53 ),
inference(sat_conversion,[],[f3608]) ).
cnf(s89,plain,
spl2_53,
inference(rat,[],[s27,s32]) ).
cnf(s90,plain,
spl2_51,
inference(rat,[],[s26,s46]) ).
cnf(s95,plain,
spl2_41,
inference(rat,[],[s21,s37]) ).
cnf(s96,plain,
spl2_39,
inference(rat,[],[s20,s38]) ).
cnf(s103,plain,
spl2_25,
inference(rat,[],[s13,s45]) ).
cnf(s108,plain,
~ spl2_15,
inference(rat,[],[s8,s28]) ).
cnf(s112,plain,
spl2_13,
inference(rat,[],[s7,s28]) ).
cnf(s114,plain,
spl2_10,
inference(rat,[],[s5,s50]) ).
cnf(s119,plain,
spl2_4,
inference(rat,[],[s2,s54]) ).
cnf(s120,plain,
~ spl2_2,
inference(rat,[],[s88,s89,s90,s95,s96,s103,s108,s112,s114,s119]) ).
cnf(s122,plain,
$false,
inference(rat,[],[s1,s120,s56]) ).
fof(f3609,plain,
$false,
inference(avatar_sat_refutation,[],[s122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL526+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 % Computer : n006.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Sun Sep 27 15:56:10 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 Running first-order model finding
% 0.10/0.43 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
% 0.17/0.54 % (3132321)Will run a generic schedule for satisfiability detection.
% 0.17/0.54 % (3132331)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3592722289:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.54 % (3132328)% WARNING: option uhcvi not known.
% 0.17/0.54 % (3132329)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3487883674:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.54 % (3132330)dis+10_1_sil=32000:sp=arity:random_seed=3177634145:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.54 % (3132328)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3483163794:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.54 % (3132327)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1123748490_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.54 % (3132332)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=72338438:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.54 % (3132333)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=236889263:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.54 % TRYING [1]
% 0.17/0.54 % TRYING [2]
% 0.17/0.54 % TRYING [3]
% 0.17/0.54 % TRYING [4]
% 0.17/0.54 % (3132331)Instruction limit reached!
% 0.17/0.54 % (3132331)------------------------------
% 0.17/0.54 % (3132331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.54 % (3132331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.54 % (3132331)CaDiCaL version: 2.1.3
% 0.17/0.54 % (3132331)Termination reason: Instruction limit
% 0.17/0.54 % (3132331)Termination phase: Saturation
% 0.17/0.54 % (3132331)Time elapsed: 0.042 s
% 0.17/0.54 % (3132331)Peak memory usage: 13 MB
% 0.17/0.54 % (3132331)Instructions burned: 117 (million)
% 0.17/0.54 % (3132351)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1503725979:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.54 % TRYING [1]
% 0.17/0.54 % TRYING [2]
% 0.17/0.54 % TRYING [3]
% 0.17/0.54 % TRYING [4]
% 0.17/0.54 % (3132330) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3132321-3132330"...
% 0.17/0.54 % (3132330)...printing done.
% 0.17/0.54 % (3132330)Refutation found. Thanks to Tanya!
% 0.17/0.54 % SZS status Theorem for theBenchmark
% 0.17/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.55 % (3132330)------------------------------
% 0.17/0.55 % (3132330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.55 % (3132330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.55 % (3132330)CaDiCaL version: 2.1.3
% 0.17/0.55 % (3132330)Termination reason: Refutation
% 0.17/0.55 % (3132330)Time elapsed: 0.066 s
% 0.17/0.55 % (3132330)Peak memory usage: 14 MB
% 0.17/0.55 % (3132330)Instructions burned: 98 (million)
% 0.17/0.55 % (3132321)Success in time 0.106 s
% 0.17/0.55 % Vampire exiting
%------------------------------------------------------------------------------