TSTP Solution File: LCL451+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL451+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:46:01 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 75
% Syntax : Number of formulae : 198 ( 60 unt; 0 def)
% Number of atoms : 365 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 262 ( 95 ~; 90 |; 2 &)
% ( 53 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 60 ( 58 usr; 58 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 199 ( 193 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f349,plain,
$false,
inference(avatar_sat_refutation,[],[f152,f157,f162,f167,f172,f177,f182,f187,f192,f197,f202,f207,f212,f217,f222,f227,f232,f237,f242,f246,f250,f254,f258,f262,f266,f270,f274,f278,f282,f294,f299,f312,f317,f324,f329,f333,f341,f345,f348]) ).
fof(f348,plain,
( spl3_37
| ~ spl3_38 ),
inference(avatar_contradiction_clause,[],[f346]) ).
fof(f346,plain,
( $false
| spl3_37
| ~ spl3_38 ),
inference(resolution,[],[f344,f340]) ).
fof(f340,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| spl3_37 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f338,plain,
( spl3_37
<=> is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).
fof(f344,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ spl3_38 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f343,plain,
( spl3_38
<=> ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).
fof(f345,plain,
( ~ spl3_14
| spl3_38 ),
inference(avatar_split_clause,[],[f146,f343,f214]) ).
fof(f214,plain,
( spl3_14
<=> implies_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f146,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_3) ).
fof(f341,plain,
( ~ spl3_37
| spl3_1 ),
inference(avatar_split_clause,[],[f132,f149,f338]) ).
fof(f149,plain,
( spl3_1
<=> cn1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f132,plain,
( cn1
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
( cn1
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f89,f106]) ).
fof(f106,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
( cn1
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> cn1 ),
inference(unused_predicate_definition_removal,[],[f66]) ).
fof(f66,plain,
( cn1
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
( cn1
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn1) ).
fof(f333,plain,
( ~ spl3_19
| spl3_36 ),
inference(avatar_split_clause,[],[f131,f331,f239]) ).
fof(f239,plain,
( spl3_19
<=> op_equiv ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f331,plain,
( spl3_36
<=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).
fof(f131,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f329,plain,
( spl3_35
| ~ spl3_20
| ~ spl3_29 ),
inference(avatar_split_clause,[],[f283,f280,f244,f327]) ).
fof(f327,plain,
( spl3_35
<=> ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).
fof(f244,plain,
( spl3_20
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f280,plain,
( spl3_29
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).
fof(f283,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(or(X0,X1)) )
| ~ spl3_20
| ~ spl3_29 ),
inference(resolution,[],[f281,f245]) ).
fof(f245,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f281,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl3_29 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f324,plain,
( ~ spl3_15
| spl3_34 ),
inference(avatar_split_clause,[],[f142,f322,f219]) ).
fof(f219,plain,
( spl3_15
<=> implies_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f322,plain,
( spl3_34
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).
fof(f142,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
fof(f317,plain,
( spl3_33
| ~ spl3_30
| ~ spl3_31
| ~ spl3_32 ),
inference(avatar_split_clause,[],[f313,f310,f297,f292,f315]) ).
fof(f315,plain,
( spl3_33
<=> ! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).
fof(f292,plain,
( spl3_30
<=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).
fof(f297,plain,
( spl3_31
<=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).
fof(f310,plain,
( spl3_32
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).
fof(f313,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1)))
| ~ spl3_30
| ~ spl3_31
| ~ spl3_32 ),
inference(forward_demodulation,[],[f311,f304]) ).
fof(f304,plain,
( ! [X0,X1] : or(X0,X1) = implies(not(X0),X1)
| ~ spl3_30
| ~ spl3_31 ),
inference(superposition,[],[f298,f293]) ).
fof(f293,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ spl3_30 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f298,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ spl3_31 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f311,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ spl3_32 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f312,plain,
( ~ spl3_2
| spl3_32 ),
inference(avatar_split_clause,[],[f141,f310,f154]) ).
fof(f154,plain,
( spl3_2
<=> modus_tollens ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f141,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
fof(f299,plain,
( ~ spl3_18
| spl3_31 ),
inference(avatar_split_clause,[],[f130,f297,f234]) ).
fof(f234,plain,
( spl3_18
<=> op_or ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
fof(f130,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f294,plain,
( ~ spl3_17
| spl3_30 ),
inference(avatar_split_clause,[],[f129,f292,f229]) ).
fof(f229,plain,
( spl3_17
<=> op_implies_and ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f129,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f282,plain,
( ~ spl3_4
| spl3_29 ),
inference(avatar_split_clause,[],[f145,f280,f164]) ).
fof(f164,plain,
( spl3_4
<=> modus_ponens ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f145,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f102]) ).
fof(f102,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f278,plain,
( ~ spl3_7
| spl3_28 ),
inference(avatar_split_clause,[],[f140,f276,f179]) ).
fof(f179,plain,
( spl3_7
<=> equivalence_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f276,plain,
( spl3_28
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).
fof(f140,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
( equivalence_1
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f13,axiom,
( equivalence_1
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_1) ).
fof(f274,plain,
( ~ spl3_6
| spl3_27 ),
inference(avatar_split_clause,[],[f139,f272,f174]) ).
fof(f174,plain,
( spl3_6
<=> equivalence_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f272,plain,
( spl3_27
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
fof(f139,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
( equivalence_2
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
fof(f270,plain,
( ~ spl3_11
| spl3_26 ),
inference(avatar_split_clause,[],[f138,f268,f199]) ).
fof(f199,plain,
( spl3_11
<=> and_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f268,plain,
( spl3_26
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
fof(f138,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
fof(f266,plain,
( ~ spl3_3
| spl3_25 ),
inference(avatar_split_clause,[],[f144,f264,f159]) ).
fof(f159,plain,
( spl3_3
<=> substitution_of_equivalents ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f264,plain,
( spl3_25
<=> ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f144,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f262,plain,
( ~ spl3_12
| spl3_24 ),
inference(avatar_split_clause,[],[f137,f260,f204]) ).
fof(f204,plain,
( spl3_12
<=> and_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f260,plain,
( spl3_24
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f137,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
fof(f258,plain,
( ~ spl3_13
| spl3_23 ),
inference(avatar_split_clause,[],[f136,f256,f209]) ).
fof(f209,plain,
( spl3_13
<=> and_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f256,plain,
( spl3_23
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f136,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f254,plain,
( ~ spl3_16
| spl3_22 ),
inference(avatar_split_clause,[],[f135,f252,f224]) ).
fof(f224,plain,
( spl3_16
<=> implies_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f252,plain,
( spl3_22
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f135,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).
fof(f250,plain,
( ~ spl3_9
| spl3_21 ),
inference(avatar_split_clause,[],[f134,f248,f189]) ).
fof(f189,plain,
( spl3_9
<=> or_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f248,plain,
( spl3_21
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f134,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
fof(f246,plain,
( ~ spl3_10
| spl3_20 ),
inference(avatar_split_clause,[],[f133,f244,f194]) ).
fof(f194,plain,
( spl3_10
<=> or_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f133,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
fof(f242,plain,
spl3_19,
inference(avatar_split_clause,[],[f126,f239]) ).
fof(f126,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f237,plain,
spl3_18,
inference(avatar_split_clause,[],[f125,f234]) ).
fof(f125,plain,
op_or,
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_or) ).
fof(f232,plain,
spl3_17,
inference(avatar_split_clause,[],[f124,f229]) ).
fof(f124,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f227,plain,
spl3_16,
inference(avatar_split_clause,[],[f123,f224]) ).
fof(f123,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f222,plain,
spl3_15,
inference(avatar_split_clause,[],[f122,f219]) ).
fof(f122,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f217,plain,
spl3_14,
inference(avatar_split_clause,[],[f121,f214]) ).
fof(f121,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f212,plain,
spl3_13,
inference(avatar_split_clause,[],[f120,f209]) ).
fof(f120,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f207,plain,
spl3_12,
inference(avatar_split_clause,[],[f119,f204]) ).
fof(f119,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f202,plain,
spl3_11,
inference(avatar_split_clause,[],[f118,f199]) ).
fof(f118,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f197,plain,
spl3_10,
inference(avatar_split_clause,[],[f117,f194]) ).
fof(f117,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f192,plain,
spl3_9,
inference(avatar_split_clause,[],[f116,f189]) ).
fof(f116,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f187,plain,
spl3_8,
inference(avatar_split_clause,[],[f115,f184]) ).
fof(f184,plain,
( spl3_8
<=> or_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f115,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f182,plain,
spl3_7,
inference(avatar_split_clause,[],[f114,f179]) ).
fof(f114,plain,
equivalence_1,
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f177,plain,
spl3_6,
inference(avatar_split_clause,[],[f113,f174]) ).
fof(f113,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f172,plain,
spl3_5,
inference(avatar_split_clause,[],[f112,f169]) ).
fof(f169,plain,
( spl3_5
<=> equivalence_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f112,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f167,plain,
spl3_4,
inference(avatar_split_clause,[],[f111,f164]) ).
fof(f111,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f162,plain,
spl3_3,
inference(avatar_split_clause,[],[f110,f159]) ).
fof(f110,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f157,plain,
spl3_2,
inference(avatar_split_clause,[],[f109,f154]) ).
fof(f109,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f152,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f108,f149]) ).
fof(f108,plain,
~ cn1,
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
~ cn1,
inference(flattening,[],[f54]) ).
fof(f54,negated_conjecture,
~ cn1,
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
cn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL451+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 13:27:42 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (1430)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (1432)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 % (1433)WARNING: value z3 for option sas not known
% 0.21/0.38 % (1431)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (1434)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (1433)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38 % (1435)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.38 % (1436)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.38 TRYING [3]
% 0.21/0.38 % (1437)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 % (1435)First to succeed.
% 0.21/0.39 % (1435)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1430"
% 0.21/0.39 TRYING [1]
% 0.21/0.39 % (1436)Also succeeded, but the first one will report.
% 0.21/0.39 % (1435)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39 % (1435)------------------------------
% 0.21/0.39 % (1435)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.39 % (1435)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (1435)Memory used [KB]: 964
% 0.21/0.39 % (1435)Time elapsed: 0.009 s
% 0.21/0.39 % (1435)Instructions burned: 10 (million)
% 0.21/0.39 % (1430)Success in time 0.026 s
%------------------------------------------------------------------------------