TSTP Solution File: SWC012+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWC012+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n014.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 : Wed Aug 31 18:38:12 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 10 unt; 0 def)
% Number of atoms : 349 ( 101 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 474 ( 179 ~; 154 |; 115 &)
% ( 5 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 110 ( 66 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f254,plain,
$false,
inference(avatar_sat_refutation,[],[f213,f222,f223,f225,f229,f253]) ).
fof(f253,plain,
( ~ spl9_2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(avatar_contradiction_clause,[],[f252]) ).
fof(f252,plain,
( $false
| ~ spl9_2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(subsumption_resolution,[],[f251,f173]) ).
fof(f173,plain,
ssList(sK2),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( ssList(sK2)
& ssList(sK5)
& sK4 = sK2
& sK3 = sK5
& ( ( app(sK4,cons(sK6,nil)) = sK5
& ssItem(sK6)
& neq(sK3,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != sK3
| app(X6,X7) != sK2
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(sK5,nil)
& neq(sK3,nil) ) )
& ssList(sK4)
& ssList(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f100,f132,f131,f130,f129,f128]) ).
fof(f128,plain,
( ? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X0 = X2
& X1 = X3
& ( ( ? [X4] :
( app(X2,cons(X4,nil)) = X3
& ssItem(X4) )
& neq(X1,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != X1
| app(X6,X7) != X0
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(X3,nil)
& neq(X1,nil) ) ) )
& ssList(X2) )
& ssList(X1) ) )
=> ( ssList(sK2)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& sK2 = X2
& X1 = X3
& ( ( ? [X4] :
( app(X2,cons(X4,nil)) = X3
& ssItem(X4) )
& neq(X1,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != X1
| app(X6,X7) != sK2
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(X3,nil)
& neq(X1,nil) ) ) )
& ssList(X2) )
& ssList(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& sK2 = X2
& X1 = X3
& ( ( ? [X4] :
( app(X2,cons(X4,nil)) = X3
& ssItem(X4) )
& neq(X1,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != X1
| app(X6,X7) != sK2
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(X3,nil)
& neq(X1,nil) ) ) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ssList(X3)
& sK2 = X2
& sK3 = X3
& ( ( ? [X4] :
( app(X2,cons(X4,nil)) = X3
& ssItem(X4) )
& neq(sK3,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != sK3
| app(X6,X7) != sK2
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(X3,nil)
& neq(sK3,nil) ) ) )
& ssList(X2) )
& ssList(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
( ? [X2] :
( ? [X3] :
( ssList(X3)
& sK2 = X2
& sK3 = X3
& ( ( ? [X4] :
( app(X2,cons(X4,nil)) = X3
& ssItem(X4) )
& neq(sK3,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != sK3
| app(X6,X7) != sK2
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(X3,nil)
& neq(sK3,nil) ) ) )
& ssList(X2) )
=> ( ? [X3] :
( ssList(X3)
& sK4 = sK2
& sK3 = X3
& ( ( ? [X4] :
( app(sK4,cons(X4,nil)) = X3
& ssItem(X4) )
& neq(sK3,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != sK3
| app(X6,X7) != sK2
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(X3,nil)
& neq(sK3,nil) ) ) )
& ssList(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
( ? [X3] :
( ssList(X3)
& sK4 = sK2
& sK3 = X3
& ( ( ? [X4] :
( app(sK4,cons(X4,nil)) = X3
& ssItem(X4) )
& neq(sK3,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != sK3
| app(X6,X7) != sK2
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(X3,nil)
& neq(sK3,nil) ) ) )
=> ( ssList(sK5)
& sK4 = sK2
& sK3 = sK5
& ( ( ? [X4] :
( app(sK4,cons(X4,nil)) = sK5
& ssItem(X4) )
& neq(sK3,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != sK3
| app(X6,X7) != sK2
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(sK5,nil)
& neq(sK3,nil) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
( ? [X4] :
( app(sK4,cons(X4,nil)) = sK5
& ssItem(X4) )
=> ( app(sK4,cons(sK6,nil)) = sK5
& ssItem(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X0 = X2
& X1 = X3
& ( ( ? [X4] :
( app(X2,cons(X4,nil)) = X3
& ssItem(X4) )
& neq(X1,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != X1
| app(X6,X7) != X0
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(X3,nil)
& neq(X1,nil) ) ) )
& ssList(X2) )
& ssList(X1) ) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ? [X4] :
( app(X2,cons(X4,nil)) = X3
& ssItem(X4) )
& neq(X1,nil)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ! [X7] :
( app(app(X6,cons(X5,nil)),X7) != X1
| app(X6,X7) != X0
| ~ ssList(X7) )
| ~ ssList(X6) ) ) )
| ( ~ neq(X3,nil)
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(app(X6,cons(X5,nil)),X7) = X1
& app(X6,X7) = X0
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ! [X4] :
( ssItem(X4)
=> app(X2,cons(X4,nil)) != X3 )
| ~ neq(X1,nil) )
& ( neq(X3,nil)
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ~ neq(X1,nil)
| ! [X7] :
( ssItem(X7)
=> app(X2,cons(X7,nil)) != X3 )
| ? [X4] :
( ? [X5] :
( ssList(X5)
& ? [X6] :
( app(X5,X6) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) ) )
& ssItem(X4) ) ) )
| X0 != X2 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ~ neq(X1,nil)
| ! [X7] :
( ssItem(X7)
=> app(X2,cons(X7,nil)) != X3 )
| ? [X4] :
( ? [X5] :
( ssList(X5)
& ? [X6] :
( app(X5,X6) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) ) )
& ssItem(X4) ) ) )
| X0 != X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f251,plain,
( ~ ssList(sK2)
| ~ spl9_2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f250]) ).
fof(f250,plain,
( sK2 != sK2
| ~ ssList(sK2)
| ~ spl9_2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(superposition,[],[f239,f154]) ).
fof(f154,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f239,plain,
( app(sK2,nil) != sK2
| ~ spl9_2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(subsumption_resolution,[],[f238,f201]) ).
fof(f201,plain,
( ssList(nil)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f200,plain,
( spl9_2
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f238,plain,
( app(sK2,nil) != sK2
| ~ ssList(nil)
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(subsumption_resolution,[],[f236,f172]) ).
fof(f172,plain,
ssList(sK5),
inference(cnf_transformation,[],[f133]) ).
fof(f236,plain,
( ~ ssList(sK5)
| ~ ssList(nil)
| app(sK2,nil) != sK2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(trivial_inequality_removal,[],[f232]) ).
fof(f232,plain,
( ~ ssList(sK5)
| sK5 != sK5
| ~ ssList(nil)
| app(sK2,nil) != sK2
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(superposition,[],[f228,f154]) ).
fof(f228,plain,
( ! [X0] :
( sK5 != app(sK5,X0)
| ~ ssList(X0)
| app(sK2,X0) != sK2 )
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(subsumption_resolution,[],[f227,f173]) ).
fof(f227,plain,
( ! [X0] :
( sK5 != app(sK5,X0)
| ~ ssList(X0)
| ~ ssList(sK2)
| app(sK2,X0) != sK2 )
| ~ spl9_4
| ~ spl9_5
| ~ spl9_6 ),
inference(subsumption_resolution,[],[f226,f211]) ).
fof(f211,plain,
( ssItem(sK6)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f209,plain,
( spl9_4
<=> ssItem(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f226,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ ssItem(sK6)
| sK5 != app(sK5,X0)
| ~ ssList(sK2)
| app(sK2,X0) != sK2 )
| ~ spl9_5
| ~ spl9_6 ),
inference(superposition,[],[f216,f221]) ).
fof(f221,plain,
( sK5 = app(sK2,cons(sK6,nil))
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f219,plain,
( spl9_6
<=> sK5 = app(sK2,cons(sK6,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f216,plain,
( ! [X6,X7,X5] :
( app(app(X6,cons(X5,nil)),X7) != sK5
| ~ ssList(X7)
| app(X6,X7) != sK2
| ~ ssList(X6)
| ~ ssItem(X5) )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f215,plain,
( spl9_5
<=> ! [X6,X5,X7] :
( ~ ssList(X7)
| app(X6,X7) != sK2
| ~ ssItem(X5)
| ~ ssList(X6)
| app(app(X6,cons(X5,nil)),X7) != sK5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
fof(f229,plain,
spl9_2,
inference(avatar_split_clause,[],[f157,f200]) ).
fof(f157,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f225,plain,
spl9_3,
inference(avatar_split_clause,[],[f194,f205]) ).
fof(f205,plain,
( spl9_3
<=> neq(sK5,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f194,plain,
neq(sK5,nil),
inference(duplicate_literal_removal,[],[f182]) ).
fof(f182,plain,
( neq(sK5,nil)
| neq(sK5,nil) ),
inference(definition_unfolding,[],[f164,f170,f170]) ).
fof(f170,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f133]) ).
fof(f164,plain,
( neq(sK3,nil)
| neq(sK3,nil) ),
inference(cnf_transformation,[],[f133]) ).
fof(f223,plain,
( spl9_5
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f183,f205,f215]) ).
fof(f183,plain,
! [X6,X7,X5] :
( ~ neq(sK5,nil)
| ~ ssList(X7)
| app(X6,X7) != sK2
| ~ ssList(X6)
| ~ ssItem(X5)
| app(app(X6,cons(X5,nil)),X7) != sK5 ),
inference(definition_unfolding,[],[f163,f170]) ).
fof(f163,plain,
! [X6,X7,X5] :
( ~ ssItem(X5)
| app(app(X6,cons(X5,nil)),X7) != sK3
| app(X6,X7) != sK2
| ~ ssList(X7)
| ~ ssList(X6)
| ~ neq(sK5,nil) ),
inference(cnf_transformation,[],[f133]) ).
fof(f222,plain,
( ~ spl9_3
| spl9_6 ),
inference(avatar_split_clause,[],[f178,f219,f205]) ).
fof(f178,plain,
( sK5 = app(sK2,cons(sK6,nil))
| ~ neq(sK5,nil) ),
inference(definition_unfolding,[],[f169,f171]) ).
fof(f171,plain,
sK4 = sK2,
inference(cnf_transformation,[],[f133]) ).
fof(f169,plain,
( app(sK4,cons(sK6,nil)) = sK5
| ~ neq(sK5,nil) ),
inference(cnf_transformation,[],[f133]) ).
fof(f213,plain,
( spl9_4
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f167,f205,f209]) ).
fof(f167,plain,
( ~ neq(sK5,nil)
| ssItem(sK6) ),
inference(cnf_transformation,[],[f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC012+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 17:57:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.48 % (20341)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.49 % (20325)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.49 % (20325)First to succeed.
% 0.20/0.49 % (20341)Also succeeded, but the first one will report.
% 0.20/0.50 % (20325)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (20325)------------------------------
% 0.20/0.50 % (20325)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (20325)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (20325)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (20325)Memory used [KB]: 6140
% 0.20/0.50 % (20325)Time elapsed: 0.031 s
% 0.20/0.50 % (20325)Instructions burned: 4 (million)
% 0.20/0.50 % (20325)------------------------------
% 0.20/0.50 % (20325)------------------------------
% 0.20/0.50 % (20318)Success in time 0.146 s
%------------------------------------------------------------------------------