TSTP Solution File: SWC002-1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWC002-1 : 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 : n022.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 18:38:08 EDT 2022
% Result : Unsatisfiable 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 76 ( 5 unt; 0 def)
% Number of atoms : 350 ( 69 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 540 ( 266 ~; 259 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f542,plain,
$false,
inference(avatar_sat_refutation,[],[f250,f259,f264,f265,f271,f276,f281,f287,f290,f300,f301,f440,f468,f492,f518,f541]) ).
fof(f541,plain,
( spl0_43
| ~ spl0_33
| ~ spl0_37
| ~ spl0_4
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f540,f489,f257,f465,f437,f515]) ).
fof(f515,plain,
( spl0_43
<=> sk6 = sk5(sk8,sk7,sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f437,plain,
( spl0_33
<=> ssItem(sk5(sk8,sk7,sk6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f465,plain,
( spl0_37
<=> geq(sk5(sk8,sk7,sk6),sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f257,plain,
( spl0_4
<=> ! [X6] :
( sk6 = X6
| ~ geq(X6,sk6)
| ~ memberP(sk4,X6)
| ~ ssItem(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f489,plain,
( spl0_40
<=> memberP(sk4,sk5(sk8,sk7,sk6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f540,plain,
( ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| sk6 = sk5(sk8,sk7,sk6)
| ~ spl0_4
| ~ spl0_40 ),
inference(resolution,[],[f491,f258]) ).
fof(f258,plain,
( ! [X6] :
( ~ memberP(sk4,X6)
| ~ geq(X6,sk6)
| ~ ssItem(X6)
| sk6 = X6 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f491,plain,
( memberP(sk4,sk5(sk8,sk7,sk6))
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f518,plain,
( ~ spl0_7
| ~ spl0_43
| ~ spl0_9
| ~ spl0_5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f513,f292,f278,f252,f261,f283,f515,f273]) ).
fof(f273,plain,
( spl0_7
<=> ssList(sk7) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f283,plain,
( spl0_9
<=> ssItem(sk6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f261,plain,
( spl0_5
<=> ssList(sk8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f252,plain,
( spl0_3
<=> sk4 = app(app(sk7,cons(sk6,nil)),sk8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f278,plain,
( spl0_8
<=> sk3 = app(sk7,sk8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f292,plain,
( spl0_10
<=> ! [X6,X7,X8] :
( ~ ssList(X7)
| sk5(X8,X7,X6) != X6
| sk4 != app(app(X7,cons(X6,nil)),X8)
| ~ ssItem(X6)
| ~ ssList(X8)
| sk3 != app(X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f513,plain,
( ~ ssList(sk8)
| ~ ssItem(sk6)
| sk6 != sk5(sk8,sk7,sk6)
| ~ ssList(sk7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f512]) ).
fof(f512,plain,
( ~ ssList(sk7)
| sk3 != sk3
| ~ ssList(sk8)
| sk6 != sk5(sk8,sk7,sk6)
| ~ ssItem(sk6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f506,f280]) ).
fof(f280,plain,
( sk3 = app(sk7,sk8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f506,plain,
( ~ ssList(sk7)
| sk6 != sk5(sk8,sk7,sk6)
| ~ ssItem(sk6)
| sk3 != app(sk7,sk8)
| ~ ssList(sk8)
| ~ spl0_3
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f504]) ).
fof(f504,plain,
( ~ ssList(sk7)
| sk6 != sk5(sk8,sk7,sk6)
| sk4 != sk4
| sk3 != app(sk7,sk8)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f293,f254]) ).
fof(f254,plain,
( sk4 = app(app(sk7,cons(sk6,nil)),sk8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f293,plain,
( ! [X8,X6,X7] :
( sk4 != app(app(X7,cons(X6,nil)),X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| sk3 != app(X7,X8)
| ~ ssList(X8)
| sk5(X8,X7,X6) != X6 )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f492,plain,
( ~ spl0_7
| spl0_40
| ~ spl0_9
| ~ spl0_5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f487,f278,f268,f252,f261,f283,f489,f273]) ).
fof(f268,plain,
( spl0_6
<=> ! [X6,X7,X8] :
( ~ ssList(X7)
| sk4 != app(app(X7,cons(X6,nil)),X8)
| ~ ssList(X8)
| ~ ssItem(X6)
| sk3 != app(X7,X8)
| memberP(sk4,sk5(X8,X7,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f487,plain,
( ~ ssList(sk8)
| ~ ssItem(sk6)
| memberP(sk4,sk5(sk8,sk7,sk6))
| ~ ssList(sk7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f486]) ).
fof(f486,plain,
( memberP(sk4,sk5(sk8,sk7,sk6))
| sk3 != sk3
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f481,f280]) ).
fof(f481,plain,
( memberP(sk4,sk5(sk8,sk7,sk6))
| ~ ssList(sk7)
| ~ ssList(sk8)
| sk3 != app(sk7,sk8)
| ~ ssItem(sk6)
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f478]) ).
fof(f478,plain,
( ~ ssItem(sk6)
| ~ ssList(sk7)
| memberP(sk4,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| sk3 != app(sk7,sk8)
| sk4 != sk4
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f269,f254]) ).
fof(f269,plain,
( ! [X8,X6,X7] :
( sk4 != app(app(X7,cons(X6,nil)),X8)
| ~ ssItem(X6)
| ~ ssList(X7)
| ~ ssList(X8)
| memberP(sk4,sk5(X8,X7,X6))
| sk3 != app(X7,X8) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f468,plain,
( ~ spl0_5
| spl0_37
| ~ spl0_9
| ~ spl0_7
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f463,f278,f252,f248,f273,f283,f465,f261]) ).
fof(f248,plain,
( spl0_2
<=> ! [X6,X7,X8] :
( ~ ssList(X7)
| sk3 != app(X7,X8)
| geq(sk5(X8,X7,X6),X6)
| sk4 != app(app(X7,cons(X6,nil)),X8)
| ~ ssItem(X6)
| ~ ssList(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f463,plain,
( ~ ssList(sk7)
| ~ ssItem(sk6)
| geq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f462]) ).
fof(f462,plain,
( ~ ssList(sk7)
| sk3 != sk3
| ~ ssList(sk8)
| geq(sk5(sk8,sk7,sk6),sk6)
| ~ ssItem(sk6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[],[f457,f280]) ).
fof(f457,plain,
( sk3 != app(sk7,sk8)
| geq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f454]) ).
fof(f454,plain,
( ~ ssList(sk7)
| geq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| sk3 != app(sk7,sk8)
| sk4 != sk4
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f249,f254]) ).
fof(f249,plain,
( ! [X8,X6,X7] :
( sk4 != app(app(X7,cons(X6,nil)),X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssList(X8)
| sk3 != app(X7,X8)
| geq(sk5(X8,X7,X6),X6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f440,plain,
( ~ spl0_7
| spl0_33
| ~ spl0_9
| ~ spl0_5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f435,f297,f278,f252,f261,f283,f437,f273]) ).
fof(f297,plain,
( spl0_11
<=> ! [X6,X7,X8] :
( ~ ssItem(X6)
| ssItem(sk5(X8,X7,X6))
| sk4 != app(app(X7,cons(X6,nil)),X8)
| sk3 != app(X7,X8)
| ~ ssList(X7)
| ~ ssList(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f435,plain,
( ~ ssList(sk8)
| ~ ssItem(sk6)
| ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f434]) ).
fof(f434,plain,
( ~ ssList(sk8)
| ~ ssItem(sk6)
| sk3 != sk3
| ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f432,f280]) ).
fof(f432,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6)
| sk3 != app(sk7,sk8)
| ssItem(sk5(sk8,sk7,sk6))
| ~ spl0_3
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f430]) ).
fof(f430,plain,
( ~ ssList(sk8)
| sk4 != sk4
| sk3 != app(sk7,sk8)
| ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ spl0_3
| ~ spl0_11 ),
inference(superposition,[],[f298,f254]) ).
fof(f298,plain,
( ! [X8,X6,X7] :
( sk4 != app(app(X7,cons(X6,nil)),X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ssItem(sk5(X8,X7,X6))
| sk3 != app(X7,X8)
| ~ ssList(X8) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f301,plain,
( spl0_11
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f229,f244,f297]) ).
fof(f244,plain,
( spl0_1
<=> neq(sk4,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f229,plain,
! [X8,X6,X7] :
( ~ neq(sk4,nil)
| ~ ssItem(X6)
| ~ ssList(X8)
| ~ ssList(X7)
| sk3 != app(X7,X8)
| ssItem(sk5(X8,X7,X6))
| sk4 != app(app(X7,cons(X6,nil)),X8) ),
inference(definition_unfolding,[],[f204,f191,f190]) ).
fof(f190,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f191,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f204,axiom,
! [X8,X6,X7] :
( sk1 != app(X7,X8)
| ~ ssItem(X6)
| ~ ssList(X8)
| sk2 != app(app(X7,cons(X6,nil)),X8)
| ~ neq(sk4,nil)
| ssItem(sk5(X8,X7,X6))
| ~ ssList(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
fof(f300,plain,
( ~ spl0_1
| spl0_10 ),
inference(avatar_split_clause,[],[f220,f292,f244]) ).
fof(f220,plain,
! [X8,X6,X7] :
( ~ ssItem(X6)
| ~ ssList(X8)
| ~ neq(sk4,nil)
| ~ ssList(X7)
| sk5(X8,X7,X6) != X6
| sk4 != app(app(X7,cons(X6,nil)),X8)
| sk3 != app(X7,X8) ),
inference(definition_unfolding,[],[f207,f190,f191]) ).
fof(f207,axiom,
! [X8,X6,X7] :
( sk2 != app(app(X7,cons(X6,nil)),X8)
| sk5(X8,X7,X6) != X6
| ~ ssList(X7)
| ~ neq(sk4,nil)
| ~ ssList(X8)
| sk1 != app(X7,X8)
| ~ ssItem(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_22) ).
fof(f290,plain,
( ~ spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f225,f268,f244]) ).
fof(f225,plain,
! [X8,X6,X7] :
( ~ ssList(X8)
| sk4 != app(app(X7,cons(X6,nil)),X8)
| sk3 != app(X7,X8)
| ~ neq(sk4,nil)
| ~ ssList(X7)
| ~ ssItem(X6)
| memberP(sk4,sk5(X8,X7,X6)) ),
inference(definition_unfolding,[],[f205,f191,f190,f190]) ).
fof(f205,axiom,
! [X8,X6,X7] :
( sk1 != app(X7,X8)
| ~ neq(sk4,nil)
| sk2 != app(app(X7,cons(X6,nil)),X8)
| ~ ssItem(X6)
| memberP(sk2,sk5(X8,X7,X6))
| ~ ssList(X8)
| ~ ssList(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_20) ).
fof(f287,plain,
( spl0_9
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f208,f244,f283]) ).
fof(f208,axiom,
( ~ neq(sk4,nil)
| ssItem(sk6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_23) ).
fof(f281,plain,
( ~ spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f212,f278,f244]) ).
fof(f212,axiom,
( sk3 = app(sk7,sk8)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_27) ).
fof(f276,plain,
( ~ spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f209,f273,f244]) ).
fof(f209,axiom,
( ssList(sk7)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_24) ).
fof(f271,plain,
( spl0_3
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f211,f244,f252]) ).
fof(f211,axiom,
( ~ neq(sk4,nil)
| sk4 = app(app(sk7,cons(sk6,nil)),sk8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_26) ).
fof(f265,plain,
spl0_1,
inference(avatar_split_clause,[],[f242,f244]) ).
fof(f242,plain,
neq(sk4,nil),
inference(duplicate_literal_removal,[],[f216]) ).
fof(f216,plain,
( neq(sk4,nil)
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f192,f190,f190]) ).
fof(f192,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f264,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_split_clause,[],[f210,f261,f244]) ).
fof(f210,axiom,
( ssList(sk8)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_25) ).
fof(f259,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f213,f257,f244]) ).
fof(f213,axiom,
! [X6] :
( sk6 = X6
| ~ ssItem(X6)
| ~ memberP(sk4,X6)
| ~ geq(X6,sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_28) ).
fof(f250,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f223,f248,f244]) ).
fof(f223,plain,
! [X8,X6,X7] :
( ~ ssList(X7)
| ~ ssList(X8)
| ~ ssItem(X6)
| sk4 != app(app(X7,cons(X6,nil)),X8)
| ~ neq(sk4,nil)
| geq(sk5(X8,X7,X6),X6)
| sk3 != app(X7,X8) ),
inference(definition_unfolding,[],[f206,f190,f191]) ).
fof(f206,axiom,
! [X8,X6,X7] :
( sk2 != app(app(X7,cons(X6,nil)),X8)
| sk1 != app(X7,X8)
| ~ ssList(X7)
| ~ neq(sk4,nil)
| ~ ssList(X8)
| ~ ssItem(X6)
| geq(sk5(X8,X7,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_21) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC002-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % 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 : n022.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 17:52:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.51 % (11564)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/34Mi)
% 0.20/0.53 % (11581)lrs+1010_1:1_bd=off:fsr=off:sd=1:sos=on:ss=axioms:i=67:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/67Mi)
% 0.20/0.54 % (11581)First to succeed.
% 0.20/0.55 % (11581)Refutation found. Thanks to Tanya!
% 0.20/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55 % (11581)------------------------------
% 0.20/0.55 % (11581)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (11581)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (11581)Termination reason: Refutation
% 0.20/0.55
% 0.20/0.55 % (11581)Memory used [KB]: 6268
% 0.20/0.55 % (11581)Time elapsed: 0.104 s
% 0.20/0.55 % (11581)Instructions burned: 11 (million)
% 0.20/0.55 % (11581)------------------------------
% 0.20/0.55 % (11581)------------------------------
% 0.20/0.55 % (11559)Success in time 0.199 s
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