TSTP Solution File: SWC179+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWC179+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 : n028.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 18:39:23 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 8 unt; 0 def)
% Number of atoms : 321 ( 91 equ)
% Maximal formula atoms : 22 ( 7 avg)
% Number of connectives : 396 ( 118 ~; 94 |; 160 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 119 ( 63 !; 56 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f733,plain,
$false,
inference(avatar_sat_refutation,[],[f646,f726,f732]) ).
fof(f732,plain,
~ spl61_8,
inference(avatar_contradiction_clause,[],[f731]) ).
fof(f731,plain,
( $false
| ~ spl61_8 ),
inference(subsumption_resolution,[],[f730,f519]) ).
fof(f519,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f730,plain,
( ~ duplicatefreeP(nil)
| ~ spl61_8 ),
inference(backward_demodulation,[],[f436,f645]) ).
fof(f645,plain,
( nil = sK33
| ~ spl61_8 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f643,plain,
( spl61_8
<=> nil = sK33 ),
introduced(avatar_definition,[new_symbols(naming,[spl61_8])]) ).
fof(f436,plain,
~ duplicatefreeP(sK33),
inference(cnf_transformation,[],[f291]) ).
fof(f291,plain,
( ssList(sK33)
& ssList(sK35)
& sK36 = sK34
& ( ( nil = sK35
& nil = sK36 )
| sP2(sK36,sK35) )
& ssList(sK36)
& sK35 = sK33
& ~ duplicatefreeP(sK33)
& ssList(sK34) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36])],[f227,f290,f289,f288,f287]) ).
fof(f287,plain,
( ? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ssList(X2)
& ? [X3] :
( X1 = X3
& ( ( nil = X2
& nil = X3 )
| sP2(X3,X2) )
& ssList(X3)
& X0 = X2
& ~ duplicatefreeP(X0) ) )
& ssList(X1) ) )
=> ( ssList(sK33)
& ? [X1] :
( ? [X2] :
( ssList(X2)
& ? [X3] :
( X1 = X3
& ( ( nil = X2
& nil = X3 )
| sP2(X3,X2) )
& ssList(X3)
& sK33 = X2
& ~ duplicatefreeP(sK33) ) )
& ssList(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f288,plain,
( ? [X1] :
( ? [X2] :
( ssList(X2)
& ? [X3] :
( X1 = X3
& ( ( nil = X2
& nil = X3 )
| sP2(X3,X2) )
& ssList(X3)
& sK33 = X2
& ~ duplicatefreeP(sK33) ) )
& ssList(X1) )
=> ( ? [X2] :
( ssList(X2)
& ? [X3] :
( sK34 = X3
& ( ( nil = X2
& nil = X3 )
| sP2(X3,X2) )
& ssList(X3)
& sK33 = X2
& ~ duplicatefreeP(sK33) ) )
& ssList(sK34) ) ),
introduced(choice_axiom,[]) ).
fof(f289,plain,
( ? [X2] :
( ssList(X2)
& ? [X3] :
( sK34 = X3
& ( ( nil = X2
& nil = X3 )
| sP2(X3,X2) )
& ssList(X3)
& sK33 = X2
& ~ duplicatefreeP(sK33) ) )
=> ( ssList(sK35)
& ? [X3] :
( sK34 = X3
& ( ( nil = sK35
& nil = X3 )
| sP2(X3,sK35) )
& ssList(X3)
& sK35 = sK33
& ~ duplicatefreeP(sK33) ) ) ),
introduced(choice_axiom,[]) ).
fof(f290,plain,
( ? [X3] :
( sK34 = X3
& ( ( nil = sK35
& nil = X3 )
| sP2(X3,sK35) )
& ssList(X3)
& sK35 = sK33
& ~ duplicatefreeP(sK33) )
=> ( sK36 = sK34
& ( ( nil = sK35
& nil = sK36 )
| sP2(sK36,sK35) )
& ssList(sK36)
& sK35 = sK33
& ~ duplicatefreeP(sK33) ) ),
introduced(choice_axiom,[]) ).
fof(f227,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ssList(X2)
& ? [X3] :
( X1 = X3
& ( ( nil = X2
& nil = X3 )
| sP2(X3,X2) )
& ssList(X3)
& X0 = X2
& ~ duplicatefreeP(X0) ) )
& ssList(X1) ) ),
inference(definition_folding,[],[f141,f226]) ).
fof(f226,plain,
! [X3,X2] :
( ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ ssItem(X7)
| ~ lt(X4,X7)
| ~ memberP(X5,X7) )
& ssList(X6) ) ) )
| ~ sP2(X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f141,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ssList(X2)
& ? [X3] :
( X1 = X3
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ ssItem(X7)
| ~ lt(X4,X7)
| ~ memberP(X5,X7) )
& ssList(X6) ) ) ) )
& ssList(X3)
& X0 = X2
& ~ duplicatefreeP(X0) ) )
& ssList(X1) ) ),
inference(flattening,[],[f140]) ).
fof(f140,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X5,X2),X6) = X3
& ! [X7] :
( ~ ssItem(X7)
| ~ lt(X4,X7)
| ~ memberP(X5,X7) )
& ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& cons(X4,nil) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) ) )
& X0 = X2
& ~ duplicatefreeP(X0)
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& lt(X4,X7)
& memberP(X5,X7) )
| ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| cons(X4,nil) != X2 ) ) ) ) )
| X0 != X2
| duplicatefreeP(X0) ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,X2),X6) != X3
| ? [X7] :
( ssItem(X7)
& lt(X4,X7)
& memberP(X5,X7) )
| ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| cons(X4,nil) != X2 ) ) ) ) )
| X0 != X2
| duplicatefreeP(X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f726,plain,
~ spl61_7,
inference(avatar_contradiction_clause,[],[f725]) ).
fof(f725,plain,
( $false
| ~ spl61_7 ),
inference(subsumption_resolution,[],[f724,f436]) ).
fof(f724,plain,
( duplicatefreeP(sK33)
| ~ spl61_7 ),
inference(resolution,[],[f709,f638]) ).
fof(f638,plain,
( sP2(sK34,sK33)
| ~ spl61_7 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f636,plain,
( spl61_7
<=> sP2(sK34,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl61_7])]) ).
fof(f709,plain,
! [X8,X9] :
( ~ sP2(X8,X9)
| duplicatefreeP(X9) ),
inference(subsumption_resolution,[],[f701,f434]) ).
fof(f434,plain,
! [X0,X1] :
( ssItem(sK30(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0,X1] :
( ( ssItem(sK30(X0,X1))
& ssList(sK31(X0,X1))
& app(app(sK31(X0,X1),X1),sK32(X0,X1)) = X0
& cons(sK30(X0,X1),nil) = X1
& ! [X5] :
( ~ lt(X5,sK30(X0,X1))
| ~ memberP(sK32(X0,X1),X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ lt(sK30(X0,X1),X6)
| ~ memberP(sK31(X0,X1),X6) )
& ssList(sK32(X0,X1)) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32])],[f282,f285,f284,f283]) ).
fof(f283,plain,
! [X0,X1] :
( ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( app(app(X3,X1),X4) = X0
& cons(X2,nil) = X1
& ! [X5] :
( ~ lt(X5,X2)
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ lt(X2,X6)
| ~ memberP(X3,X6) )
& ssList(X4) ) ) )
=> ( ssItem(sK30(X0,X1))
& ? [X3] :
( ssList(X3)
& ? [X4] :
( app(app(X3,X1),X4) = X0
& cons(sK30(X0,X1),nil) = X1
& ! [X5] :
( ~ lt(X5,sK30(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ lt(sK30(X0,X1),X6)
| ~ memberP(X3,X6) )
& ssList(X4) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f284,plain,
! [X0,X1] :
( ? [X3] :
( ssList(X3)
& ? [X4] :
( app(app(X3,X1),X4) = X0
& cons(sK30(X0,X1),nil) = X1
& ! [X5] :
( ~ lt(X5,sK30(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ lt(sK30(X0,X1),X6)
| ~ memberP(X3,X6) )
& ssList(X4) ) )
=> ( ssList(sK31(X0,X1))
& ? [X4] :
( app(app(sK31(X0,X1),X1),X4) = X0
& cons(sK30(X0,X1),nil) = X1
& ! [X5] :
( ~ lt(X5,sK30(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ lt(sK30(X0,X1),X6)
| ~ memberP(sK31(X0,X1),X6) )
& ssList(X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f285,plain,
! [X0,X1] :
( ? [X4] :
( app(app(sK31(X0,X1),X1),X4) = X0
& cons(sK30(X0,X1),nil) = X1
& ! [X5] :
( ~ lt(X5,sK30(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ lt(sK30(X0,X1),X6)
| ~ memberP(sK31(X0,X1),X6) )
& ssList(X4) )
=> ( app(app(sK31(X0,X1),X1),sK32(X0,X1)) = X0
& cons(sK30(X0,X1),nil) = X1
& ! [X5] :
( ~ lt(X5,sK30(X0,X1))
| ~ memberP(sK32(X0,X1),X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ lt(sK30(X0,X1),X6)
| ~ memberP(sK31(X0,X1),X6) )
& ssList(sK32(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f282,plain,
! [X0,X1] :
( ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( app(app(X3,X1),X4) = X0
& cons(X2,nil) = X1
& ! [X5] :
( ~ lt(X5,X2)
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ lt(X2,X6)
| ~ memberP(X3,X6) )
& ssList(X4) ) ) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f281]) ).
fof(f281,plain,
! [X3,X2] :
( ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ ssItem(X7)
| ~ lt(X4,X7)
| ~ memberP(X5,X7) )
& ssList(X6) ) ) )
| ~ sP2(X3,X2) ),
inference(nnf_transformation,[],[f226]) ).
fof(f701,plain,
! [X8,X9] :
( ~ ssItem(sK30(X8,X9))
| duplicatefreeP(X9)
| ~ sP2(X8,X9) ),
inference(superposition,[],[f537,f431]) ).
fof(f431,plain,
! [X0,X1] :
( cons(sK30(X0,X1),nil) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f286]) ).
fof(f537,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
fof(f646,plain,
( spl61_8
| spl61_7 ),
inference(avatar_split_clause,[],[f572,f636,f643]) ).
fof(f572,plain,
( sP2(sK34,sK33)
| nil = sK33 ),
inference(definition_unfolding,[],[f440,f437,f441,f437]) ).
fof(f441,plain,
sK36 = sK34,
inference(cnf_transformation,[],[f291]) ).
fof(f437,plain,
sK35 = sK33,
inference(cnf_transformation,[],[f291]) ).
fof(f440,plain,
( nil = sK35
| sP2(sK36,sK35) ),
inference(cnf_transformation,[],[f291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC179+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % 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 : n028.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 18:40:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.50 % (13877)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.51 % (13877)Instruction limit reached!
% 0.20/0.51 % (13877)------------------------------
% 0.20/0.51 % (13877)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (13876)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.51 % (13887)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52 % (13876)First to succeed.
% 0.20/0.52 % (13877)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (13877)Termination reason: Unknown
% 0.20/0.52 % (13877)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (13877)Memory used [KB]: 6396
% 0.20/0.52 % (13877)Time elapsed: 0.096 s
% 0.20/0.52 % (13877)Instructions burned: 13 (million)
% 0.20/0.52 % (13877)------------------------------
% 0.20/0.52 % (13877)------------------------------
% 0.20/0.53 % (13876)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (13876)------------------------------
% 0.20/0.53 % (13876)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (13876)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (13876)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (13876)Memory used [KB]: 6524
% 0.20/0.53 % (13876)Time elapsed: 0.102 s
% 0.20/0.53 % (13876)Instructions burned: 16 (million)
% 0.20/0.53 % (13876)------------------------------
% 0.20/0.53 % (13876)------------------------------
% 0.20/0.53 % (13875)Success in time 0.177 s
%------------------------------------------------------------------------------