TSTP Solution File: SWC096+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SWC096+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 : n017.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 18:38:47 EDT 2022
% Result : Theorem 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 11 unt; 0 def)
% Number of atoms : 231 ( 72 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 269 ( 79 ~; 68 |; 108 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 127 ( 87 !; 40 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f411,plain,
$false,
inference(resolution,[],[f390,f234]) ).
fof(f234,plain,
sP0(sK8,sK7,sK8,sK7),
inference(subsumption_resolution,[],[f184,f195]) ).
fof(f195,plain,
neq(sK8,nil),
inference(subsumption_resolution,[],[f183,f160]) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( neq(X0,nil)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| cons(X4,nil) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ssItem(sK3(X2,X3))
& ssList(sK4(X2,X3))
& app(sK4(X2,X3),cons(sK3(X2,X3),nil)) = X2
& cons(sK3(X2,X3),nil) = X3 )
| ~ sP0(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f127,f129,f128]) ).
fof(f128,plain,
! [X2,X3] :
( ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X2
& cons(X6,nil) = X3 ) )
=> ( ssItem(sK3(X2,X3))
& ? [X7] :
( ssList(X7)
& app(X7,cons(sK3(X2,X3),nil)) = X2
& cons(sK3(X2,X3),nil) = X3 ) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
! [X2,X3] :
( ? [X7] :
( ssList(X7)
& app(X7,cons(sK3(X2,X3),nil)) = X2
& cons(sK3(X2,X3),nil) = X3 )
=> ( ssList(sK4(X2,X3))
& app(sK4(X2,X3),cons(sK3(X2,X3),nil)) = X2
& cons(sK3(X2,X3),nil) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X0
| cons(X4,nil) != X1
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X2
& cons(X6,nil) = X3 ) ) )
| ~ sP0(X0,X1,X2,X3) ),
inference(rectify,[],[f126]) ).
fof(f126,plain,
! [X1,X0,X3,X2] :
( ( neq(X1,nil)
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X1
| cons(X4,nil) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X3
& cons(X6,nil) = X2 ) ) )
| ~ sP0(X1,X0,X3,X2) ),
inference(nnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X1,X0,X3,X2] :
( ( neq(X1,nil)
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X1
| cons(X4,nil) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X3
& cons(X6,nil) = X2 ) ) )
| ~ sP0(X1,X0,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f183,plain,
( neq(sK8,nil)
| sP0(sK8,sK7,sK8,sK7) ),
inference(definition_unfolding,[],[f164,f165,f166,f165]) ).
fof(f166,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
( ssList(sK5)
& ssList(sK8)
& sK5 = sK7
& sK6 = sK8
& ( sP0(sK6,sK5,sK8,sK7)
| ( neq(sK6,nil)
& ~ neq(sK8,nil) ) )
& ssList(sK7)
& ssList(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f120,f134,f133,f132,f131]) ).
fof(f131,plain,
( ? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X0 = X2
& X1 = X3
& ( sP0(X1,X0,X3,X2)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
& ssList(X1) ) )
=> ( ssList(sK5)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& sK5 = X2
& X1 = X3
& ( sP0(X1,sK5,X3,X2)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
& ssList(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& sK5 = X2
& X1 = X3
& ( sP0(X1,sK5,X3,X2)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ssList(X3)
& sK5 = X2
& sK6 = X3
& ( sP0(sK6,sK5,X3,X2)
| ( neq(sK6,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
& ssList(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
( ? [X2] :
( ? [X3] :
( ssList(X3)
& sK5 = X2
& sK6 = X3
& ( sP0(sK6,sK5,X3,X2)
| ( neq(sK6,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
=> ( ? [X3] :
( ssList(X3)
& sK5 = sK7
& sK6 = X3
& ( sP0(sK6,sK5,X3,sK7)
| ( neq(sK6,nil)
& ~ neq(X3,nil) ) ) )
& ssList(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f134,plain,
( ? [X3] :
( ssList(X3)
& sK5 = sK7
& sK6 = X3
& ( sP0(sK6,sK5,X3,sK7)
| ( neq(sK6,nil)
& ~ neq(X3,nil) ) ) )
=> ( ssList(sK8)
& sK5 = sK7
& sK6 = sK8
& ( sP0(sK6,sK5,sK8,sK7)
| ( neq(sK6,nil)
& ~ neq(sK8,nil) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X0 = X2
& X1 = X3
& ( sP0(X1,X0,X3,X2)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
& ssList(X1) ) ),
inference(definition_folding,[],[f114,f119]) ).
fof(f114,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X0 = X2
& X1 = X3
& ( ( neq(X1,nil)
& ! [X4] :
( ! [X5] :
( app(X5,cons(X4,nil)) != X1
| cons(X4,nil) != X0
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X3
& cons(X6,nil) = X2 ) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
& ssList(X1) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ~ neq(X1,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& cons(X4,nil) = X0
& ssList(X5) )
& ssItem(X4) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( cons(X6,nil) != X2
| app(X7,cons(X6,nil)) != X3
| ~ ssList(X7) ) ) ) )
| X0 != X2
| ~ ssList(X3)
| X1 != X3 ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ~ neq(X1,nil)
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& cons(X4,nil) = X0
& ssList(X5) )
& ssItem(X4) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( cons(X6,nil) != X2
| app(X7,cons(X6,nil)) != X3
| ~ ssList(X7) ) ) ) )
| X0 != X2
| ~ ssList(X3)
| X1 != X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f165,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f135]) ).
fof(f164,plain,
( sP0(sK6,sK5,sK8,sK7)
| neq(sK6,nil) ),
inference(cnf_transformation,[],[f135]) ).
fof(f184,plain,
( ~ neq(sK8,nil)
| sP0(sK8,sK7,sK8,sK7) ),
inference(definition_unfolding,[],[f163,f165,f166]) ).
fof(f163,plain,
( sP0(sK6,sK5,sK8,sK7)
| ~ neq(sK8,nil) ),
inference(cnf_transformation,[],[f135]) ).
fof(f390,plain,
! [X2,X3] : ~ sP0(sK8,sK7,X2,X3),
inference(subsumption_resolution,[],[f388,f236]) ).
fof(f236,plain,
ssList(sK4(sK8,sK7)),
inference(resolution,[],[f234,f157]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK4(X2,X3)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f388,plain,
! [X2,X3] :
( ~ sP0(sK8,sK7,X2,X3)
| ~ ssList(sK4(sK8,sK7)) ),
inference(superposition,[],[f291,f343]) ).
fof(f343,plain,
app(sK4(sK8,sK7),sK7) = sK8,
inference(forward_demodulation,[],[f237,f235]) ).
fof(f235,plain,
cons(sK3(sK8,sK7),nil) = sK7,
inference(resolution,[],[f234,f155]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| cons(sK3(X2,X3),nil) = X3 ),
inference(cnf_transformation,[],[f130]) ).
fof(f237,plain,
sK8 = app(sK4(sK8,sK7),cons(sK3(sK8,sK7),nil)),
inference(resolution,[],[f234,f156]) ).
fof(f156,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(sK4(X2,X3),cons(sK3(X2,X3),nil)) = X2 ),
inference(cnf_transformation,[],[f130]) ).
fof(f291,plain,
! [X2,X0,X1] :
( ~ sP0(app(X0,sK7),sK7,X1,X2)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f278,f238]) ).
fof(f238,plain,
ssItem(sK3(sK8,sK7)),
inference(resolution,[],[f234,f158]) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK3(X2,X3)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f278,plain,
! [X2,X0,X1] :
( ~ sP0(app(X0,sK7),sK7,X1,X2)
| ~ ssItem(sK3(sK8,sK7))
| ~ ssList(X0) ),
inference(superposition,[],[f189,f235]) ).
fof(f189,plain,
! [X2,X3,X4,X5] :
( ~ sP0(app(X5,cons(X4,nil)),cons(X4,nil),X2,X3)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f188]) ).
fof(f188,plain,
! [X2,X3,X1,X4,X5] :
( cons(X4,nil) != X1
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ sP0(app(X5,cons(X4,nil)),X1,X2,X3) ),
inference(equality_resolution,[],[f159]) ).
fof(f159,plain,
! [X2,X3,X0,X1,X4,X5] :
( app(X5,cons(X4,nil)) != X0
| cons(X4,nil) != X1
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC096+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % 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 : n017.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 17:38:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50 % (30118)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.52 % (30120)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)
% 0.20/0.52 % (30122)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.52 % (30118)First to succeed.
% 0.20/0.52 % (30144)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.20/0.52 % (30127)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 % (30113)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.53 % (30137)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)
% 0.20/0.53 % (30117)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.53 % (30126)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.53 % (30114)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)
% 0.20/0.54 % (30115)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.54 % (30133)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.54 % (30138)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.54 % (30123)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.54 % (30116)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (30124)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.54 % (30133)Refutation not found, incomplete strategy% (30133)------------------------------
% 0.20/0.54 % (30133)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (30133)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (30133)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.54
% 0.20/0.54 % (30133)Memory used [KB]: 6012
% 0.20/0.54 % (30133)Time elapsed: 0.136 s
% 0.20/0.54 % (30133)Instructions burned: 4 (million)
% 0.20/0.54 % (30133)------------------------------
% 0.20/0.54 % (30133)------------------------------
% 0.20/0.54 % (30118)Refutation found. Thanks to Tanya!
% 0.20/0.54 % SZS status Theorem for theBenchmark
% 0.20/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54 % (30118)------------------------------
% 0.20/0.54 % (30118)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (30118)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (30118)Termination reason: Refutation
% 0.20/0.54
% 0.20/0.54 % (30118)Memory used [KB]: 1663
% 0.20/0.54 % (30118)Time elapsed: 0.105 s
% 0.20/0.54 % (30118)Instructions burned: 12 (million)
% 0.20/0.54 % (30118)------------------------------
% 0.20/0.54 % (30118)------------------------------
% 0.20/0.54 % (30110)Success in time 0.185 s
%------------------------------------------------------------------------------