TSTP Solution File: SET753+4 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET753+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 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 : n007.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 18:22:07 EDT 2022
% Result : Theorem 0.14s 0.51s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 10 unt; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 162 ( 54 ~; 43 |; 48 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 119 ( 91 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f319,plain,
$false,
inference(avatar_sat_refutation,[],[f150,f273,f318]) ).
fof(f318,plain,
spl8_2,
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f317,plain,
( $false
| spl8_2 ),
inference(subsumption_resolution,[],[f307,f178]) ).
fof(f178,plain,
member(sK1(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),sK5,intersection(sK6,sK3)),sK3),
inference(unit_resulting_resolution,[],[f116,f62]) ).
fof(f62,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X2,X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X2,X1))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X2,X1)) ) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X2,X1))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X2,X1)) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( member(X0,intersection(X2,X1))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X1,X0] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f116,plain,
member(sK1(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),sK5,intersection(sK6,sK3)),intersection(sK6,sK3)),
inference(unit_resulting_resolution,[],[f80,f64]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ member(X0,image2(X1,X2))
| member(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( member(X0,image2(X1,X2))
| ! [X3] :
( ~ apply(X1,X3,X0)
| ~ member(X3,X2) ) )
& ( ( apply(X1,sK1(X0,X1,X2),X0)
& member(sK1(X0,X1,X2),X2) )
| ~ member(X0,image2(X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f49,f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X1,X4,X0)
& member(X4,X2) )
=> ( apply(X1,sK1(X0,X1,X2),X0)
& member(sK1(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( member(X0,image2(X1,X2))
| ! [X3] :
( ~ apply(X1,X3,X0)
| ~ member(X3,X2) ) )
& ( ? [X4] :
( apply(X1,X4,X0)
& member(X4,X2) )
| ~ member(X0,image2(X1,X2)) ) ),
inference(rectify,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( member(X0,image2(X1,X2))
| ! [X3] :
( ~ apply(X1,X3,X0)
| ~ member(X3,X2) ) )
& ( ? [X3] :
( apply(X1,X3,X0)
& member(X3,X2) )
| ~ member(X0,image2(X1,X2)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( member(X0,image2(X1,X2))
<=> ? [X3] :
( apply(X1,X3,X0)
& member(X3,X2) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X4,X5,X0] :
( member(X4,image2(X5,X0))
<=> ? [X2] :
( apply(X5,X2,X4)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image2) ).
fof(f80,plain,
member(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),image2(sK5,intersection(sK6,sK3))),
inference(unit_resulting_resolution,[],[f70,f58]) ).
fof(f58,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f43,f44]) ).
fof(f44,plain,
! [X0,X1] :
( ? [X3] :
( ~ member(X3,X1)
& member(X3,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( ~ member(X3,X1)
& member(X3,X0) ) ) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X1,X0] :
( ( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( ~ member(X2,X0)
& member(X2,X1) ) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X1,X0] :
( ! [X2] :
( member(X2,X1)
=> member(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f70,plain,
~ subset(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
( subset(sK3,sK7)
& subset(sK6,sK7)
& maps(sK5,sK7,sK4)
& ~ subset(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f55,f56]) ).
fof(f56,plain,
( ? [X0,X1,X2,X3,X4] :
( subset(X0,X4)
& subset(X3,X4)
& maps(X2,X4,X1)
& ~ subset(image2(X2,intersection(X3,X0)),intersection(image2(X2,X3),image2(X2,X0))) )
=> ( subset(sK3,sK7)
& subset(sK6,sK7)
& maps(sK5,sK7,sK4)
& ~ subset(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
? [X0,X1,X2,X3,X4] :
( subset(X0,X4)
& subset(X3,X4)
& maps(X2,X4,X1)
& ~ subset(image2(X2,intersection(X3,X0)),intersection(image2(X2,X3),image2(X2,X0))) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
? [X1,X0,X3,X2,X4] :
( subset(X1,X4)
& subset(X2,X4)
& maps(X3,X4,X0)
& ~ subset(image2(X3,intersection(X2,X1)),intersection(image2(X3,X2),image2(X3,X1))) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
? [X4,X1,X2,X3,X0] :
( ~ subset(image2(X3,intersection(X2,X1)),intersection(image2(X3,X2),image2(X3,X1)))
& subset(X2,X4)
& subset(X1,X4)
& maps(X3,X4,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X4,X1,X2,X3,X0] :
( ( subset(X2,X4)
& subset(X1,X4)
& maps(X3,X4,X0) )
=> subset(image2(X3,intersection(X2,X1)),intersection(image2(X3,X2),image2(X3,X1))) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X1,X4,X2,X5,X0] :
( ( subset(X4,X0)
& subset(X2,X0)
& maps(X5,X0,X1) )
=> subset(image2(X5,intersection(X2,X4)),intersection(image2(X5,X2),image2(X5,X4))) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X1,X4,X2,X5,X0] :
( ( subset(X4,X0)
& subset(X2,X0)
& maps(X5,X0,X1) )
=> subset(image2(X5,intersection(X2,X4)),intersection(image2(X5,X2),image2(X5,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa03) ).
fof(f307,plain,
( ~ member(sK1(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),sK5,intersection(sK6,sK3)),sK3)
| spl8_2 ),
inference(unit_resulting_resolution,[],[f115,f149,f66]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( member(X0,image2(X1,X2))
| ~ member(X3,X2)
| ~ apply(X1,X3,X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f149,plain,
( ~ member(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),image2(sK5,sK3))
| spl8_2 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f147,plain,
( spl8_2
<=> member(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),image2(sK5,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f115,plain,
apply(sK5,sK1(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),sK5,intersection(sK6,sK3)),sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3)))),
inference(unit_resulting_resolution,[],[f80,f65]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ member(X0,image2(X1,X2))
| apply(X1,sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f273,plain,
spl8_1,
inference(avatar_contradiction_clause,[],[f272]) ).
fof(f272,plain,
( $false
| spl8_1 ),
inference(subsumption_resolution,[],[f250,f177]) ).
fof(f177,plain,
member(sK1(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),sK5,intersection(sK6,sK3)),sK6),
inference(unit_resulting_resolution,[],[f116,f61]) ).
fof(f61,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X2,X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f250,plain,
( ~ member(sK1(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),sK5,intersection(sK6,sK3)),sK6)
| spl8_1 ),
inference(unit_resulting_resolution,[],[f145,f115,f66]) ).
fof(f145,plain,
( ~ member(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),image2(sK5,sK6))
| spl8_1 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f143,plain,
( spl8_1
<=> member(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),image2(sK5,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f150,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f138,f147,f143]) ).
fof(f138,plain,
( ~ member(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),image2(sK5,sK3))
| ~ member(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),image2(sK5,sK6)) ),
inference(resolution,[],[f79,f63]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X2,X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f79,plain,
~ member(sK0(image2(sK5,intersection(sK6,sK3)),intersection(image2(sK5,sK6),image2(sK5,sK3))),intersection(image2(sK5,sK6),image2(sK5,sK3))),
inference(unit_resulting_resolution,[],[f70,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET753+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.00/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.09/0.30 % Computer : n007.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Aug 30 14:04:01 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.14/0.45 % (29769)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)
% 0.14/0.47 % (29786)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)
% 0.14/0.47 % (29778)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.48 % (29785)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)
% 0.14/0.48 % (29777)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.48 % (29770)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.14/0.49 % (29778)Instruction limit reached!
% 0.14/0.49 % (29778)------------------------------
% 0.14/0.49 % (29778)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.49 % (29778)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.49 % (29778)Termination reason: Unknown
% 0.14/0.49 % (29778)Termination phase: Saturation
% 0.14/0.49
% 0.14/0.49 % (29778)Memory used [KB]: 6140
% 0.14/0.49 % (29778)Time elapsed: 0.072 s
% 0.14/0.49 % (29778)Instructions burned: 7 (million)
% 0.14/0.49 % (29778)------------------------------
% 0.14/0.49 % (29778)------------------------------
% 0.14/0.49 % (29777)Instruction limit reached!
% 0.14/0.49 % (29777)------------------------------
% 0.14/0.49 % (29777)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.49 % (29777)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.49 % (29777)Termination reason: Unknown
% 0.14/0.49 % (29777)Termination phase: Clausification
% 0.14/0.49
% 0.14/0.49 % (29777)Memory used [KB]: 1535
% 0.14/0.49 % (29777)Time elapsed: 0.004 s
% 0.14/0.49 % (29777)Instructions burned: 3 (million)
% 0.14/0.49 % (29777)------------------------------
% 0.14/0.49 % (29777)------------------------------
% 0.14/0.49 % (29768)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)
% 0.14/0.50 % (29770)First to succeed.
% 0.14/0.50 % (29763)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.14/0.50 % (29765)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)
% 0.14/0.50 % (29766)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)
% 0.14/0.50 % (29767)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)
% 0.14/0.51 % (29765)Instruction limit reached!
% 0.14/0.51 % (29765)------------------------------
% 0.14/0.51 % (29765)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.51 % (29765)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.51 % (29765)Termination reason: Unknown
% 0.14/0.51 % (29765)Termination phase: Saturation
% 0.14/0.51
% 0.14/0.51 % (29765)Memory used [KB]: 1535
% 0.14/0.51 % (29765)Time elapsed: 0.004 s
% 0.14/0.51 % (29765)Instructions burned: 4 (million)
% 0.14/0.51 % (29765)------------------------------
% 0.14/0.51 % (29765)------------------------------
% 0.14/0.51 % (29764)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)
% 0.14/0.51 % (29770)Refutation found. Thanks to Tanya!
% 0.14/0.51 % SZS status Theorem for theBenchmark
% 0.14/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.51 % (29770)------------------------------
% 0.14/0.51 % (29770)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.51 % (29770)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.51 % (29770)Termination reason: Refutation
% 0.14/0.51
% 0.14/0.51 % (29770)Memory used [KB]: 6140
% 0.14/0.51 % (29770)Time elapsed: 0.088 s
% 0.14/0.51 % (29770)Instructions burned: 10 (million)
% 0.14/0.51 % (29770)------------------------------
% 0.14/0.51 % (29770)------------------------------
% 0.14/0.51 % (29762)Success in time 0.202 s
%------------------------------------------------------------------------------