TSTP Solution File: SET763+4 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET763+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 : n019.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 18:22:09 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 13 unt; 0 def)
% Number of atoms : 247 ( 7 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 275 ( 94 ~; 80 |; 74 &)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 169 ( 138 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f198,plain,
$false,
inference(avatar_sat_refutation,[],[f87,f99,f197]) ).
fof(f197,plain,
spl8_2,
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f193,plain,
( $false
| spl8_2 ),
inference(resolution,[],[f191,f106]) ).
fof(f106,plain,
( member(sK4(empty_set,sK1),sK1)
| spl8_2 ),
inference(resolution,[],[f86,f63]) ).
fof(f63,plain,
! [X0,X1] :
( subset(X1,X0)
| member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ( member(sK4(X0,X1),X1)
& ~ member(sK4(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f45,f46]) ).
fof(f46,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& ~ member(X3,X0) )
=> ( member(sK4(X0,X1),X1)
& ~ member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X3] :
( member(X3,X1)
& ~ member(X3,X0) ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,plain,
! [X1,X0] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) ) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X1,X0] :
( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
<=> subset(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f86,plain,
( ~ subset(sK1,empty_set)
| spl8_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f84,plain,
( spl8_2
<=> subset(sK1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f191,plain,
! [X0] : ~ member(X0,sK1),
inference(subsumption_resolution,[],[f177,f88]) ).
fof(f88,plain,
! [X0] :
( ~ member(X0,sK1)
| member(X0,sK3) ),
inference(resolution,[],[f61,f64]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ subset(X1,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f61,plain,
subset(sK1,sK3),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
( subset(sK1,sK3)
& ~ equal_set(sK1,empty_set)
& maps(sK2,sK3,sK0)
& equal_set(image2(sK2,sK1),empty_set) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f41,f42]) ).
fof(f42,plain,
( ? [X0,X1,X2,X3] :
( subset(X1,X3)
& ~ equal_set(X1,empty_set)
& maps(X2,X3,X0)
& equal_set(image2(X2,X1),empty_set) )
=> ( subset(sK1,sK3)
& ~ equal_set(sK1,empty_set)
& maps(sK2,sK3,sK0)
& equal_set(image2(sK2,sK1),empty_set) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
? [X0,X1,X2,X3] :
( subset(X1,X3)
& ~ equal_set(X1,empty_set)
& maps(X2,X3,X0)
& equal_set(image2(X2,X1),empty_set) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
? [X2,X1,X3,X0] :
( subset(X1,X0)
& ~ equal_set(X1,empty_set)
& maps(X3,X0,X2)
& equal_set(image2(X3,X1),empty_set) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
? [X1,X2,X3,X0] :
( ~ equal_set(X1,empty_set)
& equal_set(image2(X3,X1),empty_set)
& maps(X3,X0,X2)
& subset(X1,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X1,X2,X3,X0] :
( ( equal_set(image2(X3,X1),empty_set)
& maps(X3,X0,X2)
& subset(X1,X0) )
=> equal_set(X1,empty_set) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0,X2,X1,X5] :
( ( equal_set(image2(X5,X2),empty_set)
& subset(X2,X0)
& maps(X5,X0,X1) )
=> equal_set(X2,empty_set) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0,X2,X1,X5] :
( ( equal_set(image2(X5,X2),empty_set)
& subset(X2,X0)
& maps(X5,X0,X1) )
=> equal_set(X2,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa13) ).
fof(f177,plain,
! [X0] :
( ~ member(X0,sK3)
| ~ member(X0,sK1) ),
inference(resolution,[],[f154,f115]) ).
fof(f115,plain,
! [X0] : ~ member(X0,image2(sK2,sK1)),
inference(subsumption_resolution,[],[f112,f71]) ).
fof(f71,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f112,plain,
! [X0] :
( member(X0,empty_set)
| ~ member(X0,image2(sK2,sK1)) ),
inference(resolution,[],[f104,f64]) ).
fof(f104,plain,
subset(image2(sK2,sK1),empty_set),
inference(resolution,[],[f58,f73]) ).
fof(f73,plain,
! [X0,X1] :
( ~ equal_set(X1,X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( ( equal_set(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X1,X0) ) ),
inference(rectify,[],[f56]) ).
fof(f56,plain,
! [X1,X0] :
( ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X1,X0] :
( ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f58,plain,
equal_set(image2(sK2,sK1),empty_set),
inference(cnf_transformation,[],[f43]) ).
fof(f154,plain,
! [X8,X9] :
( member(sK5(sK0,sK2,X8),image2(sK2,X9))
| ~ member(X8,X9)
| ~ member(X8,sK3) ),
inference(resolution,[],[f91,f70]) ).
fof(f70,plain,
! [X2,X3,X0,X1] :
( ~ apply(X1,X3,X0)
| ~ member(X3,X2)
| member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( member(X0,image2(X1,X2))
| ! [X3] :
( ~ apply(X1,X3,X0)
| ~ member(X3,X2) ) )
& ( ( apply(X1,sK6(X0,X1,X2),X0)
& member(sK6(X0,X1,X2),X2) )
| ~ member(X0,image2(X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f52,f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X1,X4,X0)
& member(X4,X2) )
=> ( apply(X1,sK6(X0,X1,X2),X0)
& member(sK6(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f52,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,[],[f51]) ).
fof(f51,plain,
! [X1,X2,X0] :
( ( member(X1,image2(X2,X0))
| ! [X3] :
( ~ apply(X2,X3,X1)
| ~ member(X3,X0) ) )
& ( ? [X3] :
( apply(X2,X3,X1)
& member(X3,X0) )
| ~ member(X1,image2(X2,X0)) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X1,X2,X0] :
( member(X1,image2(X2,X0))
<=> ? [X3] :
( apply(X2,X3,X1)
& member(X3,X0) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X0,X4,X5] :
( ? [X2] :
( member(X2,X0)
& apply(X5,X2,X4) )
<=> member(X4,image2(X5,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2) ).
fof(f91,plain,
! [X0] :
( apply(sK2,X0,sK5(sK0,sK2,X0))
| ~ member(X0,sK3) ),
inference(resolution,[],[f59,f67]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,X0)
| ~ maps(X2,X0,X1)
| apply(X2,X3,sK5(X1,X2,X3)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ maps(X2,X0,X1)
| ( ! [X3] :
( ( apply(X2,X3,sK5(X1,X2,X3))
& member(sK5(X1,X2,X3),X1) )
| ~ member(X3,X0) )
& ! [X5,X6,X7] :
( ~ member(X7,X1)
| ~ member(X5,X0)
| X6 = X7
| ~ apply(X2,X5,X7)
| ~ member(X6,X1)
| ~ apply(X2,X5,X6) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f48,f49]) ).
fof(f49,plain,
! [X1,X2,X3] :
( ? [X4] :
( apply(X2,X3,X4)
& member(X4,X1) )
=> ( apply(X2,X3,sK5(X1,X2,X3))
& member(sK5(X1,X2,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ maps(X2,X0,X1)
| ( ! [X3] :
( ? [X4] :
( apply(X2,X3,X4)
& member(X4,X1) )
| ~ member(X3,X0) )
& ! [X5,X6,X7] :
( ~ member(X7,X1)
| ~ member(X5,X0)
| X6 = X7
| ~ apply(X2,X5,X7)
| ~ member(X6,X1)
| ~ apply(X2,X5,X6) ) ) ),
inference(rectify,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ maps(X2,X0,X1)
| ( ! [X6] :
( ? [X7] :
( apply(X2,X6,X7)
& member(X7,X1) )
| ~ member(X6,X0) )
& ! [X3,X4,X5] :
( ~ member(X5,X1)
| ~ member(X3,X0)
| X4 = X5
| ~ apply(X2,X3,X5)
| ~ member(X4,X1)
| ~ apply(X2,X3,X4) ) ) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( ! [X4,X3,X5] :
( X4 = X5
| ~ apply(X2,X3,X4)
| ~ apply(X2,X3,X5)
| ~ member(X5,X1)
| ~ member(X4,X1)
| ~ member(X3,X0) )
& ! [X6] :
( ? [X7] :
( apply(X2,X6,X7)
& member(X7,X1) )
| ~ member(X6,X0) ) )
| ~ maps(X2,X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( maps(X2,X0,X1)
=> ( ! [X4,X3,X5] :
( ( member(X5,X1)
& member(X4,X1)
& member(X3,X0) )
=> ( ( apply(X2,X3,X4)
& apply(X2,X3,X5) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X0)
=> ? [X7] :
( apply(X2,X6,X7)
& member(X7,X1) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( ! [X4,X3,X5] :
( ( member(X5,X1)
& member(X4,X1)
& member(X3,X0) )
=> ( ( apply(X2,X3,X4)
& apply(X2,X3,X5) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X0)
=> ? [X7] :
( apply(X2,X6,X7)
& member(X7,X1) ) ) )
<=> maps(X2,X0,X1) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X1,X5] :
( ( ! [X2,X6,X7] :
( ( member(X2,X0)
& member(X7,X1)
& member(X6,X1) )
=> ( ( apply(X5,X2,X7)
& apply(X5,X2,X6) )
=> X6 = X7 ) )
& ! [X2] :
( member(X2,X0)
=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) ) )
<=> maps(X5,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
fof(f59,plain,
maps(sK2,sK3,sK0),
inference(cnf_transformation,[],[f43]) ).
fof(f99,plain,
spl8_1,
inference(avatar_contradiction_clause,[],[f98]) ).
fof(f98,plain,
( $false
| spl8_1 ),
inference(subsumption_resolution,[],[f95,f71]) ).
fof(f95,plain,
( member(sK4(sK1,empty_set),empty_set)
| spl8_1 ),
inference(resolution,[],[f82,f63]) ).
fof(f82,plain,
( ~ subset(empty_set,sK1)
| spl8_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f80,plain,
( spl8_1
<=> subset(empty_set,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f87,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f78,f84,f80]) ).
fof(f78,plain,
( ~ subset(sK1,empty_set)
| ~ subset(empty_set,sK1) ),
inference(resolution,[],[f60,f74]) ).
fof(f74,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f60,plain,
~ equal_set(sK1,empty_set),
inference(cnf_transformation,[],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET763+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.12/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 14:22:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.51 % (9460)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.51 % (9468)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.51 % (9461)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.51 % (9467)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)
% 0.20/0.51 % (9449)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 % (9454)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)
% 0.20/0.52 % (9455)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 % (9454)First to succeed.
% 0.20/0.53 % (9455)Also succeeded, but the first one will report.
% 0.20/0.53 % (9454)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 % (9454)------------------------------
% 0.20/0.53 % (9454)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (9454)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (9454)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (9454)Memory used [KB]: 6012
% 0.20/0.53 % (9454)Time elapsed: 0.110 s
% 0.20/0.53 % (9454)Instructions burned: 3 (million)
% 0.20/0.53 % (9454)------------------------------
% 0.20/0.53 % (9454)------------------------------
% 0.20/0.53 % (9442)Success in time 0.171 s
%------------------------------------------------------------------------------