TSTP Solution File: SET798+4 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET798+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n008.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 18:25:40 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 9 unt; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 158 ( 47 ~; 31 |; 57 &)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 103 ( 74 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f198,plain,
$false,
inference(avatar_sat_refutation,[],[f194,f197]) ).
fof(f197,plain,
~ spl9_1,
inference(avatar_contradiction_clause,[],[f196]) ).
fof(f196,plain,
( $false
| ~ spl9_1 ),
inference(subsumption_resolution,[],[f195,f117]) ).
fof(f117,plain,
~ lower_bound(sK8,sK5,sK7),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
( order(sK5,sK4)
& subset(sK7,sK6)
& ~ lower_bound(sK8,sK5,sK7)
& lower_bound(sK8,sK5,sK6)
& subset(sK7,sK4)
& subset(sK6,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f49,f82,f81,f80]) ).
fof(f80,plain,
( ? [X0,X1] :
( order(X1,X0)
& ? [X2,X3] :
( subset(X3,X2)
& ? [X4] :
( ~ lower_bound(X4,X1,X3)
& lower_bound(X4,X1,X2) )
& subset(X3,X0)
& subset(X2,X0) ) )
=> ( order(sK5,sK4)
& ? [X3,X2] :
( subset(X3,X2)
& ? [X4] :
( ~ lower_bound(X4,sK5,X3)
& lower_bound(X4,sK5,X2) )
& subset(X3,sK4)
& subset(X2,sK4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
( ? [X3,X2] :
( subset(X3,X2)
& ? [X4] :
( ~ lower_bound(X4,sK5,X3)
& lower_bound(X4,sK5,X2) )
& subset(X3,sK4)
& subset(X2,sK4) )
=> ( subset(sK7,sK6)
& ? [X4] :
( ~ lower_bound(X4,sK5,sK7)
& lower_bound(X4,sK5,sK6) )
& subset(sK7,sK4)
& subset(sK6,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( ? [X4] :
( ~ lower_bound(X4,sK5,sK7)
& lower_bound(X4,sK5,sK6) )
=> ( ~ lower_bound(sK8,sK5,sK7)
& lower_bound(sK8,sK5,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0,X1] :
( order(X1,X0)
& ? [X2,X3] :
( subset(X3,X2)
& ? [X4] :
( ~ lower_bound(X4,X1,X3)
& lower_bound(X4,X1,X2) )
& subset(X3,X0)
& subset(X2,X0) ) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
? [X0,X1] :
( ? [X3,X2] :
( ? [X4] :
( ~ lower_bound(X4,X1,X3)
& lower_bound(X4,X1,X2) )
& subset(X3,X2)
& subset(X3,X0)
& subset(X2,X0) )
& order(X1,X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
~ ! [X0,X1] :
( order(X1,X0)
=> ! [X3,X2] :
( ( subset(X3,X2)
& subset(X3,X0)
& subset(X2,X0) )
=> ! [X4] :
( lower_bound(X4,X1,X2)
=> lower_bound(X4,X1,X3) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,negated_conjecture,
~ ! [X3,X5] :
( order(X5,X3)
=> ! [X4,X2] :
( ( subset(X4,X3)
& subset(X2,X3)
& subset(X2,X4) )
=> ! [X7] :
( lower_bound(X7,X5,X4)
=> lower_bound(X7,X5,X2) ) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f22,conjecture,
! [X3,X5] :
( order(X5,X3)
=> ! [X4,X2] :
( ( subset(X4,X3)
& subset(X2,X3)
& subset(X2,X4) )
=> ! [X7] :
( lower_bound(X7,X5,X4)
=> lower_bound(X7,X5,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV10) ).
fof(f195,plain,
( lower_bound(sK8,sK5,sK7)
| ~ spl9_1 ),
inference(resolution,[],[f188,f87]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ apply(X2,X0,sK0(X0,X1,X2))
| lower_bound(X0,X2,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( apply(X2,X0,X3)
| ~ member(X3,X1) )
| ~ lower_bound(X0,X2,X1) )
& ( lower_bound(X0,X2,X1)
| ( ~ apply(X2,X0,sK0(X0,X1,X2))
& member(sK0(X0,X1,X2),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f53,f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ apply(X2,X0,X4)
& member(X4,X1) )
=> ( ~ apply(X2,X0,sK0(X0,X1,X2))
& member(sK0(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( apply(X2,X0,X3)
| ~ member(X3,X1) )
| ~ lower_bound(X0,X2,X1) )
& ( lower_bound(X0,X2,X1)
| ? [X4] :
( ~ apply(X2,X0,X4)
& member(X4,X1) ) ) ),
inference(rectify,[],[f52]) ).
fof(f52,plain,
! [X1,X2,X0] :
( ( ! [X3] :
( apply(X0,X1,X3)
| ~ member(X3,X2) )
| ~ lower_bound(X1,X0,X2) )
& ( lower_bound(X1,X0,X2)
| ? [X3] :
( ~ apply(X0,X1,X3)
& member(X3,X2) ) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X1,X2,X0] :
( ! [X3] :
( apply(X0,X1,X3)
| ~ member(X3,X2) )
<=> lower_bound(X1,X0,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ! [X3] :
( member(X3,X2)
=> apply(X0,X1,X3) )
<=> lower_bound(X1,X0,X2) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X5,X7,X3] :
( lower_bound(X7,X5,X3)
<=> ! [X2] :
( member(X2,X3)
=> apply(X5,X7,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_bound) ).
fof(f188,plain,
( apply(sK5,sK8,sK0(sK8,sK7,sK5))
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f186,plain,
( spl9_1
<=> apply(sK5,sK8,sK0(sK8,sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f194,plain,
spl9_1,
inference(avatar_split_clause,[],[f182,f186]) ).
fof(f182,plain,
apply(sK5,sK8,sK0(sK8,sK7,sK5)),
inference(resolution,[],[f180,f159]) ).
fof(f159,plain,
member(sK0(sK8,sK7,sK5),sK6),
inference(resolution,[],[f157,f118]) ).
fof(f118,plain,
subset(sK7,sK6),
inference(cnf_transformation,[],[f83]) ).
fof(f157,plain,
! [X0] :
( ~ subset(sK7,X0)
| member(sK0(sK8,sK7,sK5),X0) ),
inference(resolution,[],[f156,f111]) ).
fof(f111,plain,
! [X3,X0,X1] :
( ~ member(X3,X1)
| member(X3,X0)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ( ~ member(sK3(X0,X1),X0)
& member(sK3(X0,X1),X1) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1) )
| ~ subset(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f77,f78]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X0)
& member(X2,X1) )
=> ( ~ member(sK3(X0,X1),X0)
& member(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ? [X2] :
( ~ member(X2,X0)
& member(X2,X1) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1) )
| ~ subset(X1,X0) ) ),
inference(rectify,[],[f76]) ).
fof(f76,plain,
! [X1,X0] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f156,plain,
member(sK0(sK8,sK7,sK5),sK7),
inference(resolution,[],[f86,f117]) ).
fof(f86,plain,
! [X2,X0,X1] :
( lower_bound(X0,X2,X1)
| member(sK0(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f180,plain,
! [X0] :
( ~ member(X0,sK6)
| apply(sK5,sK8,X0) ),
inference(resolution,[],[f88,f116]) ).
fof(f116,plain,
lower_bound(sK8,sK5,sK6),
inference(cnf_transformation,[],[f83]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( ~ lower_bound(X0,X2,X1)
| ~ member(X3,X1)
| apply(X2,X0,X3) ),
inference(cnf_transformation,[],[f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET798+4 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n008.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 14:24:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47 % (19302)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.47 % (19316)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.47 TRYING [1]
% 0.19/0.48 % (19316)First to succeed.
% 0.19/0.48 TRYING [2]
% 0.19/0.48 TRYING [3]
% 0.19/0.48 TRYING [4]
% 0.19/0.48 % (19316)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (19316)------------------------------
% 0.19/0.49 % (19316)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (19316)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (19316)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (19316)Memory used [KB]: 5628
% 0.19/0.49 % (19316)Time elapsed: 0.077 s
% 0.19/0.49 % (19316)Instructions burned: 7 (million)
% 0.19/0.49 % (19316)------------------------------
% 0.19/0.49 % (19316)------------------------------
% 0.19/0.49 % (19290)Success in time 0.135 s
%------------------------------------------------------------------------------