TSTP Solution File: SET578+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n014.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 18:24:58 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 11 unt; 0 def)
% Number of atoms : 198 ( 21 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 232 ( 95 ~; 76 |; 44 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 86 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f102,plain,
$false,
inference(subsumption_resolution,[],[f101,f93]) ).
fof(f93,plain,
~ member(sK3(sK2,intersection(sK0,sK1)),sK2),
inference(subsumption_resolution,[],[f92,f79]) ).
fof(f79,plain,
( member(sK3(intersection(sK0,sK1),sK2),sK2)
| ~ member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
inference(resolution,[],[f76,f45]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X1,X0)
| member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ( ~ member(sK3(X0,X1),X0)
& member(sK3(X0,X1),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X3] :
( ~ member(X3,X0)
& member(X3,X1) )
=> ( ~ member(sK3(X0,X1),X0)
& member(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X3] :
( ~ member(X3,X0)
& member(X3,X1) ) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( ~ member(X2,X0)
& member(X2,X1) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( subset(X1,X0)
<=> ! [X2] :
( member(X2,X1)
=> member(X2,X0) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f76,plain,
( ~ subset(sK2,intersection(sK0,sK1))
| ~ member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
inference(resolution,[],[f73,f46]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f73,plain,
( ~ subset(intersection(sK0,sK1),sK2)
| ~ subset(sK2,intersection(sK0,sK1)) ),
inference(forward_demodulation,[],[f72,f53]) ).
fof(f53,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(rectify,[],[f10]) ).
fof(f10,plain,
! [X1,X0] : intersection(X0,X1) = intersection(X1,X0),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f72,plain,
( ~ subset(intersection(sK0,sK1),sK2)
| ~ subset(sK2,intersection(sK1,sK0)) ),
inference(forward_demodulation,[],[f66,f53]) ).
fof(f66,plain,
( ~ subset(intersection(sK1,sK0),sK2)
| ~ subset(sK2,intersection(sK1,sK0)) ),
inference(extensionality_resolution,[],[f35,f44]) ).
fof(f44,plain,
sK2 != intersection(sK1,sK0),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
( sK2 != intersection(sK1,sK0)
& ! [X3] :
( ( ( member(X3,sK0)
& member(X3,sK1) )
| ~ member(X3,sK2) )
& ( member(X3,sK2)
| ~ member(X3,sK0)
| ~ member(X3,sK1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f24]) ).
fof(f24,plain,
( ? [X0,X1,X2] :
( intersection(X1,X0) != X2
& ! [X3] :
( ( ( member(X3,X0)
& member(X3,X1) )
| ~ member(X3,X2) )
& ( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1) ) ) )
=> ( sK2 != intersection(sK1,sK0)
& ! [X3] :
( ( ( member(X3,sK0)
& member(X3,sK1) )
| ~ member(X3,sK2) )
& ( member(X3,sK2)
| ~ member(X3,sK0)
| ~ member(X3,sK1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0,X1,X2] :
( intersection(X1,X0) != X2
& ! [X3] :
( ( ( member(X3,X0)
& member(X3,X1) )
| ~ member(X3,X2) )
& ( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1) ) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
? [X2,X0,X1] :
( intersection(X0,X2) != X1
& ! [X3] :
( ( ( member(X3,X2)
& member(X3,X0) )
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X2)
| ~ member(X3,X0) ) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
? [X2,X0,X1] :
( intersection(X0,X2) != X1
& ! [X3] :
( ( ( member(X3,X2)
& member(X3,X0) )
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X2)
| ~ member(X3,X0) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
? [X2,X0,X1] :
( intersection(X0,X2) != X1
& ! [X3] :
( ( member(X3,X2)
& member(X3,X0) )
<=> member(X3,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,plain,
~ ! [X1,X0,X2] :
( ! [X3] :
( ( member(X3,X2)
& member(X3,X0) )
<=> member(X3,X1) )
=> intersection(X0,X2) = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X1,X0,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& member(X3,X2) ) )
=> intersection(X1,X2) = X0 ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X1,X0,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X1)
& member(X3,X2) ) )
=> intersection(X1,X2) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th19) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f92,plain,
( ~ member(sK3(intersection(sK0,sK1),sK2),sK2)
| ~ member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
inference(subsumption_resolution,[],[f91,f43]) ).
fof(f43,plain,
! [X3] :
( member(X3,sK0)
| ~ member(X3,sK2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f91,plain,
( ~ member(sK3(intersection(sK0,sK1),sK2),sK0)
| ~ member(sK3(intersection(sK0,sK1),sK2),sK2)
| ~ member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
inference(resolution,[],[f88,f42]) ).
fof(f42,plain,
! [X3] :
( member(X3,sK1)
| ~ member(X3,sK2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f88,plain,
( ~ member(sK3(intersection(sK0,sK1),sK2),sK1)
| ~ member(sK3(sK2,intersection(sK0,sK1)),sK2)
| ~ member(sK3(intersection(sK0,sK1),sK2),sK0) ),
inference(resolution,[],[f40,f78]) ).
fof(f78,plain,
( ~ member(sK3(intersection(sK0,sK1),sK2),intersection(sK0,sK1))
| ~ member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
inference(resolution,[],[f76,f46]) ).
fof(f40,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X2,X1,X0] :
( ( member(X2,intersection(X1,X0))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X1,X0)) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X2,X1,X0] :
( ( member(X2,intersection(X1,X0))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X1,X0)) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X2,X1,X0] :
( member(X2,intersection(X1,X0))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f101,plain,
member(sK3(sK2,intersection(sK0,sK1)),sK2),
inference(subsumption_resolution,[],[f100,f98]) ).
fof(f98,plain,
member(sK3(sK2,intersection(sK0,sK1)),sK0),
inference(resolution,[],[f97,f39]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f97,plain,
member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)),
inference(subsumption_resolution,[],[f96,f81]) ).
fof(f81,plain,
( member(sK3(intersection(sK0,sK1),sK2),sK2)
| member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)) ),
inference(resolution,[],[f77,f45]) ).
fof(f77,plain,
( ~ subset(sK2,intersection(sK0,sK1))
| member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)) ),
inference(resolution,[],[f73,f45]) ).
fof(f96,plain,
( member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1))
| ~ member(sK3(intersection(sK0,sK1),sK2),sK2) ),
inference(resolution,[],[f95,f43]) ).
fof(f95,plain,
( ~ member(sK3(intersection(sK0,sK1),sK2),sK0)
| member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)) ),
inference(subsumption_resolution,[],[f94,f81]) ).
fof(f94,plain,
( ~ member(sK3(intersection(sK0,sK1),sK2),sK2)
| ~ member(sK3(intersection(sK0,sK1),sK2),sK0)
| member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)) ),
inference(resolution,[],[f87,f42]) ).
fof(f87,plain,
( ~ member(sK3(intersection(sK0,sK1),sK2),sK1)
| member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1))
| ~ member(sK3(intersection(sK0,sK1),sK2),sK0) ),
inference(resolution,[],[f40,f80]) ).
fof(f80,plain,
( ~ member(sK3(intersection(sK0,sK1),sK2),intersection(sK0,sK1))
| member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)) ),
inference(resolution,[],[f77,f46]) ).
fof(f100,plain,
( ~ member(sK3(sK2,intersection(sK0,sK1)),sK0)
| member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
inference(resolution,[],[f99,f41]) ).
fof(f41,plain,
! [X3] :
( ~ member(X3,sK1)
| ~ member(X3,sK0)
| member(X3,sK2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f99,plain,
member(sK3(sK2,intersection(sK0,sK1)),sK1),
inference(resolution,[],[f97,f38]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n014.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 14:03:03 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.20/0.50 % (21588)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/498Mi)
% 0.20/0.50 % (21580)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 0.20/0.51 % (21588)First to succeed.
% 0.20/0.51 % (21572)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.51 TRYING [1]
% 0.20/0.51 TRYING [2]
% 0.20/0.51 % (21588)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (21588)------------------------------
% 0.20/0.51 % (21588)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (21588)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (21588)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (21588)Memory used [KB]: 895
% 0.20/0.51 % (21588)Time elapsed: 0.059 s
% 0.20/0.51 % (21588)Instructions burned: 3 (million)
% 0.20/0.51 % (21588)------------------------------
% 0.20/0.51 % (21588)------------------------------
% 0.20/0.51 % (21565)Success in time 0.154 s
%------------------------------------------------------------------------------