TSTP Solution File: SET199+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET199+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_uns --cores 0 -t %d %s
% Computer : n021.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 18:19:44 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 105 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 40 ~; 26 |; 31 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 74 ( 59 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f84,plain,
$false,
inference(subsumption_resolution,[],[f83,f68]) ).
fof(f68,plain,
member(sK0(intersection(sK1,sK2),sK3),sK1),
inference(unit_resulting_resolution,[],[f34,f51,f29]) ).
fof(f29,plain,
! [X3,X0,X1] :
( ~ subset(X1,X0)
| member(X3,X0)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ( member(sK0(X0,X1),X1)
& ~ member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| member(X3,X0) )
| ~ subset(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16]) ).
fof(f16,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X1)
& ~ member(X2,X0) )
=> ( member(sK0(X0,X1),X1)
& ~ member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ? [X2] :
( member(X2,X1)
& ~ member(X2,X0) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| member(X3,X0) )
| ~ subset(X1,X0) ) ),
inference(rectify,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( ( subset(X0,X1)
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f51,plain,
member(sK0(intersection(sK1,sK2),sK3),sK3),
inference(resolution,[],[f46,f31]) ).
fof(f31,plain,
! [X0,X1] :
( member(sK0(X0,X1),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f46,plain,
~ subset(sK3,intersection(sK1,sK2)),
inference(forward_demodulation,[],[f32,f38]) ).
fof(f38,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f24]) ).
fof(f24,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(f32,plain,
~ subset(sK3,intersection(sK2,sK1)),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( subset(sK3,sK1)
& subset(sK3,sK2)
& ~ subset(sK3,intersection(sK2,sK1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f18,f19]) ).
fof(f19,plain,
( ? [X0,X1,X2] :
( subset(X2,X0)
& subset(X2,X1)
& ~ subset(X2,intersection(X1,X0)) )
=> ( subset(sK3,sK1)
& subset(sK3,sK2)
& ~ subset(sK3,intersection(sK2,sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2] :
( subset(X2,X0)
& subset(X2,X1)
& ~ subset(X2,intersection(X1,X0)) ),
inference(rectify,[],[f12]) ).
fof(f12,plain,
? [X1,X0,X2] :
( subset(X2,X1)
& subset(X2,X0)
& ~ subset(X2,intersection(X0,X1)) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
? [X1,X2,X0] :
( ~ subset(X2,intersection(X0,X1))
& subset(X2,X1)
& subset(X2,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,plain,
~ ! [X1,X2,X0] :
( ( subset(X2,X1)
& subset(X2,X0) )
=> subset(X2,intersection(X0,X1)) ),
inference(rectify,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X1,X2,X0] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,intersection(X1,X2)) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X1,X2,X0] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_of_subsets) ).
fof(f34,plain,
subset(sK3,sK1),
inference(cnf_transformation,[],[f20]) ).
fof(f83,plain,
~ member(sK0(intersection(sK1,sK2),sK3),sK1),
inference(subsumption_resolution,[],[f79,f67]) ).
fof(f67,plain,
member(sK0(intersection(sK1,sK2),sK3),sK2),
inference(unit_resulting_resolution,[],[f33,f51,f29]) ).
fof(f33,plain,
subset(sK3,sK2),
inference(cnf_transformation,[],[f20]) ).
fof(f79,plain,
( ~ member(sK0(intersection(sK1,sK2),sK3),sK2)
| ~ member(sK0(intersection(sK1,sK2),sK3),sK1) ),
inference(resolution,[],[f52,f37]) ).
fof(f37,plain,
! [X2,X0,X1] :
( member(X1,intersection(X2,X0))
| ~ member(X1,X2)
| ~ member(X1,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( member(X1,intersection(X2,X0))
| ~ member(X1,X2)
| ~ member(X1,X0) )
& ( ( member(X1,X2)
& member(X1,X0) )
| ~ member(X1,intersection(X2,X0)) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X2,X1,X0] :
( ( member(X1,intersection(X0,X2))
| ~ member(X1,X0)
| ~ member(X1,X2) )
& ( ( member(X1,X0)
& member(X1,X2) )
| ~ member(X1,intersection(X0,X2)) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X2,X1,X0] :
( ( member(X1,intersection(X0,X2))
| ~ member(X1,X0)
| ~ member(X1,X2) )
& ( ( member(X1,X0)
& member(X1,X2) )
| ~ member(X1,intersection(X0,X2)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X2,X1,X0] :
( member(X1,intersection(X0,X2))
<=> ( member(X1,X0)
& member(X1,X2) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X0,X2,X1] :
( ( member(X2,X1)
& member(X2,X0) )
<=> member(X2,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f52,plain,
~ member(sK0(intersection(sK1,sK2),sK3),intersection(sK1,sK2)),
inference(resolution,[],[f46,f30]) ).
fof(f30,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET199+3 : TPTP v8.1.0. Released v2.2.0.
% 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
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 13:22:41 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.51 % (14344)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)
% 0.20/0.51 % (14352)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)
% 0.20/0.51 % (14337)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)
% 0.20/0.52 % (14337)First to succeed.
% 0.20/0.52 % (14336)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 % (14344)Instruction limit reached!
% 0.20/0.52 % (14344)------------------------------
% 0.20/0.52 % (14344)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (14344)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (14344)Termination reason: Unknown
% 0.20/0.52 % (14344)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (14344)Memory used [KB]: 6012
% 0.20/0.52 % (14344)Time elapsed: 0.075 s
% 0.20/0.52 % (14344)Instructions burned: 4 (million)
% 0.20/0.52 % (14344)------------------------------
% 0.20/0.52 % (14344)------------------------------
% 0.20/0.52 % (14337)Refutation found. Thanks to Tanya!
% 0.20/0.52 % SZS status Theorem for theBenchmark
% 0.20/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (14337)------------------------------
% 0.20/0.53 % (14337)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (14337)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (14337)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (14337)Memory used [KB]: 6012
% 0.20/0.53 % (14337)Time elapsed: 0.109 s
% 0.20/0.53 % (14337)Instructions burned: 3 (million)
% 0.20/0.53 % (14337)------------------------------
% 0.20/0.53 % (14337)------------------------------
% 0.20/0.53 % (14329)Success in time 0.175 s
%------------------------------------------------------------------------------