TSTP Solution File: SET014+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET014+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 : 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 18:18:21 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 128 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 47 ~; 39 |; 29 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 59 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f99,plain,
$false,
inference(avatar_sat_refutation,[],[f70,f81,f98]) ).
fof(f98,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f97]) ).
fof(f97,plain,
( $false
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f95,f45]) ).
fof(f45,plain,
~ subset(union(sK2,sK3),sK1),
inference(backward_demodulation,[],[f38,f28]) ).
fof(f28,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f38,plain,
~ subset(union(sK3,sK2),sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
( subset(sK2,sK1)
& ~ subset(union(sK3,sK2),sK1)
& subset(sK3,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f21,f22]) ).
fof(f22,plain,
( ? [X0,X1,X2] :
( subset(X1,X0)
& ~ subset(union(X2,X1),X0)
& subset(X2,X0) )
=> ( subset(sK2,sK1)
& ~ subset(union(sK3,sK2),sK1)
& subset(sK3,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
? [X0,X1,X2] :
( subset(X1,X0)
& ~ subset(union(X2,X1),X0)
& subset(X2,X0) ),
inference(rectify,[],[f11]) ).
fof(f11,plain,
? [X0,X2,X1] :
( subset(X2,X0)
& ~ subset(union(X1,X2),X0)
& subset(X1,X0) ),
inference(flattening,[],[f10]) ).
fof(f10,plain,
? [X2,X1,X0] :
( ~ subset(union(X1,X2),X0)
& subset(X2,X0)
& subset(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,plain,
~ ! [X2,X1,X0] :
( ( subset(X2,X0)
& subset(X1,X0) )
=> subset(union(X1,X2),X0) ),
inference(rectify,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X1,X0,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(union(X0,X2),X1) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X1,X0,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(union(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_subset) ).
fof(f95,plain,
( subset(union(sK2,sK3),sK1)
| ~ spl5_1 ),
inference(resolution,[],[f82,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ( member(sK4(X0,X1),X1)
& ~ member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| member(X3,X0) )
| ~ subset(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X1)
& ~ member(X2,X0) )
=> ( member(sK4(X0,X1),X1)
& ~ member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f25,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,[],[f24]) ).
fof(f24,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,[],[f12]) ).
fof(f12,plain,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f82,plain,
( member(sK4(sK1,union(sK2,sK3)),sK1)
| ~ spl5_1 ),
inference(resolution,[],[f65,f53]) ).
fof(f53,plain,
! [X0] :
( ~ member(X0,sK3)
| member(X0,sK1) ),
inference(resolution,[],[f40,f37]) ).
fof(f37,plain,
subset(sK3,sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X3,X0,X1] :
( ~ subset(X1,X0)
| ~ member(X3,X1)
| member(X3,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f65,plain,
( member(sK4(sK1,union(sK2,sK3)),sK3)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f63,plain,
( spl5_1
<=> member(sK4(sK1,union(sK2,sK3)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f81,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f80,plain,
( $false
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f79,f45]) ).
fof(f79,plain,
( subset(union(sK2,sK3),sK1)
| ~ spl5_2 ),
inference(resolution,[],[f71,f41]) ).
fof(f71,plain,
( member(sK4(sK1,union(sK2,sK3)),sK1)
| ~ spl5_2 ),
inference(resolution,[],[f69,f54]) ).
fof(f54,plain,
! [X1] :
( ~ member(X1,sK2)
| member(X1,sK1) ),
inference(resolution,[],[f40,f39]) ).
fof(f39,plain,
subset(sK2,sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f69,plain,
( member(sK4(sK1,union(sK2,sK3)),sK2)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f67,plain,
( spl5_2
<=> member(sK4(sK1,union(sK2,sK3)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f70,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f61,f67,f63]) ).
fof(f61,plain,
( member(sK4(sK1,union(sK2,sK3)),sK2)
| member(sK4(sK1,union(sK2,sK3)),sK3) ),
inference(resolution,[],[f52,f36]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X2,X1))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X2,X1)) )
& ( member(X0,union(X2,X1))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X1,X0)) )
& ( member(X2,union(X1,X0))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X1,X0)) )
& ( member(X2,union(X1,X0))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,plain,
! [X2,X0,X1] :
( ( member(X2,X1)
| member(X2,X0) )
<=> member(X2,union(X1,X0)) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f52,plain,
member(sK4(sK1,union(sK2,sK3)),union(sK2,sK3)),
inference(resolution,[],[f42,f45]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X1,X0)
| member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 12:56:10 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.48 % (30092)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.48 % (30065)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)
% 0.19/0.49 % (30078)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)
% 0.19/0.49 % (30087)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)
% 0.19/0.49 % (30084)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.49 % (30065)Refutation not found, incomplete strategy% (30065)------------------------------
% 0.19/0.49 % (30065)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (30065)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (30065)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.49
% 0.19/0.49 % (30065)Memory used [KB]: 5884
% 0.19/0.49 % (30065)Time elapsed: 0.094 s
% 0.19/0.49 % (30065)Instructions burned: 1 (million)
% 0.19/0.49 % (30065)------------------------------
% 0.19/0.49 % (30065)------------------------------
% 0.19/0.49 % (30063)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.49 % (30078)First to succeed.
% 0.19/0.49 % (30064)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)
% 0.19/0.49 % (30070)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)
% 0.19/0.50 % (30086)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)
% 0.19/0.50 % (30074)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)
% 0.19/0.50 % (30078)Refutation found. Thanks to Tanya!
% 0.19/0.50 % SZS status Theorem for theBenchmark
% 0.19/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50 % (30078)------------------------------
% 0.19/0.50 % (30078)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (30078)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (30078)Termination reason: Refutation
% 0.19/0.50
% 0.19/0.50 % (30078)Memory used [KB]: 6012
% 0.19/0.50 % (30078)Time elapsed: 0.061 s
% 0.19/0.50 % (30078)Instructions burned: 4 (million)
% 0.19/0.50 % (30078)------------------------------
% 0.19/0.50 % (30078)------------------------------
% 0.19/0.50 % (30060)Success in time 0.158 s
%------------------------------------------------------------------------------