TSTP Solution File: SET587+3 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET587+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 : n027.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 18:21:30 EDT 2022
% Result : Theorem 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 4 unt; 0 def)
% Number of atoms : 183 ( 26 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 200 ( 78 ~; 79 |; 28 &)
% ( 11 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 66 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f387,plain,
$false,
inference(avatar_sat_refutation,[],[f66,f69,f98,f125,f301,f386]) ).
fof(f386,plain,
( ~ spl5_1
| spl5_6 ),
inference(avatar_contradiction_clause,[],[f382]) ).
fof(f382,plain,
( $false
| ~ spl5_1
| spl5_6 ),
inference(unit_resulting_resolution,[],[f354,f355,f99]) ).
fof(f99,plain,
( ! [X0] :
( ~ member(X0,sK3)
| member(X0,sK2) )
| ~ spl5_1 ),
inference(resolution,[],[f68,f46]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ subset(X1,X0)
| member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ( ~ member(sK1(X0,X1),X0)
& member(sK1(X0,X1),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X3] :
( ~ member(X3,X0)
& member(X3,X1) )
=> ( ~ member(sK1(X0,X1),X0)
& member(sK1(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f23,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,[],[f22]) ).
fof(f22,plain,
! [X1,X0] :
( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
<=> subset(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f68,plain,
( subset(sK3,sK2)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f61,plain,
( spl5_1
<=> subset(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f355,plain,
( member(sK1(empty_set,difference(sK3,sK2)),sK3)
| spl5_6 ),
inference(resolution,[],[f134,f53]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(rectify,[],[f35]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ( member(X1,difference(X2,X0))
| member(X1,X0)
| ~ member(X1,X2) )
& ( ( ~ member(X1,X0)
& member(X1,X2) )
| ~ member(X1,difference(X2,X0)) ) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ( member(X1,difference(X2,X0))
| member(X1,X0)
| ~ member(X1,X2) )
& ( ( ~ member(X1,X0)
& member(X1,X2) )
| ~ member(X1,difference(X2,X0)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X2,X0,X1] :
( member(X1,difference(X2,X0))
<=> ( ~ member(X1,X0)
& member(X1,X2) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X2,X0] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f134,plain,
( member(sK1(empty_set,difference(sK3,sK2)),difference(sK3,sK2))
| spl5_6 ),
inference(resolution,[],[f119,f44]) ).
fof(f44,plain,
! [X0,X1] :
( subset(X1,X0)
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f119,plain,
( ~ subset(difference(sK3,sK2),empty_set)
| spl5_6 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f118,plain,
( spl5_6
<=> subset(difference(sK3,sK2),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f354,plain,
( ~ member(sK1(empty_set,difference(sK3,sK2)),sK2)
| spl5_6 ),
inference(resolution,[],[f134,f54]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f301,plain,
( ~ spl5_5
| ~ spl5_6
| spl5_2 ),
inference(avatar_split_clause,[],[f284,f64,f118,f115]) ).
fof(f115,plain,
( spl5_5
<=> subset(empty_set,difference(sK3,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f64,plain,
( spl5_2
<=> empty_set = difference(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f284,plain,
( ~ subset(difference(sK3,sK2),empty_set)
| ~ subset(empty_set,difference(sK3,sK2))
| spl5_2 ),
inference(extensionality_resolution,[],[f37,f65]) ).
fof(f65,plain,
( empty_set != difference(sK3,sK2)
| spl5_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f37,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
! [X1,X0] :
( ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
! [X1,X0] :
( ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( ( subset(X1,X0)
& subset(X0,X1) )
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f125,plain,
spl5_5,
inference(avatar_contradiction_clause,[],[f122]) ).
fof(f122,plain,
( $false
| spl5_5 ),
inference(unit_resulting_resolution,[],[f40,f116,f44]) ).
fof(f116,plain,
( ~ subset(empty_set,difference(sK3,sK2))
| spl5_5 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f98,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f95]) ).
fof(f95,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(unit_resulting_resolution,[],[f70,f71,f40,f82]) ).
fof(f82,plain,
( ! [X0] :
( member(X0,empty_set)
| member(X0,sK2)
| ~ member(X0,sK3) )
| ~ spl5_2 ),
inference(superposition,[],[f55,f67]) ).
fof(f67,plain,
( empty_set = difference(sK3,sK2)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f55,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f71,plain,
( ~ member(sK1(sK2,sK3),sK2)
| spl5_1 ),
inference(resolution,[],[f45,f62]) ).
fof(f62,plain,
( ~ subset(sK3,sK2)
| spl5_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f70,plain,
( member(sK1(sK2,sK3),sK3)
| spl5_1 ),
inference(resolution,[],[f44,f62]) ).
fof(f69,plain,
( spl5_2
| spl5_1 ),
inference(avatar_split_clause,[],[f47,f61,f64]) ).
fof(f47,plain,
( subset(sK3,sK2)
| empty_set = difference(sK3,sK2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
( ( ~ subset(sK3,sK2)
| empty_set != difference(sK3,sK2) )
& ( subset(sK3,sK2)
| empty_set = difference(sK3,sK2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f27,f28]) ).
fof(f28,plain,
( ? [X0,X1] :
( ( ~ subset(X1,X0)
| empty_set != difference(X1,X0) )
& ( subset(X1,X0)
| empty_set = difference(X1,X0) ) )
=> ( ( ~ subset(sK3,sK2)
| empty_set != difference(sK3,sK2) )
& ( subset(sK3,sK2)
| empty_set = difference(sK3,sK2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
? [X0,X1] :
( ( ~ subset(X1,X0)
| empty_set != difference(X1,X0) )
& ( subset(X1,X0)
| empty_set = difference(X1,X0) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
? [X1,X0] :
( ( ~ subset(X0,X1)
| difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
? [X1,X0] :
( difference(X0,X1) = empty_set
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X1,X0] :
( subset(X0,X1)
<=> difference(X0,X1) = empty_set ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X1,X0] :
( subset(X0,X1)
<=> difference(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(f66,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f48,f64,f61]) ).
fof(f48,plain,
( empty_set != difference(sK3,sK2)
| ~ subset(sK3,sK2) ),
inference(cnf_transformation,[],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % 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 : n027.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 14:18:16 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.50 % (13333)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.21/0.50 % (13312)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)
% 0.21/0.51 % (13311)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.51 % (13317)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)
% 0.21/0.51 % (13326)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.21/0.51 % (13333)First to succeed.
% 0.21/0.51 % (13325)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.21/0.51 % (13325)Refutation not found, incomplete strategy% (13325)------------------------------
% 0.21/0.51 % (13325)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (13325)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51 % (13325)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.51
% 0.21/0.51 % (13325)Memory used [KB]: 5884
% 0.21/0.51 % (13325)Time elapsed: 0.111 s
% 0.21/0.51 % (13325)Instructions burned: 1 (million)
% 0.21/0.51 % (13325)------------------------------
% 0.21/0.51 % (13325)------------------------------
% 0.21/0.51 % (13327)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)
% 0.21/0.52 % (13307)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)
% 0.21/0.52 % (13317)Also succeeded, but the first one will report.
% 0.21/0.52 % (13329)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)
% 0.21/0.52 % (13333)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Theorem for theBenchmark
% 0.21/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52 % (13333)------------------------------
% 0.21/0.52 % (13333)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (13333)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (13333)Termination reason: Refutation
% 0.21/0.52
% 0.21/0.52 % (13333)Memory used [KB]: 6140
% 0.21/0.52 % (13333)Time elapsed: 0.111 s
% 0.21/0.52 % (13333)Instructions burned: 9 (million)
% 0.21/0.52 % (13333)------------------------------
% 0.21/0.52 % (13333)------------------------------
% 0.21/0.52 % (13303)Success in time 0.166 s
%------------------------------------------------------------------------------