TSTP Solution File: SET162+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET162+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 : n020.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 18:19:35 EDT 2022
% Result : Theorem 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 12 unt; 0 def)
% Number of atoms : 145 ( 18 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 156 ( 62 ~; 64 |; 17 &)
% ( 11 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 54 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f130,plain,
$false,
inference(avatar_sat_refutation,[],[f94,f100,f107,f113,f127,f129]) ).
fof(f129,plain,
~ spl4_8,
inference(avatar_contradiction_clause,[],[f128]) ).
fof(f128,plain,
( $false
| ~ spl4_8 ),
inference(resolution,[],[f112,f38]) ).
fof(f38,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f112,plain,
( member(sK1(union(sK0,empty_set),sK0),empty_set)
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f110,plain,
( spl4_8
<=> member(sK1(union(sK0,empty_set),sK0),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f127,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[],[f126]) ).
fof(f126,plain,
( $false
| ~ spl4_7 ),
inference(resolution,[],[f106,f62]) ).
fof(f62,plain,
~ sQ3_eqProxy(union(sK0,empty_set),sK0),
inference(resolution,[],[f56,f61]) ).
fof(f61,plain,
! [X0,X1] :
( sQ3_eqProxy(X1,X0)
| ~ sQ3_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( sQ3_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ3_eqProxy])]) ).
fof(f56,plain,
~ sQ3_eqProxy(sK0,union(sK0,empty_set)),
inference(equality_proxy_replacement,[],[f39,f54]) ).
fof(f39,plain,
sK0 != union(sK0,empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
sK0 != union(sK0,empty_set),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f20]) ).
fof(f20,plain,
( ? [X0] : union(X0,empty_set) != X0
=> sK0 != union(sK0,empty_set) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0] : union(X0,empty_set) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0] : union(X0,empty_set) = X0,
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_empty_set) ).
fof(f106,plain,
( sQ3_eqProxy(union(sK0,empty_set),sK0)
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f104,plain,
( spl4_7
<=> sQ3_eqProxy(union(sK0,empty_set),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f113,plain,
( spl4_6
| spl4_8
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f108,f87,f110,f91]) ).
fof(f91,plain,
( spl4_6
<=> member(sK1(union(sK0,empty_set),sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f87,plain,
( spl4_5
<=> member(sK1(union(sK0,empty_set),sK0),union(sK0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f108,plain,
( member(sK1(union(sK0,empty_set),sK0),empty_set)
| member(sK1(union(sK0,empty_set),sK0),sK0)
| ~ spl4_5 ),
inference(resolution,[],[f88,f33]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X2,X1))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( member(X0,union(X2,X1))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X2,X1)) ) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
! [X0,X2,X1] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
! [X0,X2,X1] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X2,X1] :
( member(X0,union(X1,X2))
<=> ( member(X0,X1)
| member(X0,X2) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f88,plain,
( member(sK1(union(sK0,empty_set),sK0),union(sK0,empty_set))
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f107,plain,
( spl4_7
| spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f101,f91,f87,f104]) ).
fof(f101,plain,
( member(sK1(union(sK0,empty_set),sK0),union(sK0,empty_set))
| sQ3_eqProxy(union(sK0,empty_set),sK0)
| spl4_6 ),
inference(resolution,[],[f93,f58]) ).
fof(f58,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| sQ3_eqProxy(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(equality_proxy_replacement,[],[f40,f54]) ).
fof(f40,plain,
! [X0,X1] :
( X0 = X1
| member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( ! [X2] :
( ( member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X0)
| ~ member(X2,X1) ) )
| X0 != X1 )
& ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) )
& ( 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(X3,X0)
| member(X3,X1) ) )
=> ( ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) )
& ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( ( ! [X2] :
( ( member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X0)
| ~ member(X2,X1) ) )
| X0 != X1 )
& ( X0 = X1
| ? [X3] :
( ( ~ member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X0)
| member(X3,X1) ) ) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X1,X0] :
( ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 )
& ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
<=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X0] :
( X0 = X1
<=> ! [X2] :
( member(X2,X1)
<=> member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f93,plain,
( ~ member(sK1(union(sK0,empty_set),sK0),sK0)
| spl4_6 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f100,plain,
( ~ spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f98,f87,f91]) ).
fof(f98,plain,
( ~ member(sK1(union(sK0,empty_set),sK0),sK0)
| spl4_5 ),
inference(resolution,[],[f89,f35]) ).
fof(f35,plain,
! [X2,X0,X1] :
( member(X0,union(X2,X1))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f89,plain,
( ~ member(sK1(union(sK0,empty_set),sK0),union(sK0,empty_set))
| spl4_5 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f94,plain,
( ~ spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f85,f91,f87]) ).
fof(f85,plain,
( ~ member(sK1(union(sK0,empty_set),sK0),sK0)
| ~ member(sK1(union(sK0,empty_set),sK0),union(sK0,empty_set)) ),
inference(resolution,[],[f62,f57]) ).
fof(f57,plain,
! [X0,X1] :
( sQ3_eqProxy(X0,X1)
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(equality_proxy_replacement,[],[f41,f54]) ).
fof(f41,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET162+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
% 0.13/0.34 % Computer : n020.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 13:26:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.49 % (9766)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.49 % (9766)Refutation not found, incomplete strategy% (9766)------------------------------
% 0.21/0.49 % (9766)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.50 % (9775)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)
% 0.21/0.50 % (9766)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.50 % (9766)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.50
% 0.21/0.50 % (9766)Memory used [KB]: 5884
% 0.21/0.50 % (9766)Time elapsed: 0.102 s
% 0.21/0.50 % (9766)Instructions burned: 1 (million)
% 0.21/0.50 % (9766)------------------------------
% 0.21/0.50 % (9766)------------------------------
% 0.21/0.50 % (9777)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.50 % (9777)Refutation not found, incomplete strategy% (9777)------------------------------
% 0.21/0.50 % (9777)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.50 % (9777)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.50 % (9777)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.50
% 0.21/0.50 % (9777)Memory used [KB]: 5884
% 0.21/0.50 % (9777)Time elapsed: 0.096 s
% 0.21/0.50 % (9777)Instructions burned: 3 (million)
% 0.21/0.50 % (9777)------------------------------
% 0.21/0.50 % (9777)------------------------------
% 0.21/0.50 % (9789)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)
% 0.21/0.51 % (9763)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.21/0.51 % (9785)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 % (9779)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)
% 0.21/0.51 % (9780)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)
% 0.21/0.51 % (9785)First to succeed.
% 0.21/0.51 % (9767)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.51 % (9775)Refutation not found, incomplete strategy% (9775)------------------------------
% 0.21/0.51 % (9775)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (9765)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)
% 0.21/0.51 % (9772)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.21/0.51 % (9775)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51 % (9775)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.51
% 0.21/0.51 % (9775)Memory used [KB]: 5884
% 0.21/0.51 % (9775)Time elapsed: 0.117 s
% 0.21/0.51 % (9775)Instructions burned: 4 (million)
% 0.21/0.51 % (9775)------------------------------
% 0.21/0.51 % (9775)------------------------------
% 0.21/0.51 % (9763)Also succeeded, but the first one will report.
% 0.21/0.51 % (9785)Refutation found. Thanks to Tanya!
% 0.21/0.51 % SZS status Theorem for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51 % (9785)------------------------------
% 0.21/0.51 % (9785)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (9785)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51 % (9785)Termination reason: Refutation
% 0.21/0.51
% 0.21/0.51 % (9785)Memory used [KB]: 6012
% 0.21/0.51 % (9785)Time elapsed: 0.114 s
% 0.21/0.51 % (9785)Instructions burned: 2 (million)
% 0.21/0.51 % (9785)------------------------------
% 0.21/0.51 % (9785)------------------------------
% 0.21/0.51 % (9762)Success in time 0.161 s
%------------------------------------------------------------------------------