TSTP Solution File: SET016+4 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET016+4 : 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 : n006.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 18:18:23 EDT 2022
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 123 ( 42 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 43 ~; 36 |; 17 &)
% ( 10 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 76 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f242,plain,
$false,
inference(avatar_sat_refutation,[],[f161,f182,f241]) ).
fof(f241,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f240]) ).
fof(f240,plain,
( $false
| ~ spl4_1 ),
inference(subsumption_resolution,[],[f237,f46]) ).
fof(f46,plain,
~ member(sK0,singleton(sK2)),
inference(unit_resulting_resolution,[],[f41,f39]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( member(X1,singleton(X0))
| X0 != X1 )
& ( X0 = X1
| ~ member(X1,singleton(X0)) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X1,X0] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X1,X0] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2,X0] :
( member(X2,singleton(X0))
<=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f41,plain,
sK2 != sK0,
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
( equal_set(unordered_pair(singleton(sK2),unordered_pair(sK2,sK1)),unordered_pair(singleton(sK0),unordered_pair(sK0,sK3)))
& sK2 != sK0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f30,f31]) ).
fof(f31,plain,
( ? [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X2),unordered_pair(X2,X1)),unordered_pair(singleton(X0),unordered_pair(X0,X3)))
& X0 != X2 )
=> ( equal_set(unordered_pair(singleton(sK2),unordered_pair(sK2,sK1)),unordered_pair(singleton(sK0),unordered_pair(sK0,sK3)))
& sK2 != sK0 ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
? [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X2),unordered_pair(X2,X1)),unordered_pair(singleton(X0),unordered_pair(X0,X3)))
& X0 != X2 ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
? [X3,X0,X1,X2] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X0)),unordered_pair(singleton(X3),unordered_pair(X3,X2)))
& X1 != X3 ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ! [X2,X1,X0,X3] :
( equal_set(unordered_pair(singleton(X1),unordered_pair(X1,X0)),unordered_pair(singleton(X3),unordered_pair(X3,X2)))
=> X1 = X3 ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X1,X0,X6,X5] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X5),unordered_pair(X5,X6)))
=> X0 = X5 ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X1,X0,X6,X5] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X5),unordered_pair(X5,X6)))
=> X0 = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI50a) ).
fof(f237,plain,
( member(sK0,singleton(sK2))
| ~ spl4_1 ),
inference(superposition,[],[f44,f156]) ).
fof(f156,plain,
( unordered_pair(sK0,sK3) = singleton(sK2)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f154,plain,
( spl4_1
<=> unordered_pair(sK0,sK3) = singleton(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f44,plain,
! [X2,X0] : member(X2,unordered_pair(X2,X0)),
inference(equality_resolution,[],[f36]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,unordered_pair(X1,X0))
| X1 != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( X0 = X2
| X1 = X2
| ~ member(X2,unordered_pair(X1,X0)) )
& ( member(X2,unordered_pair(X1,X0))
| ( X0 != X2
& X1 != X2 ) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X1,X2,X0] :
( ( X0 = X1
| X0 = X2
| ~ member(X0,unordered_pair(X2,X1)) )
& ( member(X0,unordered_pair(X2,X1))
| ( X0 != X1
& X0 != X2 ) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X1,X2,X0] :
( ( X0 = X1
| X0 = X2
| ~ member(X0,unordered_pair(X2,X1)) )
& ( member(X0,unordered_pair(X2,X1))
| ( X0 != X1
& X0 != X2 ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X1,X2,X0] :
( ( X0 = X1
| X0 = X2 )
<=> member(X0,unordered_pair(X2,X1)) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X2,X1,X0] :
( ( X0 = X2
| X1 = X2 )
<=> member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f182,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f181]) ).
fof(f181,plain,
( $false
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f163,f45]) ).
fof(f45,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( member(X1,singleton(X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f163,plain,
( ~ member(sK0,singleton(sK0))
| ~ spl4_2 ),
inference(backward_demodulation,[],[f46,f160]) ).
fof(f160,plain,
( singleton(sK0) = singleton(sK2)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f158,plain,
( spl4_2
<=> singleton(sK0) = singleton(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f161,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f151,f158,f154]) ).
fof(f151,plain,
( singleton(sK0) = singleton(sK2)
| unordered_pair(sK0,sK3) = singleton(sK2) ),
inference(resolution,[],[f85,f38]) ).
fof(f38,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ member(X2,unordered_pair(X1,X0))
| X1 = X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f85,plain,
member(singleton(sK2),unordered_pair(singleton(sK0),unordered_pair(sK0,sK3))),
inference(unit_resulting_resolution,[],[f44,f64,f35]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
! [X1,X0] :
( subset(X1,X0)
=> ! [X2] :
( member(X2,X1)
=> member(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f18,plain,
! [X1,X0] :
( ! [X2] :
( member(X2,X1)
=> member(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f64,plain,
subset(unordered_pair(singleton(sK2),unordered_pair(sK2,sK1)),unordered_pair(singleton(sK0),unordered_pair(sK0,sK3))),
inference(unit_resulting_resolution,[],[f42,f33]) ).
fof(f33,plain,
! [X0,X1] :
( ~ equal_set(X1,X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X1,X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( equal_set(X1,X0)
=> ( subset(X0,X1)
& subset(X1,X0) ) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> equal_set(X1,X0) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f42,plain,
equal_set(unordered_pair(singleton(sK2),unordered_pair(sK2,sK1)),unordered_pair(singleton(sK0),unordered_pair(sK0,sK3))),
inference(cnf_transformation,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET016+4 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Aug 30 12:52:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.47 % (16227)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)
% 0.18/0.48 % (16227)First to succeed.
% 0.18/0.48 % (16243)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)
% 0.18/0.48 % (16243)Refutation not found, incomplete strategy% (16243)------------------------------
% 0.18/0.48 % (16243)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.48 % (16243)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.48 % (16243)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.48
% 0.18/0.48 % (16243)Memory used [KB]: 1407
% 0.18/0.48 % (16243)Time elapsed: 0.083 s
% 0.18/0.48 % (16243)Instructions burned: 2 (million)
% 0.18/0.48 % (16243)------------------------------
% 0.18/0.48 % (16243)------------------------------
% 0.18/0.48 % (16242)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)
% 0.18/0.48 % (16227)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (16227)------------------------------
% 0.18/0.48 % (16227)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.48 % (16227)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.48 % (16227)Termination reason: Refutation
% 0.18/0.48
% 0.18/0.48 % (16227)Memory used [KB]: 6012
% 0.18/0.48 % (16227)Time elapsed: 0.083 s
% 0.18/0.48 % (16227)Instructions burned: 11 (million)
% 0.18/0.48 % (16227)------------------------------
% 0.18/0.48 % (16227)------------------------------
% 0.18/0.48 % (16219)Success in time 0.151 s
%------------------------------------------------------------------------------