TSTP Solution File: SET016+4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -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 : Tue Apr 30 15:04:20 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 10 unt; 0 def)
% Number of atoms : 137 ( 40 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 133 ( 52 ~; 45 |; 20 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 79 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f486,plain,
$false,
inference(avatar_sat_refutation,[],[f417,f435,f485]) ).
fof(f485,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f484]) ).
fof(f484,plain,
( $false
| ~ spl7_1 ),
inference(subsumption_resolution,[],[f478,f456]) ).
fof(f456,plain,
( sK0 != sK1
| ~ spl7_1 ),
inference(superposition,[],[f54,f449]) ).
fof(f449,plain,
( sK1 = sK2
| ~ spl7_1 ),
inference(resolution,[],[f443,f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2,X0] :
( member(X2,singleton(X0))
<=> X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
fof(f443,plain,
( member(sK1,singleton(sK2))
| ~ spl7_1 ),
inference(superposition,[],[f84,f412]) ).
fof(f412,plain,
( unordered_pair(sK0,sK1) = singleton(sK2)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f410,plain,
( spl7_1
<=> unordered_pair(sK0,sK1) = singleton(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f84,plain,
! [X2,X1] : member(X2,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f82]) ).
fof(f82,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 ) )
& ( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 ) )
& ( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( X0 = X2
| X0 = X1 ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( X1 = X2
| X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
fof(f54,plain,
sK0 != sK2,
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
( sK0 != sK2
& equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f29]) ).
fof(f29,plain,
( ? [X0,X1,X2,X3] :
( X0 != X2
& equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3))) )
=> ( sK0 != sK2
& equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
? [X0,X1,X2,X3] :
( X0 != X2
& equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3))) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ! [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3)))
=> X0 = X2 ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X5,X6] :
( 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,
! [X0,X1,X5,X6] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X5),unordered_pair(X5,X6)))
=> X0 = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI50a) ).
fof(f478,plain,
( sK0 = sK1
| ~ spl7_1 ),
inference(resolution,[],[f477,f69]) ).
fof(f477,plain,
( member(sK0,singleton(sK1))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f444,f449]) ).
fof(f444,plain,
( member(sK0,singleton(sK2))
| ~ spl7_1 ),
inference(superposition,[],[f85,f412]) ).
fof(f85,plain,
! [X2,X1] : member(X1,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f81]) ).
fof(f81,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1 ),
inference(cnf_transformation,[],[f52]) ).
fof(f435,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f434,plain,
( $false
| ~ spl7_2 ),
inference(subsumption_resolution,[],[f428,f54]) ).
fof(f428,plain,
( sK0 = sK2
| ~ spl7_2 ),
inference(resolution,[],[f427,f69]) ).
fof(f427,plain,
( member(sK2,singleton(sK0))
| ~ spl7_2 ),
inference(superposition,[],[f83,f416]) ).
fof(f416,plain,
( singleton(sK0) = singleton(sK2)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f414,plain,
( spl7_2
<=> singleton(sK0) = singleton(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f83,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f417,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f383,f414,f410]) ).
fof(f383,plain,
( singleton(sK0) = singleton(sK2)
| unordered_pair(sK0,sK1) = singleton(sK2) ),
inference(resolution,[],[f381,f80]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f381,plain,
member(singleton(sK2),unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))),
inference(resolution,[],[f179,f105]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X2),X1)
| member(X0,X1) ),
inference(resolution,[],[f56,f85]) ).
fof(f56,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f32,f33]) ).
fof(f33,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f179,plain,
subset(unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)),unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))),
inference(resolution,[],[f53,f60]) ).
fof(f60,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( equal_set(X0,X1)
=> ( subset(X1,X0)
& subset(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f53,plain,
equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Apr 30 01:22:40 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 % (4906)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.39 % (4909)WARNING: value z3 for option sas not known
% 0.22/0.39 % (4907)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39 % (4910)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39 % (4913)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.39 % (4912)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.39 % (4911)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.39 % (4908)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39 % (4909)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [1]
% 0.22/0.40 TRYING [2]
% 0.22/0.40 TRYING [4]
% 0.22/0.40 % (4909)First to succeed.
% 0.22/0.40 % (4909)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (4909)------------------------------
% 0.22/0.40 % (4909)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.40 % (4909)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (4909)Memory used [KB]: 970
% 0.22/0.40 % (4909)Time elapsed: 0.015 s
% 0.22/0.40 % (4909)Instructions burned: 18 (million)
% 0.22/0.40 % (4909)------------------------------
% 0.22/0.40 % (4909)------------------------------
% 0.22/0.40 % (4906)Success in time 0.031 s
%------------------------------------------------------------------------------