TSTP Solution File: SET082+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.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 : Sun May 5 09:11:02 EDT 2024
% Result : Theorem 0.10s 0.37s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 6 unt; 0 def)
% Number of atoms : 83 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 81 ( 26 ~; 23 |; 24 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 33 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1109,plain,
$false,
inference(subsumption_resolution,[],[f1105,f136]) ).
fof(f136,plain,
null_class != singleton(sK0),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
( null_class != singleton(sK0)
& ~ member(sK0,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f71,f85]) ).
fof(f85,plain,
( ? [X0] :
( singleton(X0) != null_class
& ~ member(X0,universal_class) )
=> ( null_class != singleton(sK0)
& ~ member(sK0,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
? [X0] :
( singleton(X0) != null_class
& ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X0] :
( ~ member(X0,universal_class)
=> singleton(X0) = null_class ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X0] :
( ~ member(X0,universal_class)
=> singleton(X0) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f1105,plain,
null_class = singleton(sK0),
inference(resolution,[],[f1097,f135]) ).
fof(f135,plain,
~ member(sK0,universal_class),
inference(cnf_transformation,[],[f86]) ).
fof(f1097,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f1096]) ).
fof(f1096,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f147,f1090]) ).
fof(f1090,plain,
! [X0] :
( sK1(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[],[f1081,f148]) ).
fof(f148,plain,
! [X0] :
( member(sK1(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( disjoint(sK1(X0),X0)
& member(sK1(X0),X0)
& member(sK1(X0),universal_class) )
| null_class = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f72,f87]) ).
fof(f87,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
=> ( disjoint(sK1(X0),X0)
& member(sK1(X0),X0)
& member(sK1(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
| null_class = X0 ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( null_class != X0
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( null_class != X0
=> ? [X2] :
( disjoint(X2,X0)
& member(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).
fof(f1081,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f1079]) ).
fof(f1079,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f204,f142]) ).
fof(f142,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f204,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( ( X1 = X2
| X0 = X2 )
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f147,plain,
! [X0] :
( member(sK1(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32 % Computer : n015.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri May 3 16:24:38 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (27252)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.34 % (27255)WARNING: value z3 for option sas not known
% 0.10/0.34 % (27255)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)
% 0.10/0.34 % (27258)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)
% 0.10/0.34 % (27253)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.34 % (27256)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.34 % (27254)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.34 % (27257)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)
% 0.10/0.34 % (27259)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)
% 0.10/0.36 TRYING [1]
% 0.10/0.36 TRYING [2]
% 0.10/0.36 TRYING [1]
% 0.10/0.37 % (27255)First to succeed.
% 0.10/0.37 % (27255)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27252"
% 0.10/0.37 TRYING [2]
% 0.10/0.37 % (27255)Refutation found. Thanks to Tanya!
% 0.10/0.37 % SZS status Theorem for theBenchmark
% 0.10/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.37 % (27255)------------------------------
% 0.10/0.37 % (27255)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.10/0.37 % (27255)Termination reason: Refutation
% 0.10/0.37
% 0.10/0.37 % (27255)Memory used [KB]: 1297
% 0.10/0.37 % (27255)Time elapsed: 0.031 s
% 0.10/0.37 % (27255)Instructions burned: 52 (million)
% 0.10/0.37 % (27252)Success in time 0.044 s
%------------------------------------------------------------------------------