TSTP Solution File: SET103+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET103+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 : n024.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 09:11:14 EDT 2024
% Result : Theorem 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 13 unt; 0 def)
% Number of atoms : 123 ( 42 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 42 ~; 38 |; 32 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 64 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1837,plain,
$false,
inference(trivial_inequality_removal,[],[f1829]) ).
fof(f1829,plain,
ordered_pair(sK0,sK1) != ordered_pair(sK0,sK1),
inference(superposition,[],[f135,f1721]) ).
fof(f1721,plain,
! [X0] : unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,sK1),
inference(superposition,[],[f165,f1708]) ).
fof(f1708,plain,
null_class = singleton(sK1),
inference(resolution,[],[f1698,f350]) ).
fof(f350,plain,
! [X0] : ~ member(sK1,X0),
inference(resolution,[],[f348,f140]) ).
fof(f140,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f348,plain,
! [X0] :
( ~ subclass(X0,universal_class)
| ~ member(sK1,X0) ),
inference(resolution,[],[f173,f136]) ).
fof(f136,plain,
~ member(sK1,universal_class),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
( ~ member(sK1,universal_class)
& ordered_pair(sK0,sK1) != unordered_pair(singleton(sK0),unordered_pair(sK0,null_class)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f71,f85]) ).
fof(f85,plain,
( ? [X0,X1] :
( ~ member(X1,universal_class)
& ordered_pair(X0,X1) != unordered_pair(singleton(X0),unordered_pair(X0,null_class)) )
=> ( ~ member(sK1,universal_class)
& ordered_pair(sK0,sK1) != unordered_pair(singleton(sK0),unordered_pair(sK0,null_class)) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
? [X0,X1] :
( ~ member(X1,universal_class)
& ordered_pair(X0,X1) != unordered_pair(singleton(X0),unordered_pair(X0,null_class)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( member(X1,universal_class)
| ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,null_class)) ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X0,X1] :
( member(X1,universal_class)
| ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,null_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_1_of_ordered_pair) ).
fof(f173,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
fof(f1698,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f1697]) ).
fof(f1697,plain,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f147,f1689]) ).
fof(f1689,plain,
! [X0] :
( sK2(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[],[f1684,f148]) ).
fof(f148,plain,
! [X0] :
( member(sK2(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( disjoint(sK2(X0),X0)
& member(sK2(X0),X0)
& member(sK2(X0),universal_class) )
| null_class = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f72,f87]) ).
fof(f87,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
=> ( disjoint(sK2(X0),X0)
& member(sK2(X0),X0)
& member(sK2(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(f1684,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f1682]) ).
fof(f1682,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(sK2(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f165,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f135,plain,
ordered_pair(sK0,sK1) != unordered_pair(singleton(sK0),unordered_pair(sK0,null_class)),
inference(cnf_transformation,[],[f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET103+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri May 3 16:45:53 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % (6701)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (6704)WARNING: value z3 for option sas not known
% 0.12/0.35 % (6705)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 % (6706)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)
% 0.12/0.35 % (6704)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)
% 0.12/0.35 % (6703)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35 % (6707)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)
% 0.12/0.35 % (6702)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 % (6708)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)
% 0.12/0.38 TRYING [1]
% 0.12/0.38 TRYING [2]
% 0.12/0.38 TRYING [1]
% 0.12/0.38 TRYING [2]
% 0.18/0.40 % (6707)First to succeed.
% 0.18/0.41 % (6707)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6701"
% 0.18/0.41 % (6707)Refutation found. Thanks to Tanya!
% 0.18/0.41 % SZS status Theorem for theBenchmark
% 0.18/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.41 % (6707)------------------------------
% 0.18/0.41 % (6707)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.41 % (6707)Termination reason: Refutation
% 0.18/0.41
% 0.18/0.41 % (6707)Memory used [KB]: 1553
% 0.18/0.41 % (6707)Time elapsed: 0.053 s
% 0.18/0.41 % (6707)Instructions burned: 92 (million)
% 0.18/0.41 % (6701)Success in time 0.069 s
%------------------------------------------------------------------------------