TSTP Solution File: SEU142+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU142+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.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 09:27:21 EDT 2024
% Result : Theorem 24.59s 3.88s
% Output : Refutation 24.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 17 unt; 0 def)
% Number of atoms : 165 ( 60 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 191 ( 73 ~; 74 |; 30 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 109 ( 101 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f223332,plain,
$false,
inference(subsumption_resolution,[],[f223174,f209531]) ).
fof(f209531,plain,
~ in(sK15(sK9,unordered_pair(sK9,sK9)),unordered_pair(sK9,sK9)),
inference(unit_resulting_resolution,[],[f402,f209274,f249]) ).
fof(f249,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X2)
| sP1(X4,X1,X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ sP1(sK16(X0,X1,X2),X1,X0)
| ~ in(sK16(X0,X1,X2),X2) )
& ( sP1(sK16(X0,X1,X2),X1,X0)
| in(sK16(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP1(X4,X1,X0) )
& ( sP1(X4,X1,X0)
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f145,f146]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP1(X3,X1,X0)
| ~ in(X3,X2) )
& ( sP1(X3,X1,X0)
| in(X3,X2) ) )
=> ( ( ~ sP1(sK16(X0,X1,X2),X1,X0)
| ~ in(sK16(X0,X1,X2),X2) )
& ( sP1(sK16(X0,X1,X2),X1,X0)
| in(sK16(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ sP1(X3,X1,X0)
| ~ in(X3,X2) )
& ( sP1(X3,X1,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP1(X4,X1,X0) )
& ( sP1(X4,X1,X0)
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ sP1(X3,X1,X0)
| ~ in(X3,X2) )
& ( sP1(X3,X1,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ sP1(X3,X1,X0) )
& ( sP1(X3,X1,X0)
| ~ in(X3,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2] :
( sP2(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> sP1(X3,X1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f209274,plain,
~ sP1(sK15(sK9,unordered_pair(sK9,sK9)),sK9,sK9),
inference(unit_resulting_resolution,[],[f209164,f209164,f253]) ).
fof(f253,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( X0 != X1
& X0 != X2 ) )
& ( X0 = X1
| X0 = X2
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f149]) ).
fof(f149,plain,
! [X3,X1,X0] :
( ( sP1(X3,X1,X0)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ sP1(X3,X1,X0) ) ),
inference(flattening,[],[f148]) ).
fof(f148,plain,
! [X3,X1,X0] :
( ( sP1(X3,X1,X0)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ sP1(X3,X1,X0) ) ),
inference(nnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X3,X1,X0] :
( sP1(X3,X1,X0)
<=> ( X1 = X3
| X0 = X3 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f209164,plain,
sK9 != sK15(sK9,unordered_pair(sK9,sK9)),
inference(unit_resulting_resolution,[],[f510,f152308,f299]) ).
fof(f299,plain,
! [X0,X1] :
( ~ in(X0,X1)
| sK15(X0,X1) != X0
| sP0(X0,X1) ),
inference(inner_rewriting,[],[f244]) ).
fof(f244,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK15(X0,X1) != X0
| ~ in(sK15(X0,X1),X1) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( sK15(X0,X1) != X0
| ~ in(sK15(X0,X1),X1) )
& ( sK15(X0,X1) = X0
| in(sK15(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f140,f141]) ).
fof(f141,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK15(X0,X1) != X0
| ~ in(sK15(X0,X1),X1) )
& ( sK15(X0,X1) = X0
| in(sK15(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f140,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f152308,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(unit_resulting_resolution,[],[f293,f402,f250]) ).
fof(f250,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ sP1(X4,X1,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f147]) ).
fof(f293,plain,
! [X2,X1] : sP1(X2,X1,X2),
inference(equality_resolution,[],[f254]) ).
fof(f254,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| X0 != X2 ),
inference(cnf_transformation,[],[f150]) ).
fof(f510,plain,
~ sP0(sK9,unordered_pair(sK9,sK9)),
inference(unit_resulting_resolution,[],[f180,f246]) ).
fof(f246,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( singleton(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f7,f102]) ).
fof(f7,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f180,plain,
singleton(sK9) != unordered_pair(sK9,sK9),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
singleton(sK9) != unordered_pair(sK9,sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f72,f116]) ).
fof(f116,plain,
( ? [X0] : singleton(X0) != unordered_pair(X0,X0)
=> singleton(sK9) != unordered_pair(sK9,sK9) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
? [X0] : singleton(X0) != unordered_pair(X0,X0),
inference(ennf_transformation,[],[f58]) ).
fof(f58,negated_conjecture,
~ ! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(negated_conjecture,[],[f57]) ).
fof(f57,conjecture,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f402,plain,
! [X0,X1] : sP2(X0,X1,unordered_pair(X1,X0)),
inference(superposition,[],[f294,f222]) ).
fof(f222,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f294,plain,
! [X0,X1] : sP2(X0,X1,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f256]) ).
fof(f256,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP2(X0,X1,X2) )
& ( sP2(X0,X1,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP2(X0,X1,X2) ),
inference(definition_folding,[],[f9,f105,f104]) ).
fof(f9,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f223174,plain,
in(sK15(sK9,unordered_pair(sK9,sK9)),unordered_pair(sK9,sK9)),
inference(unit_resulting_resolution,[],[f510,f209164,f243]) ).
fof(f243,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK15(X0,X1) = X0
| in(sK15(X0,X1),X1) ),
inference(cnf_transformation,[],[f142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU142+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n032.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri May 3 11:02:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (5891)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34 % (5896)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 % (5894)WARNING: value z3 for option sas not known
% 0.12/0.35 % (5892)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 % (5897)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 % (5898)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)
% 0.12/0.35 % (5895)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 % (5894)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 % (5893)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 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 TRYING [3]
% 0.12/0.36 TRYING [1]
% 0.12/0.37 TRYING [2]
% 0.12/0.37 TRYING [4]
% 0.17/0.40 TRYING [3]
% 0.17/0.40 TRYING [5]
% 0.17/0.47 TRYING [6]
% 0.17/0.50 TRYING [4]
% 2.15/0.63 TRYING [7]
% 3.36/0.82 TRYING [5]
% 4.25/0.94 TRYING [8]
% 7.85/1.45 TRYING [1]
% 7.85/1.45 TRYING [2]
% 7.85/1.45 TRYING [3]
% 7.85/1.45 TRYING [4]
% 7.85/1.47 TRYING [5]
% 7.85/1.49 TRYING [9]
% 7.85/1.49 TRYING [6]
% 8.49/1.53 TRYING [6]
% 9.53/1.68 TRYING [7]
% 12.06/2.04 TRYING [8]
% 14.61/2.43 TRYING [10]
% 16.78/2.78 TRYING [9]
% 20.39/3.23 TRYING [7]
% 24.59/3.87 % (5898)First to succeed.
% 24.59/3.87 % (5898)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5891"
% 24.59/3.88 % (5898)Refutation found. Thanks to Tanya!
% 24.59/3.88 % SZS status Theorem for theBenchmark
% 24.59/3.88 % SZS output start Proof for theBenchmark
% See solution above
% 24.59/3.88 % (5898)------------------------------
% 24.59/3.88 % (5898)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 24.59/3.88 % (5898)Termination reason: Refutation
% 24.59/3.88
% 24.59/3.88 % (5898)Memory used [KB]: 52049
% 24.59/3.88 % (5898)Time elapsed: 3.524 s
% 24.59/3.88 % (5898)Instructions burned: 12393 (million)
% 24.59/3.88 % (5891)Success in time 3.509 s
%------------------------------------------------------------------------------