TSTP Solution File: SEU149+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU149+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 : n023.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 09:27:24 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 158 ( 95 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 192 ( 69 ~; 71 |; 40 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 89 ( 76 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f471,plain,
$false,
inference(trivial_inequality_removal,[],[f470]) ).
fof(f470,plain,
sK4 != sK4,
inference(superposition,[],[f185,f460]) ).
fof(f460,plain,
sK4 = sK5,
inference(resolution,[],[f452,f309]) ).
fof(f309,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f260]) ).
fof(f260,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK13(X0,X1) != X0
| ~ in(sK13(X0,X1),X1) )
& ( sK13(X0,X1) = X0
| in(sK13(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f153,f154]) ).
fof(f154,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK13(X0,X1) != X0
| ~ in(sK13(X0,X1),X1) )
& ( sK13(X0,X1) = X0
| in(sK13(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f153,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f152]) ).
fof(f152,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f452,plain,
in(sK5,singleton(sK4)),
inference(resolution,[],[f310,f365]) ).
fof(f365,plain,
sP0(sK5,sK6,singleton(sK4)),
inference(superposition,[],[f363,f184]) ).
fof(f184,plain,
singleton(sK4) = unordered_pair(sK5,sK6),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
( sK4 != sK5
& singleton(sK4) = unordered_pair(sK5,sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f81,f122]) ).
fof(f122,plain,
( ? [X0,X1,X2] :
( X0 != X1
& singleton(X0) = unordered_pair(X1,X2) )
=> ( sK4 != sK5
& singleton(sK4) = unordered_pair(sK5,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
? [X0,X1,X2] :
( X0 != X1
& singleton(X0) = unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,negated_conjecture,
~ ! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
inference(negated_conjecture,[],[f72]) ).
fof(f72,conjecture,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f363,plain,
! [X0,X1] : sP0(X1,X0,unordered_pair(X1,X0)),
inference(superposition,[],[f312,f237]) ).
fof(f237,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(f312,plain,
! [X0,X1] : sP0(X1,X0,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f272]) ).
fof(f272,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f10,f114]) ).
fof(f114,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f10,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(f310,plain,
! [X2,X1,X4] :
( ~ sP0(X4,X1,X2)
| in(X4,X2) ),
inference(equality_resolution,[],[f268]) ).
fof(f268,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( sK14(X0,X1,X2) != X0
& sK14(X0,X1,X2) != X1 )
| ~ in(sK14(X0,X1,X2),X2) )
& ( sK14(X0,X1,X2) = X0
| sK14(X0,X1,X2) = X1
| in(sK14(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f158,f159]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK14(X0,X1,X2) != X0
& sK14(X0,X1,X2) != X1 )
| ~ in(sK14(X0,X1,X2),X2) )
& ( sK14(X0,X1,X2) = X0
| sK14(X0,X1,X2) = X1
| in(sK14(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f157]) ).
fof(f157,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f156]) ).
fof(f156,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f114]) ).
fof(f185,plain,
sK4 != sK5,
inference(cnf_transformation,[],[f123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU149+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 11:24:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (5577)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (5580)WARNING: value z3 for option sas not known
% 0.15/0.38 % (5578)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (5579)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (5580)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)
% 0.15/0.38 % (5582)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)
% 0.15/0.38 % (5581)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (5583)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)
% 0.15/0.38 % (5584)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (5583)First to succeed.
% 0.15/0.39 % (5583)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5577"
% 0.15/0.39 % (5583)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (5583)------------------------------
% 0.15/0.39 % (5583)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (5583)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (5583)Memory used [KB]: 949
% 0.15/0.39 % (5583)Time elapsed: 0.011 s
% 0.15/0.39 % (5583)Instructions burned: 15 (million)
% 0.15/0.39 % (5577)Success in time 0.029 s
%------------------------------------------------------------------------------