TSTP Solution File: SEU142+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU142+1 : 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 : n010.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 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 16 unt; 0 def)
% Number of atoms : 164 ( 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(f751,plain,
$false,
inference(unit_resulting_resolution,[],[f73,f325,f297,f43]) ).
fof(f43,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f24,f25]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,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,[],[f23]) ).
fof(f23,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,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f297,plain,
sK3 != sK5(sK3,unordered_pair(sK3,sK3)),
inference(unit_resulting_resolution,[],[f73,f134,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ~ in(X0,X1)
| sK5(X0,X1) != X0
| sP0(X0,X1) ),
inference(inner_rewriting,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(unit_resulting_resolution,[],[f59,f68,f48]) ).
fof(f48,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ sP1(X4,X1,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ sP1(sK6(X0,X1,X2),X1,X0)
| ~ in(sK6(X0,X1,X2),X2) )
& ( sP1(sK6(X0,X1,X2),X1,X0)
| in(sK6(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,[sK6])],[f29,f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP1(X3,X1,X0)
| ~ in(X3,X2) )
& ( sP1(X3,X1,X0)
| in(X3,X2) ) )
=> ( ( ~ sP1(sK6(X0,X1,X2),X1,X0)
| ~ in(sK6(X0,X1,X2),X2) )
& ( sP1(sK6(X0,X1,X2),X1,X0)
| in(sK6(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,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,[],[f28]) ).
fof(f28,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,[],[f16]) ).
fof(f16,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(f68,plain,
! [X0,X1] : sP2(X0,X1,unordered_pair(X1,X0)),
inference(superposition,[],[f60,f37]) ).
fof(f37,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f60,plain,
! [X0,X1] : sP2(X0,X1,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f54]) ).
fof(f54,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,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,[],[f17]) ).
fof(f17,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP2(X0,X1,X2) ),
inference(definition_folding,[],[f4,f16,f15]) ).
fof(f15,plain,
! [X3,X1,X0] :
( sP1(X3,X1,X0)
<=> ( X1 = X3
| X0 = X3 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f59,plain,
! [X2,X1] : sP1(X2,X1,X2),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| X0 != X2 ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( X0 != X1
& X0 != X2 ) )
& ( X0 = X1
| X0 = X2
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f33]) ).
fof(f33,plain,
! [X3,X1,X0] :
( ( sP1(X3,X1,X0)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ sP1(X3,X1,X0) ) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X3,X1,X0] :
( ( sP1(X3,X1,X0)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ sP1(X3,X1,X0) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f325,plain,
~ in(sK5(sK3,unordered_pair(sK3,sK3)),unordered_pair(sK3,sK3)),
inference(unit_resulting_resolution,[],[f68,f315,f47]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X2)
| sP1(X4,X1,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f315,plain,
~ sP1(sK5(sK3,unordered_pair(sK3,sK3)),sK3,sK3),
inference(unit_resulting_resolution,[],[f297,f297,f51]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f34]) ).
fof(f73,plain,
~ sP0(sK3,unordered_pair(sK3,sK3)),
inference(unit_resulting_resolution,[],[f36,f46]) ).
fof(f46,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( singleton(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f3,f13]) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f36,plain,
singleton(sK3) != unordered_pair(sK3,sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
singleton(sK3) != unordered_pair(sK3,sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f10,f18]) ).
fof(f18,plain,
( ? [X0] : singleton(X0) != unordered_pair(X0,X0)
=> singleton(sK3) != unordered_pair(sK3,sK3) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
? [X0] : singleton(X0) != unordered_pair(X0,X0),
inference(ennf_transformation,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU142+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 11:30:48 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (15507)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (15510)WARNING: value z3 for option sas not known
% 0.14/0.38 % (15512)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)
% 0.14/0.38 % (15513)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)
% 0.14/0.38 % (15510)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)
% 0.14/0.38 % (15509)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (15514)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)
% 0.14/0.39 % (15508)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.40 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.40 TRYING [4]
% 0.21/0.40 % (15514)First to succeed.
% 0.21/0.40 % (15514)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15507"
% 0.21/0.40 % (15511)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (15514)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.40 % (15514)------------------------------
% 0.21/0.40 % (15514)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.40 % (15514)Termination reason: Refutation
% 0.21/0.40
% 0.21/0.40 % (15514)Memory used [KB]: 1000
% 0.21/0.40 % (15514)Time elapsed: 0.022 s
% 0.21/0.40 % (15514)Instructions burned: 34 (million)
% 0.21/0.40 % (15507)Success in time 0.041 s
%------------------------------------------------------------------------------