TSTP Solution File: SET957+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 09:19:48 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 6 unt; 0 def)
% Number of atoms : 161 ( 55 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 165 ( 49 ~; 62 |; 42 &)
% ( 5 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 104 ( 73 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1336,plain,
$false,
inference(trivial_inequality_removal,[],[f1335]) ).
fof(f1335,plain,
sK0 != sK0,
inference(superposition,[],[f34,f1267]) ).
fof(f1267,plain,
sK0 = sK3,
inference(duplicate_literal_removal,[],[f1262]) ).
fof(f1262,plain,
( sK0 = sK3
| sK0 = sK3 ),
inference(resolution,[],[f1261,f1250]) ).
fof(f1250,plain,
( in(sK6(sK3,sK0),sK3)
| sK0 = sK3 ),
inference(duplicate_literal_removal,[],[f1249]) ).
fof(f1249,plain,
( sK0 = sK3
| sK0 = sK3
| in(sK6(sK3,sK0),sK3) ),
inference(resolution,[],[f1248,f40]) ).
fof(f40,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| X0 = X1
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0) )
& ( in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f21,f22]) ).
fof(f22,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0) )
& ( in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f1248,plain,
( ~ in(sK6(sK3,sK0),sK0)
| sK0 = sK3 ),
inference(duplicate_literal_removal,[],[f1244]) ).
fof(f1244,plain,
( ~ in(sK6(sK3,sK0),sK0)
| sK0 = sK3
| ~ in(sK6(sK3,sK0),sK0)
| sK0 = sK3 ),
inference(resolution,[],[f1143,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f1143,plain,
( in(sK6(sK3,sK0),sK3)
| ~ in(sK6(sK3,sK0),sK0)
| sK0 = sK3 ),
inference(superposition,[],[f32,f1142]) ).
fof(f1142,plain,
( sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
| sK0 = sK3 ),
inference(duplicate_literal_removal,[],[f1139]) ).
fof(f1139,plain,
( sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
| sK0 = sK3
| sK0 = sK3
| sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0))) ),
inference(resolution,[],[f1126,f109]) ).
fof(f109,plain,
! [X0] :
( in(sK6(X0,sK0),X0)
| sK0 = X0
| sK6(X0,sK0) = ordered_pair(sK7(sK1,sK2,sK6(X0,sK0)),sK8(sK1,sK2,sK6(X0,sK0))) ),
inference(resolution,[],[f105,f40]) ).
fof(f105,plain,
! [X0] :
( ~ in(X0,sK0)
| ordered_pair(sK7(sK1,sK2,X0),sK8(sK1,sK2,X0)) = X0 ),
inference(resolution,[],[f44,f30]) ).
fof(f30,plain,
subset(sK0,cartesian_product2(sK1,sK2)),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( sK0 != sK3
& ! [X6,X7] :
( ( in(ordered_pair(X6,X7),sK0)
| ~ in(ordered_pair(X6,X7),sK3) )
& ( in(ordered_pair(X6,X7),sK3)
| ~ in(ordered_pair(X6,X7),sK0) ) )
& subset(sK3,cartesian_product2(sK4,sK5))
& subset(sK0,cartesian_product2(sK1,sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f18,f19]) ).
fof(f19,plain,
( ? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& ! [X6,X7] :
( ( in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X6,X7),X3) )
& ( in(ordered_pair(X6,X7),X3)
| ~ in(ordered_pair(X6,X7),X0) ) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) )
=> ( sK0 != sK3
& ! [X7,X6] :
( ( in(ordered_pair(X6,X7),sK0)
| ~ in(ordered_pair(X6,X7),sK3) )
& ( in(ordered_pair(X6,X7),sK3)
| ~ in(ordered_pair(X6,X7),sK0) ) )
& subset(sK3,cartesian_product2(sK4,sK5))
& subset(sK0,cartesian_product2(sK1,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& ! [X6,X7] :
( ( in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X6,X7),X3) )
& ( in(ordered_pair(X6,X7),X3)
| ~ in(ordered_pair(X6,X7),X0) ) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
? [X0,X1,X2,X3,X4,X5] :
( X0 != X3
& ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) )
=> X0 = X3 ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( ! [X6,X7] :
( in(ordered_pair(X6,X7),X0)
<=> in(ordered_pair(X6,X7),X3) )
& subset(X3,cartesian_product2(X4,X5))
& subset(X0,cartesian_product2(X1,X2)) )
=> X0 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).
fof(f44,plain,
! [X2,X3,X0,X1] :
( ~ subset(X0,cartesian_product2(X1,X2))
| ~ in(X3,X0)
| ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3 ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ( ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3
& in(sK8(X1,X2,X3),X2)
& in(sK7(X1,X2,X3),X1) )
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f17,f24]) ).
fof(f24,plain,
! [X1,X2,X3] :
( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
=> ( ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3
& in(sK8(X1,X2,X3),X2)
& in(sK7(X1,X2,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
~ ( ! [X4,X5] :
~ ( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f1126,plain,
( ~ in(sK6(sK3,sK0),sK3)
| sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
| sK0 = sK3 ),
inference(duplicate_literal_removal,[],[f1116]) ).
fof(f1116,plain,
( ~ in(sK6(sK3,sK0),sK3)
| sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
| sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
| sK0 = sK3 ),
inference(superposition,[],[f108,f233]) ).
fof(f233,plain,
( sK6(sK3,sK0) = ordered_pair(sK7(sK4,sK5,sK6(sK3,sK0)),sK8(sK4,sK5,sK6(sK3,sK0)))
| sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
| sK0 = sK3 ),
inference(resolution,[],[f109,f106]) ).
fof(f106,plain,
! [X0] :
( ~ in(X0,sK3)
| ordered_pair(sK7(sK4,sK5,X0),sK8(sK4,sK5,X0)) = X0 ),
inference(resolution,[],[f44,f31]) ).
fof(f31,plain,
subset(sK3,cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f20]) ).
fof(f108,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK3)
| ordered_pair(X0,X1) = ordered_pair(sK7(sK1,sK2,ordered_pair(X0,X1)),sK8(sK1,sK2,ordered_pair(X0,X1))) ),
inference(resolution,[],[f105,f33]) ).
fof(f33,plain,
! [X6,X7] :
( in(ordered_pair(X6,X7),sK0)
| ~ in(ordered_pair(X6,X7),sK3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X6,X7] :
( in(ordered_pair(X6,X7),sK3)
| ~ in(ordered_pair(X6,X7),sK0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f1261,plain,
( ~ in(sK6(sK3,sK0),sK3)
| sK0 = sK3 ),
inference(duplicate_literal_removal,[],[f1256]) ).
fof(f1256,plain,
( ~ in(sK6(sK3,sK0),sK3)
| sK0 = sK3
| sK0 = sK3 ),
inference(resolution,[],[f1144,f1248]) ).
fof(f1144,plain,
( in(sK6(sK3,sK0),sK0)
| ~ in(sK6(sK3,sK0),sK3)
| sK0 = sK3 ),
inference(superposition,[],[f33,f1142]) ).
fof(f34,plain,
sK0 != sK3,
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.29 % Computer : n015.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri May 3 16:35:23 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % (23583)Running in auto input_syntax mode. Trying TPTP
% 0.09/0.31 % (23589)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)
% 0.09/0.31 % (23588)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)
% 0.09/0.31 % (23586)WARNING: value z3 for option sas not known
% 0.14/0.31 % (23587)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.31 % (23585)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.31 % (23584)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.31 % (23586)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)
% 0.14/0.31 % (23590)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)
% 0.14/0.31 TRYING [1]
% 0.14/0.31 TRYING [2]
% 0.14/0.31 TRYING [1]
% 0.14/0.31 TRYING [3]
% 0.14/0.31 TRYING [2]
% 0.14/0.32 TRYING [3]
% 0.14/0.36 TRYING [4]
% 0.14/0.37 % (23589)First to succeed.
% 0.14/0.37 % (23589)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23583"
% 0.14/0.37 % (23589)Refutation found. Thanks to Tanya!
% 0.14/0.37 % SZS status Theorem for theBenchmark
% 0.14/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37 % (23589)------------------------------
% 0.14/0.37 % (23589)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37 % (23589)Termination reason: Refutation
% 0.14/0.37
% 0.14/0.37 % (23589)Memory used [KB]: 1753
% 0.14/0.37 % (23589)Time elapsed: 0.061 s
% 0.14/0.37 % (23589)Instructions burned: 151 (million)
% 0.14/0.37 % (23583)Success in time 0.076 s
%------------------------------------------------------------------------------