TSTP Solution File: SEU164+3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU164+3 : 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 : n009.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 : Tue Apr 30 15:22:44 EDT 2024
% Result : Theorem 22.13s 3.52s
% Output : Refutation 22.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 59 ( 10 unt; 0 def)
% Number of atoms : 262 ( 50 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 314 ( 111 ~; 126 |; 57 &)
% ( 12 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 156 ( 132 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f70293,plain,
$false,
inference(trivial_inequality_removal,[],[f69864]) ).
fof(f69864,plain,
sK1 != sK1,
inference(superposition,[],[f49,f68694]) ).
fof(f68694,plain,
! [X0] : union(powerset(X0)) = X0,
inference(resolution,[],[f68690,f72]) ).
fof(f72,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f5,f18]) ).
fof(f18,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f5,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f68690,plain,
! [X0] : sP0(powerset(X0),X0),
inference(subsumption_resolution,[],[f68645,f6071]) ).
fof(f6071,plain,
! [X0,X1] :
( ~ in(sK6(powerset(X0),X1),X1)
| sP0(powerset(X0),X1)
| ~ in(sK6(powerset(X0),X1),X0) ),
inference(resolution,[],[f1069,f74]) ).
fof(f74,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f1069,plain,
! [X0,X1] :
( ~ subset(singleton(sK6(powerset(X0),X1)),X0)
| ~ in(sK6(powerset(X0),X1),X1)
| sP0(powerset(X0),X1) ),
inference(resolution,[],[f650,f80]) ).
fof(f80,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f62]) ).
fof(f62,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK5(X0,X1),X0)
| ~ in(sK5(X0,X1),X1) )
& ( subset(sK5(X0,X1),X0)
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f34,f35]) ).
fof(f35,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK5(X0,X1),X0)
| ~ in(sK5(X0,X1),X1) )
& ( subset(sK5(X0,X1),X0)
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f650,plain,
! [X0,X1] :
( ~ in(singleton(sK6(X0,X1)),X0)
| sP0(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(resolution,[],[f70,f78]) ).
fof(f78,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f77]) ).
fof(f77,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f58]) ).
fof(f58,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f30,f31]) ).
fof(f31,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,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,[],[f29]) ).
fof(f29,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,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f70,plain,
! [X3,X0,X1] :
( ~ in(sK6(X0,X1),X3)
| ~ in(X3,X0)
| sP0(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK6(X0,X1),X3) )
| ~ in(sK6(X0,X1),X1) )
& ( ( in(sK7(X0,X1),X0)
& in(sK6(X0,X1),sK7(X0,X1)) )
| in(sK6(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK8(X0,X5),X0)
& in(X5,sK8(X0,X5)) )
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f38,f41,f40,f39]) ).
fof(f39,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK6(X0,X1),X3) )
| ~ in(sK6(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK6(X0,X1),X4) )
| in(sK6(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK6(X0,X1),X4) )
=> ( in(sK7(X0,X1),X0)
& in(sK6(X0,X1),sK7(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK8(X0,X5),X0)
& in(X5,sK8(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f68645,plain,
! [X0] :
( in(sK6(powerset(X0),X0),X0)
| sP0(powerset(X0),X0) ),
inference(factoring,[],[f12618]) ).
fof(f12618,plain,
! [X0,X1] :
( in(sK6(powerset(X0),X1),X1)
| in(sK6(powerset(X0),X1),X0)
| sP0(powerset(X0),X1) ),
inference(duplicate_literal_removal,[],[f12600]) ).
fof(f12600,plain,
! [X0,X1] :
( sP0(powerset(X0),X1)
| in(sK6(powerset(X0),X1),X1)
| in(sK6(powerset(X0),X1),X0)
| sP0(powerset(X0),X1)
| in(sK6(powerset(X0),X1),X1) ),
inference(resolution,[],[f1500,f68]) ).
fof(f68,plain,
! [X0,X1] :
( in(sK6(X0,X1),sK7(X0,X1))
| sP0(X0,X1)
| in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f1500,plain,
! [X2,X0,X1] :
( ~ in(X2,sK7(powerset(X0),X1))
| sP0(powerset(X0),X1)
| in(sK6(powerset(X0),X1),X1)
| in(X2,X0) ),
inference(resolution,[],[f307,f54]) ).
fof(f54,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f26,f27]) ).
fof(f27,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f307,plain,
! [X0,X1] :
( subset(sK7(powerset(X0),X1),X0)
| in(sK6(powerset(X0),X1),X1)
| sP0(powerset(X0),X1) ),
inference(resolution,[],[f69,f81]) ).
fof(f81,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f61]) ).
fof(f61,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f69,plain,
! [X0,X1] :
( in(sK7(X0,X1),X0)
| in(sK6(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f49,plain,
sK1 != union(powerset(sK1)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
sK1 != union(powerset(sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f14,f20]) ).
fof(f20,plain,
( ? [X0] : union(powerset(X0)) != X0
=> sK1 != union(powerset(sK1)) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0] : union(powerset(X0)) != X0,
inference(ennf_transformation,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0] : union(powerset(X0)) = X0,
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU164+3 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n009.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 : Mon Apr 29 20:16:56 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (11837)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (11841)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (11839)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.38 % (11840)WARNING: value z3 for option sas not known
% 0.21/0.38 % (11840)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)
% 0.21/0.38 % (11843)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)
% 0.21/0.38 % (11838)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 TRYING [4]
% 0.21/0.38 % (11842)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)
% 0.21/0.38 % (11844)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)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [5]
% 0.21/0.40 TRYING [3]
% 0.21/0.41 TRYING [6]
% 0.21/0.44 TRYING [4]
% 0.21/0.45 TRYING [7]
% 0.21/0.51 TRYING [5]
% 0.21/0.51 TRYING [8]
% 1.48/0.62 TRYING [9]
% 2.36/0.68 TRYING [6]
% 2.93/0.77 TRYING [10]
% 4.46/1.01 TRYING [11]
% 5.52/1.15 TRYING [7]
% 7.11/1.41 TRYING [12]
% 7.88/1.47 TRYING [1]
% 7.88/1.47 TRYING [2]
% 7.88/1.48 TRYING [3]
% 7.88/1.48 TRYING [4]
% 7.88/1.49 TRYING [5]
% 7.88/1.52 TRYING [6]
% 8.32/1.55 TRYING [7]
% 8.50/1.62 TRYING [8]
% 9.83/1.75 TRYING [9]
% 11.04/1.97 TRYING [10]
% 11.92/2.05 TRYING [13]
% 13.23/2.29 TRYING [11]
% 16.89/2.79 TRYING [12]
% 18.09/2.96 TRYING [14]
% 21.85/3.51 % (11840)First to succeed.
% 22.13/3.52 % (11840)Refutation found. Thanks to Tanya!
% 22.13/3.52 % SZS status Theorem for theBenchmark
% 22.13/3.52 % SZS output start Proof for theBenchmark
% See solution above
% 22.13/3.52 % (11840)------------------------------
% 22.13/3.53 % (11840)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 22.13/3.53 % (11840)Termination reason: Refutation
% 22.13/3.53
% 22.13/3.53 % (11840)Memory used [KB]: 60362
% 22.13/3.53 % (11840)Time elapsed: 3.138 s
% 22.13/3.53 % (11840)Instructions burned: 6227 (million)
% 22.13/3.53 % (11840)------------------------------
% 22.13/3.53 % (11840)------------------------------
% 22.13/3.53 % (11837)Success in time 3.167 s
%------------------------------------------------------------------------------