TSTP Solution File: SEU164+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU164+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 : 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 14.82s 2.41s
% Output : Refutation 14.82s
% 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(f70340,plain,
$false,
inference(trivial_inequality_removal,[],[f69910]) ).
fof(f69910,plain,
sK1 != sK1,
inference(superposition,[],[f46,f68739]) ).
fof(f68739,plain,
! [X0] : union(powerset(X0)) = X0,
inference(resolution,[],[f68735,f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f5,f19]) ).
fof(f19,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(f68735,plain,
! [X0] : sP0(powerset(X0),X0),
inference(subsumption_resolution,[],[f68690,f6074]) ).
fof(f6074,plain,
! [X0,X1] :
( ~ in(sK6(powerset(X0),X1),X1)
| sP0(powerset(X0),X1)
| ~ in(sK6(powerset(X0),X1),X0) ),
inference(resolution,[],[f1075,f71]) ).
fof(f71,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f1075,plain,
! [X0,X1] :
( ~ subset(singleton(sK6(powerset(X0),X1)),X0)
| ~ in(sK6(powerset(X0),X1),X1)
| sP0(powerset(X0),X1) ),
inference(resolution,[],[f658,f75]) ).
fof(f75,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f59]) ).
fof(f59,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,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])],[f35,f36]) ).
fof(f36,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(f35,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,[],[f34]) ).
fof(f34,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(f658,plain,
! [X0,X1] :
( ~ in(singleton(sK6(X0,X1)),X0)
| sP0(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(resolution,[],[f67,f73]) ).
fof(f73,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f72]) ).
fof(f72,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f55]) ).
fof(f55,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,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])],[f31,f32]) ).
fof(f32,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(f31,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,[],[f30]) ).
fof(f30,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(f67,plain,
! [X3,X0,X1] :
( ~ in(sK6(X0,X1),X3)
| ~ in(X3,X0)
| sP0(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,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])],[f39,f42,f41,f40]) ).
fof(f40,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(f41,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(f42,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK8(X0,X5),X0)
& in(X5,sK8(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f39,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,[],[f38]) ).
fof(f38,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,[],[f19]) ).
fof(f68690,plain,
! [X0] :
( in(sK6(powerset(X0),X0),X0)
| sP0(powerset(X0),X0) ),
inference(factoring,[],[f12627]) ).
fof(f12627,plain,
! [X0,X1] :
( in(sK6(powerset(X0),X1),X1)
| in(sK6(powerset(X0),X1),X0)
| sP0(powerset(X0),X1) ),
inference(duplicate_literal_removal,[],[f12609]) ).
fof(f12609,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,[],[f1501,f65]) ).
fof(f65,plain,
! [X0,X1] :
( in(sK6(X0,X1),sK7(X0,X1))
| sP0(X0,X1)
| in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f1501,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,[],[f311,f51]) ).
fof(f51,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,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])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f27,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,[],[f26]) ).
fof(f26,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,[],[f18]) ).
fof(f18,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(f311,plain,
! [X0,X1] :
( subset(sK7(powerset(X0),X1),X0)
| in(sK6(powerset(X0),X1),X1)
| sP0(powerset(X0),X1) ),
inference(resolution,[],[f66,f76]) ).
fof(f76,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f58]) ).
fof(f58,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f37]) ).
fof(f66,plain,
! [X0,X1] :
( in(sK7(X0,X1),X0)
| in(sK6(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f46,plain,
sK1 != union(powerset(sK1)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
sK1 != union(powerset(sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f15,f21]) ).
fof(f21,plain,
( ? [X0] : union(powerset(X0)) != X0
=> sK1 != union(powerset(sK1)) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0] : union(powerset(X0)) != X0,
inference(ennf_transformation,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X0] : union(powerset(X0)) = X0,
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : SEU164+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.27 % Computer : n009.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Mon Apr 29 20:50:25 EDT 2024
% 0.07/0.27 % CPUTime :
% 0.10/0.27 % (30952)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.28 % (30955)WARNING: value z3 for option sas not known
% 0.10/0.28 % (30954)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.28 % (30956)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.28 % (30953)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.28 % (30957)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)
% 0.10/0.28 % (30958)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)
% 0.10/0.28 % (30955)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)
% 0.10/0.28 % (30959)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)
% 0.10/0.28 TRYING [1]
% 0.10/0.28 TRYING [2]
% 0.10/0.28 TRYING [3]
% 0.10/0.28 TRYING [1]
% 0.10/0.28 TRYING [4]
% 0.10/0.28 TRYING [2]
% 0.10/0.29 TRYING [3]
% 0.10/0.29 TRYING [5]
% 0.10/0.30 TRYING [6]
% 0.10/0.31 TRYING [4]
% 0.10/0.32 TRYING [7]
% 0.10/0.37 TRYING [5]
% 0.10/0.37 TRYING [8]
% 0.10/0.44 TRYING [9]
% 0.10/0.48 TRYING [6]
% 0.10/0.53 TRYING [10]
% 3.07/0.74 TRYING [7]
% 3.50/0.78 TRYING [11]
% 5.65/1.12 TRYING [12]
% 7.70/1.38 TRYING [1]
% 7.70/1.38 TRYING [2]
% 7.70/1.38 TRYING [3]
% 7.70/1.38 TRYING [4]
% 7.70/1.39 TRYING [5]
% 7.70/1.40 TRYING [6]
% 7.70/1.43 TRYING [7]
% 8.38/1.47 TRYING [8]
% 8.83/1.54 TRYING [9]
% 8.83/1.57 TRYING [13]
% 8.83/1.61 TRYING [8]
% 9.42/1.68 TRYING [10]
% 10.82/1.88 TRYING [11]
% 13.02/2.17 TRYING [14]
% 13.02/2.18 TRYING [12]
% 14.82/2.41 % (30955)First to succeed.
% 14.82/2.41 % (30955)Refutation found. Thanks to Tanya!
% 14.82/2.41 % SZS status Theorem for theBenchmark
% 14.82/2.41 % SZS output start Proof for theBenchmark
% See solution above
% 14.82/2.41 % (30955)------------------------------
% 14.82/2.41 % (30955)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 14.82/2.41 % (30955)Termination reason: Refutation
% 14.82/2.41
% 14.82/2.41 % (30955)Memory used [KB]: 60384
% 14.82/2.41 % (30955)Time elapsed: 2.131 s
% 14.82/2.41 % (30955)Instructions burned: 6232 (million)
% 14.82/2.41 % (30955)------------------------------
% 14.82/2.41 % (30955)------------------------------
% 14.82/2.41 % (30952)Success in time 2.139 s
%------------------------------------------------------------------------------