TSTP Solution File: SEU147+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU147+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 : n032.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 09:27:23 EDT 2024
% Result : Theorem 0.11s 0.34s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 139 ( 39 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 160 ( 61 ~; 62 |; 24 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 73 ( 67 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f162,plain,
$false,
inference(unit_resulting_resolution,[],[f75,f135,f122,f50]) ).
fof(f50,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK3(X0,X1) = X0
| in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( sK3(X0,X1) != X0
| ~ in(sK3(X0,X1),X1) )
& ( sK3(X0,X1) = X0
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f28,f29]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK3(X0,X1) != X0
| ~ in(sK3(X0,X1),X1) )
& ( sK3(X0,X1) = X0
| in(sK3(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,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,[],[f27]) ).
fof(f27,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,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f122,plain,
empty_set != sK3(empty_set,powerset(empty_set)),
inference(unit_resulting_resolution,[],[f75,f96,f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ in(X0,X1)
| sK3(X0,X1) != X0
| sP0(X0,X1) ),
inference(inner_rewriting,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK3(X0,X1) != X0
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f96,plain,
! [X0] : in(X0,powerset(X0)),
inference(unit_resulting_resolution,[],[f44,f64,f55]) ).
fof(f55,plain,
! [X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( ~ subset(sK4(X0,X1),X0)
| ~ in(sK4(X0,X1),X1) )
& ( subset(sK4(X0,X1),X0)
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f33,f34]) ).
fof(f34,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK4(X0,X1),X0)
| ~ in(sK4(X0,X1),X1) )
& ( subset(sK4(X0,X1),X0)
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1] :
( ( sP1(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) ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( sP1(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) ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( sP1(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f64,plain,
! [X0] : sP1(X0,powerset(X0)),
inference(equality_resolution,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( sP1(X0,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( powerset(X0) = X1
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f3,f22]) ).
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(f44,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f135,plain,
~ in(sK3(empty_set,powerset(empty_set)),powerset(empty_set)),
inference(unit_resulting_resolution,[],[f64,f125,f54]) ).
fof(f54,plain,
! [X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f125,plain,
~ subset(sK3(empty_set,powerset(empty_set)),empty_set),
inference(unit_resulting_resolution,[],[f122,f43]) ).
fof(f43,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f75,plain,
~ sP0(empty_set,powerset(empty_set)),
inference(unit_resulting_resolution,[],[f41,f53]) ).
fof(f53,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( singleton(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f2,f20]) ).
fof(f2,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f41,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
powerset(empty_set) != singleton(empty_set),
inference(flattening,[],[f12]) ).
fof(f12,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : SEU147+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n032.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 11:40:39 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (8732)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (8735)WARNING: value z3 for option sas not known
% 0.11/0.34 % (8733)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34 % (8735)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)
% 0.11/0.34 % (8739)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)
% 0.11/0.34 % (8734)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34 % (8737)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)
% 0.11/0.34 % (8738)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)
% 0.11/0.34 % (8736)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 % (8739)First to succeed.
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [4]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 % (8739)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8732"
% 0.11/0.34 % (8739)Refutation found. Thanks to Tanya!
% 0.11/0.34 % SZS status Theorem for theBenchmark
% 0.11/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.34 % (8739)------------------------------
% 0.11/0.34 % (8739)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.34 % (8739)Termination reason: Refutation
% 0.11/0.34
% 0.11/0.34 % (8739)Memory used [KB]: 838
% 0.11/0.34 % (8739)Time elapsed: 0.006 s
% 0.11/0.34 % (8739)Instructions burned: 8 (million)
% 0.11/0.34 % (8732)Success in time 0.02 s
%------------------------------------------------------------------------------