TSTP Solution File: SEU147+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU147+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 : n020.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 0.21s 0.39s
% Output : Refutation 0.21s
% 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(f159,plain,
$false,
inference(unit_resulting_resolution,[],[f72,f132,f119,f47]) ).
fof(f47,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK3(X0,X1) = X0
| in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,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])],[f25,f26]) ).
fof(f26,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(f25,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,[],[f24]) ).
fof(f24,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,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f119,plain,
empty_set != sK3(empty_set,powerset(empty_set)),
inference(unit_resulting_resolution,[],[f72,f93,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(X0,X1)
| sK3(X0,X1) != X0
| sP0(X0,X1) ),
inference(inner_rewriting,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK3(X0,X1) != X0
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f93,plain,
! [X0] : in(X0,powerset(X0)),
inference(unit_resulting_resolution,[],[f41,f61,f52]) ).
fof(f52,plain,
! [X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,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])],[f30,f31]) ).
fof(f31,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(f30,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,[],[f29]) ).
fof(f29,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,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( sP1(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f61,plain,
! [X0] : sP1(X0,powerset(X0)),
inference(equality_resolution,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( sP1(X0,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( powerset(X0) = X1
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f3,f19]) ).
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(f41,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f132,plain,
~ in(sK3(empty_set,powerset(empty_set)),powerset(empty_set)),
inference(unit_resulting_resolution,[],[f61,f122,f51]) ).
fof(f51,plain,
! [X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f122,plain,
~ subset(sK3(empty_set,powerset(empty_set)),empty_set),
inference(unit_resulting_resolution,[],[f119,f40]) ).
fof(f40,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f72,plain,
~ sP0(empty_set,powerset(empty_set)),
inference(unit_resulting_resolution,[],[f38,f50]) ).
fof(f50,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( singleton(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f2,f17]) ).
fof(f2,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f38,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
powerset(empty_set) != singleton(empty_set),
inference(flattening,[],[f9]) ).
fof(f9,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SEU147+3 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.05/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 10:54:16 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (31023)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (31027)WARNING: value z3 for option sas not known
% 0.21/0.38 % (31025)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (31026)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 % (31029)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 % (31027)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 % (31030)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 % (31028)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (31031)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)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [4]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 % (31031)First to succeed.
% 0.21/0.39 % (31031)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31023"
% 0.21/0.39 % (31031)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39 % (31031)------------------------------
% 0.21/0.39 % (31031)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.39 % (31031)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (31031)Memory used [KB]: 838
% 0.21/0.39 % (31031)Time elapsed: 0.007 s
% 0.21/0.39 % (31031)Instructions burned: 8 (million)
% 0.21/0.39 % (31023)Success in time 0.024 s
%------------------------------------------------------------------------------