TSTP Solution File: SET867+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : Tue Apr 30 15:13:50 EDT 2024
% Result : Theorem 0.11s 0.35s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 112 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 128 ( 48 ~; 45 |; 25 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 67 ( 56 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f64,plain,
$false,
inference(unit_resulting_resolution,[],[f60,f49,f48,f36]) ).
fof(f36,plain,
! [X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ in(X3,X1)
| sP0(X0,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( ~ sP0(X0,sK3(X0,X1))
| ~ in(sK3(X0,X1),X1) )
& ( sP0(X0,sK3(X0,X1))
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP0(X0,X3) )
& ( sP0(X0,X3)
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f19,f20]) ).
fof(f20,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ sP0(X0,X2)
| ~ in(X2,X1) )
& ( sP0(X0,X2)
| in(X2,X1) ) )
=> ( ( ~ sP0(X0,sK3(X0,X1))
| ~ in(sK3(X0,X1),X1) )
& ( sP0(X0,sK3(X0,X1))
| in(sK3(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ( ~ sP0(X0,X2)
| ~ in(X2,X1) )
& ( sP0(X0,X2)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP0(X0,X3) )
& ( sP0(X0,X3)
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ( ~ sP0(X0,X2)
| ~ in(X2,X1) )
& ( sP0(X0,X2)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ sP0(X0,X2) )
& ( sP0(X0,X2)
| ~ in(X2,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( sP1(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> sP0(X0,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f48,plain,
! [X0] : sP1(X0,union(X0)),
inference(equality_resolution,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( sP1(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f3,f12,f11]) ).
fof(f11,plain,
! [X0,X2] :
( sP0(X0,X2)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f3,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(f49,plain,
in(sK2(union(empty_set)),union(empty_set)),
inference(unit_resulting_resolution,[],[f31,f34]) ).
fof(f34,plain,
! [X0] :
( in(sK2(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0] :
( ( empty_set = X0
| in(sK2(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f15,f16]) ).
fof(f16,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f14]) ).
fof(f14,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f31,plain,
empty_set != union(empty_set),
inference(cnf_transformation,[],[f9]) ).
fof(f9,plain,
empty_set != union(empty_set),
inference(flattening,[],[f8]) ).
fof(f8,negated_conjecture,
empty_set != union(empty_set),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
empty_set = union(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
fof(f60,plain,
! [X0] : ~ sP0(empty_set,X0),
inference(unit_resulting_resolution,[],[f47,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ( in(sK4(X0,X1),X0)
& in(X1,sK4(X0,X1)) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
=> ( in(sK4(X0,X1),X0)
& in(X1,sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X0,X2] :
( ( sP0(X0,X2)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ sP0(X0,X2) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f47,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f33]) ).
fof(f33,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n020.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 : Tue Apr 30 01:33:17 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (6416)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (6420)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 % (6423)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 % (6421)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 % (6422)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 % (6423)First to succeed.
% 0.11/0.35 % (6422)Also succeeded, but the first one will report.
% 0.11/0.35 % (6423)Refutation found. Thanks to Tanya!
% 0.11/0.35 % SZS status Theorem for theBenchmark
% 0.11/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.35 % (6423)------------------------------
% 0.11/0.35 % (6423)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.35 % (6423)Termination reason: Refutation
% 0.11/0.35
% 0.11/0.35 % (6423)Memory used [KB]: 757
% 0.11/0.35 % (6423)Time elapsed: 0.004 s
% 0.11/0.35 % (6423)Instructions burned: 4 (million)
% 0.11/0.35 % (6423)------------------------------
% 0.11/0.35 % (6423)------------------------------
% 0.11/0.35 % (6416)Success in time 0.017 s
%------------------------------------------------------------------------------