TSTP Solution File: SET985+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET985+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 : n025.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 09:19:52 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 98 ( 40 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 94 ( 29 ~; 40 |; 17 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 38 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f81,plain,
$false,
inference(subsumption_resolution,[],[f78,f26]) ).
fof(f26,plain,
empty(empty_set),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f78,plain,
~ empty(empty_set),
inference(superposition,[],[f23,f73]) ).
fof(f73,plain,
empty_set = sK0,
inference(subsumption_resolution,[],[f70,f27]) ).
fof(f27,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f70,plain,
( ~ subset(empty_set,sK3)
| empty_set = sK0 ),
inference(superposition,[],[f25,f66]) ).
fof(f66,plain,
( empty_set = sK1
| empty_set = sK0 ),
inference(subsumption_resolution,[],[f65,f29]) ).
fof(f29,plain,
! [X0,X1] :
( empty_set != cartesian_product2(X0,X1)
| empty_set = X0
| empty_set = X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) )
& ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) )
& ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
<=> ( empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f65,plain,
( empty_set = sK1
| empty_set = sK0
| empty_set = cartesian_product2(sK0,sK1) ),
inference(trivial_inequality_removal,[],[f64]) ).
fof(f64,plain,
( empty_set != empty_set
| empty_set = sK1
| empty_set = sK0
| empty_set = cartesian_product2(sK0,sK1) ),
inference(superposition,[],[f29,f57]) ).
fof(f57,plain,
( empty_set = cartesian_product2(sK1,sK0)
| empty_set = cartesian_product2(sK0,sK1) ),
inference(subsumption_resolution,[],[f51,f25]) ).
fof(f51,plain,
( empty_set = cartesian_product2(sK0,sK1)
| subset(sK1,sK3)
| empty_set = cartesian_product2(sK1,sK0) ),
inference(resolution,[],[f33,f46]) ).
fof(f46,plain,
( subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3))
| empty_set = cartesian_product2(sK1,sK0) ),
inference(subsumption_resolution,[],[f40,f25]) ).
fof(f40,plain,
( empty_set = cartesian_product2(sK1,sK0)
| subset(sK1,sK3)
| subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(resolution,[],[f32,f24]) ).
fof(f24,plain,
( subset(cartesian_product2(sK1,sK0),cartesian_product2(sK3,sK2))
| subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ~ subset(sK1,sK3)
& ( subset(cartesian_product2(sK1,sK0),cartesian_product2(sK3,sK2))
| subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) )
& ~ empty(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f15,f14]) ).
fof(f14,plain,
( ? [X0] :
( ? [X1,X2,X3] :
( ~ subset(X1,X3)
& ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
| subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ) )
& ~ empty(X0) )
=> ( ? [X3,X2,X1] :
( ~ subset(X1,X3)
& ( subset(cartesian_product2(X1,sK0),cartesian_product2(X3,X2))
| subset(cartesian_product2(sK0,X1),cartesian_product2(X2,X3)) ) )
& ~ empty(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ? [X3,X2,X1] :
( ~ subset(X1,X3)
& ( subset(cartesian_product2(X1,sK0),cartesian_product2(X3,X2))
| subset(cartesian_product2(sK0,X1),cartesian_product2(X2,X3)) ) )
=> ( ~ subset(sK1,sK3)
& ( subset(cartesian_product2(sK1,sK0),cartesian_product2(sK3,sK2))
| subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0] :
( ? [X1,X2,X3] :
( ~ subset(X1,X3)
& ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
| subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ! [X1,X2,X3] :
( ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
| subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
=> subset(X1,X3) ) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0] :
( ~ empty(X0)
=> ! [X1,X2,X3] :
( ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
| subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
=> subset(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| empty_set = cartesian_product2(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( ( subset(X1,X3)
& subset(X0,X2) )
| empty_set = cartesian_product2(X0,X1)
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(flattening,[],[f12]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( ( subset(X1,X3)
& subset(X0,X2) )
| empty_set = cartesian_product2(X0,X1)
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| empty_set = cartesian_product2(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| empty_set = cartesian_product2(X0,X1)
| subset(X1,X3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
~ subset(sK1,sK3),
inference(cnf_transformation,[],[f16]) ).
fof(f23,plain,
~ empty(sK0),
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET985+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 3 17:01:23 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (22638)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (22642)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36 % (22640)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.36 % (22645)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)
% 0.14/0.36 % (22644)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)
% 0.14/0.36 % (22639)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36 % (22643)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)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 % (22645)First to succeed.
% 0.14/0.37 TRYING [3]
% 0.14/0.37 TRYING [1]
% 0.14/0.37 % (22645)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22638"
% 0.14/0.37 % (22644)Also succeeded, but the first one will report.
% 0.14/0.37 TRYING [2]
% 0.14/0.37 % (22643)Also succeeded, but the first one will report.
% 0.14/0.37 TRYING [1]
% 0.14/0.37 % (22645)Refutation found. Thanks to Tanya!
% 0.14/0.37 % SZS status Theorem for theBenchmark
% 0.14/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37 % (22645)------------------------------
% 0.14/0.37 % (22645)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37 % (22645)Termination reason: Refutation
% 0.14/0.37
% 0.14/0.37 % (22645)Memory used [KB]: 760
% 0.14/0.37 % (22645)Time elapsed: 0.005 s
% 0.14/0.37 % (22645)Instructions burned: 5 (million)
% 0.14/0.37 % (22638)Success in time 0.012 s
%------------------------------------------------------------------------------