TSTP Solution File: SET979+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET979+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.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 May 21 03:25:00 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 18 ~; 7 |; 3 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 19 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f60,plain,
$false,
inference(trivial_inequality_removal,[],[f59]) ).
fof(f59,plain,
cartesian_product2(unordered_pair(sK0,sK1),sK2) != cartesian_product2(unordered_pair(sK0,sK1),sK2),
inference(forward_demodulation,[],[f53,f26]) ).
fof(f26,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_enumset1) ).
fof(f53,plain,
cartesian_product2(unordered_pair(sK0,sK1),sK2) != cartesian_product2(set_union2(singleton(sK0),singleton(sK1)),sK2),
inference(superposition,[],[f35,f29]) ).
fof(f29,plain,
! [X2,X0,X1] : cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(f35,plain,
cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)),
inference(trivial_inequality_removal,[],[f34]) ).
fof(f34,plain,
( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != cartesian_product2(sK2,unordered_pair(sK0,sK1))
| cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
inference(forward_demodulation,[],[f33,f26]) ).
fof(f33,plain,
( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != cartesian_product2(sK2,set_union2(singleton(sK0),singleton(sK1)))
| cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
inference(backward_demodulation,[],[f22,f30]) ).
fof(f30,plain,
! [X2,X0,X1] : cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f22,plain,
( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
| cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
| cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f16]) ).
fof(f16,plain,
( ? [X0,X1,X2] :
( cartesian_product2(X2,unordered_pair(X0,X1)) != set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
| cartesian_product2(unordered_pair(X0,X1),X2) != set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) )
=> ( cartesian_product2(sK2,unordered_pair(sK0,sK1)) != set_union2(cartesian_product2(sK2,singleton(sK0)),cartesian_product2(sK2,singleton(sK1)))
| cartesian_product2(unordered_pair(sK0,sK1),sK2) != set_union2(cartesian_product2(singleton(sK0),sK2),cartesian_product2(singleton(sK1),sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0,X1,X2] :
( cartesian_product2(X2,unordered_pair(X0,X1)) != set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
| cartesian_product2(unordered_pair(X0,X1),X2) != set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
& cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
& cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET979+1 : TPTP v8.2.0. Released v3.2.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 : Mon May 20 11:24:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (14474)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (14481)WARNING: value z3 for option sas not known
% 0.14/0.38 % (14480)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (14479)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (14481)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)
% 0.14/0.38 % (14482)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (14485)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)
% 0.14/0.38 % (14484)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)
% 0.14/0.38 % (14483)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (14484)First to succeed.
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (14484)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14474"
% 0.14/0.38 % (14483)Also succeeded, but the first one will report.
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (14484)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (14484)------------------------------
% 0.14/0.38 % (14484)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (14484)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (14484)Memory used [KB]: 774
% 0.14/0.38 % (14484)Time elapsed: 0.004 s
% 0.14/0.38 % (14484)Instructions burned: 5 (million)
% 0.14/0.38 % (14474)Success in time 0.023 s
%------------------------------------------------------------------------------