TSTP Solution File: SET021-6 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET021-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.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 09:09:51 EDT 2024
% Result : Unsatisfiable 0.16s 0.37s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 43 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f816,plain,
$false,
inference(trivial_inequality_removal,[],[f815]) ).
fof(f815,plain,
v != v,
inference(superposition,[],[f93,f756]) ).
fof(f756,plain,
v = second(ordered_pair(u,v)),
inference(resolution,[],[f743,f195]) ).
fof(f195,plain,
member(v,universal_class),
inference(resolution,[],[f15,f92]) ).
fof(f92,axiom,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f743,plain,
( ~ member(v,universal_class)
| v = second(ordered_pair(u,v)) ),
inference(resolution,[],[f727,f190]) ).
fof(f190,plain,
member(u,universal_class),
inference(resolution,[],[f14,f92]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f727,plain,
! [X0] :
( ~ member(u,X0)
| v = second(ordered_pair(u,v))
| ~ member(v,universal_class) ),
inference(resolution,[],[f602,f102]) ).
fof(f102,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f9,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f602,plain,
! [X0,X1] :
( ~ member(v,singleton(X1))
| ~ member(u,X0)
| second(ordered_pair(u,v)) = X1 ),
inference(resolution,[],[f579,f253]) ).
fof(f253,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f252]) ).
fof(f252,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f8,f12]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f579,plain,
! [X0,X1] :
( member(second(ordered_pair(u,v)),X0)
| ~ member(u,X1)
| ~ member(v,X0) ),
inference(resolution,[],[f16,f489]) ).
fof(f489,plain,
! [X0,X1] :
( ~ member(ordered_pair(u,v),cross_product(X0,X1))
| member(second(ordered_pair(u,v)),X1) ),
inference(superposition,[],[f15,f476]) ).
fof(f476,plain,
ordered_pair(u,v) = ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),
inference(resolution,[],[f17,f92]) ).
fof(f17,axiom,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),cross_product(X0,X1))
| ~ member(X3,X1)
| ~ member(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f93,axiom,
v != second(ordered_pair(u,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET021-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n004.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 16:48:23 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.32 % (4264)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33 % (4267)WARNING: value z3 for option sas not known
% 0.16/0.33 % (4269)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)
% 0.16/0.33 % (4265)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33 % (4268)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33 % (4267)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)
% 0.16/0.33 % (4271)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)
% 0.16/0.33 % (4270)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)
% 0.16/0.33 % (4266)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.36 TRYING [1]
% 0.16/0.36 TRYING [2]
% 0.16/0.37 % (4270)First to succeed.
% 0.16/0.37 % (4270)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4264"
% 0.16/0.37 % (4270)Refutation found. Thanks to Tanya!
% 0.16/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.37 % (4270)------------------------------
% 0.16/0.37 % (4270)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.37 % (4270)Termination reason: Refutation
% 0.16/0.37
% 0.16/0.37 % (4270)Memory used [KB]: 1401
% 0.16/0.37 % (4270)Time elapsed: 0.036 s
% 0.16/0.37 % (4270)Instructions burned: 64 (million)
% 0.16/0.37 % (4264)Success in time 0.052 s
%------------------------------------------------------------------------------