TSTP Solution File: SET021-7 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET021-7 : 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 : n015.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 15:04:24 EDT 2024
% Result : Unsatisfiable 0.17s 0.43s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 34 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2273,plain,
$false,
inference(trivial_inequality_removal,[],[f2270]) ).
fof(f2270,plain,
v != v,
inference(superposition,[],[f159,f2209]) ).
fof(f2209,plain,
v = second(ordered_pair(u,v)),
inference(resolution,[],[f2183,f446]) ).
fof(f446,plain,
member(v,universal_class),
inference(resolution,[],[f15,f158]) ).
fof(f158,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(f2183,plain,
( ~ member(v,universal_class)
| v = second(ordered_pair(u,v)) ),
inference(resolution,[],[f2150,f426]) ).
fof(f426,plain,
member(u,universal_class),
inference(resolution,[],[f14,f158]) ).
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(f2150,plain,
! [X0] :
( ~ member(u,X0)
| v = second(ordered_pair(u,v))
| ~ member(v,universal_class) ),
inference(resolution,[],[f2121,f122]) ).
fof(f122,axiom,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_in_its_singleton) ).
fof(f2121,plain,
! [X0,X1] :
( ~ member(v,singleton(X1))
| ~ member(u,X0)
| second(ordered_pair(u,v)) = X1 ),
inference(resolution,[],[f2108,f125]) ).
fof(f125,axiom,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f2108,plain,
! [X0,X1] :
( member(second(ordered_pair(u,v)),X0)
| ~ member(u,X1)
| ~ member(v,X0) ),
inference(resolution,[],[f16,f1713]) ).
fof(f1713,plain,
! [X0,X1] :
( ~ member(ordered_pair(u,v),cross_product(X0,X1))
| member(second(ordered_pair(u,v)),X1) ),
inference(superposition,[],[f15,f1698]) ).
fof(f1698,plain,
ordered_pair(u,v) = ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),
inference(resolution,[],[f17,f158]) ).
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(f159,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
% 0.09/0.10 % Problem : SET021-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.09/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n015.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 02:02:32 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % (18171)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (18174)WARNING: value z3 for option sas not known
% 0.11/0.35 % (18175)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35 % (18176)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)
% 0.11/0.35 % (18178)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)
% 0.11/0.35 % (18177)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)
% 0.11/0.35 % (18173)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35 % (18172)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35 % (18174)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)
% 0.11/0.39 TRYING [1]
% 0.11/0.40 TRYING [2]
% 0.17/0.43 % (18177)First to succeed.
% 0.17/0.43 % (18177)Refutation found. Thanks to Tanya!
% 0.17/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.43 % (18177)------------------------------
% 0.17/0.43 % (18177)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.43 % (18177)Termination reason: Refutation
% 0.17/0.43
% 0.17/0.43 % (18177)Memory used [KB]: 2116
% 0.17/0.43 % (18177)Time elapsed: 0.084 s
% 0.17/0.43 % (18177)Instructions burned: 150 (million)
% 0.17/0.43 % (18177)------------------------------
% 0.17/0.43 % (18177)------------------------------
% 0.17/0.43 % (18171)Success in time 0.105 s
%------------------------------------------------------------------------------