TSTP Solution File: SET505-6 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET505-6 : 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 : n012.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 15:08:27 EDT 2024
% Result : Unsatisfiable 1.90s 0.79s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 18
% Syntax : Number of formulae : 62 ( 17 unt; 0 def)
% Number of atoms : 125 ( 39 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 113 ( 50 ~; 63 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 4 con; 0-3 aty)
% Number of variables : 87 ( 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6958,plain,
$false,
inference(subsumption_resolution,[],[f6957,f396]) ).
fof(f396,plain,
member(universal_class,universal_class),
inference(resolution,[],[f14,f113]) ).
fof(f113,axiom,
member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_universal_class_not_set_1) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f6957,plain,
~ member(universal_class,universal_class),
inference(subsumption_resolution,[],[f6914,f4451]) ).
fof(f4451,plain,
! [X0] : ~ member(X0,null_class),
inference(subsumption_resolution,[],[f4450,f4385]) ).
fof(f4385,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_inequality_removal,[],[f4383]) ).
fof(f4383,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[],[f30,f4173]) ).
fof(f4173,plain,
! [X0,X1] : null_class = restrict(null_class,X0,X1),
inference(resolution,[],[f4031,f3094]) ).
fof(f3094,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f3087,f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f3087,plain,
! [X0] : subclass(null_class,X0),
inference(subsumption_resolution,[],[f3081,f4]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f3081,plain,
! [X0] :
( ~ subclass(null_class,universal_class)
| subclass(null_class,X0) ),
inference(duplicate_literal_removal,[],[f3059]) ).
fof(f3059,plain,
! [X0] :
( ~ subclass(null_class,universal_class)
| subclass(null_class,X0)
| subclass(null_class,X0) ),
inference(resolution,[],[f160,f1011]) ).
fof(f1011,plain,
! [X0] :
( ~ member(not_subclass_element(null_class,X0),universal_class)
| subclass(null_class,X0) ),
inference(forward_demodulation,[],[f986,f970]) ).
fof(f970,plain,
null_class = complement(universal_class),
inference(resolution,[],[f967,f4]) ).
fof(f967,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(duplicate_literal_removal,[],[f950]) ).
fof(f950,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class ),
inference(resolution,[],[f159,f120]) ).
fof(f120,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[],[f66,f24]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f66,axiom,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f159,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 ),
inference(resolution,[],[f1,f66]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f986,plain,
! [X0] :
( ~ member(not_subclass_element(null_class,X0),universal_class)
| subclass(complement(universal_class),X0) ),
inference(superposition,[],[f121,f970]) ).
fof(f121,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) ),
inference(resolution,[],[f2,f24]) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f160,plain,
! [X2,X0,X1] :
( member(not_subclass_element(X0,X2),X1)
| ~ subclass(X0,X1)
| subclass(X0,X2) ),
inference(resolution,[],[f1,f2]) ).
fof(f4031,plain,
! [X2,X0,X1] : subclass(restrict(X0,X1,X2),X0),
inference(superposition,[],[f3999,f28]) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
fof(f3999,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f3961]) ).
fof(f3961,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f128,f3]) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f128,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f21,f2]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f30,axiom,
! [X0,X4] :
( restrict(X0,singleton(X4),universal_class) != null_class
| ~ member(X4,domain_of(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f4450,plain,
! [X0] :
( ~ member(X0,null_class)
| member(X0,domain_of(null_class)) ),
inference(superposition,[],[f1038,f4397]) ).
fof(f4397,plain,
null_class = cantor(null_class),
inference(resolution,[],[f4385,f1128]) ).
fof(f1128,plain,
! [X0] :
( member(regular(cantor(X0)),domain_of(X0))
| null_class = cantor(X0) ),
inference(resolution,[],[f1038,f66]) ).
fof(f1038,plain,
! [X0,X1] :
( ~ member(X1,cantor(X0))
| member(X1,domain_of(X0)) ),
inference(superposition,[],[f21,f77]) ).
fof(f77,axiom,
! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cantor_class) ).
fof(f6914,plain,
( member(universal_class,null_class)
| ~ member(universal_class,universal_class) ),
inference(superposition,[],[f124,f6898]) ).
fof(f6898,plain,
null_class = singleton(universal_class),
inference(subsumption_resolution,[],[f6897,f4]) ).
fof(f6897,plain,
( null_class = singleton(universal_class)
| ~ subclass(universal_class,universal_class) ),
inference(duplicate_literal_removal,[],[f6889]) ).
fof(f6889,plain,
( null_class = singleton(universal_class)
| ~ subclass(universal_class,universal_class)
| null_class = singleton(universal_class) ),
inference(resolution,[],[f6121,f785]) ).
fof(f785,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f784]) ).
fof(f784,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f66,f775]) ).
fof(f775,plain,
! [X0] :
( regular(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[],[f767,f66]) ).
fof(f767,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f766]) ).
fof(f766,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f8,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f6121,plain,
! [X0] :
( ~ member(universal_class,singleton(X0))
| singleton(X0) = null_class
| ~ subclass(universal_class,X0) ),
inference(duplicate_literal_removal,[],[f6120]) ).
fof(f6120,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| singleton(X0) = null_class
| ~ member(universal_class,singleton(X0))
| singleton(X0) = null_class ),
inference(superposition,[],[f6030,f775]) ).
fof(f6030,plain,
! [X0] :
( ~ subclass(universal_class,regular(X0))
| null_class = X0
| ~ member(universal_class,X0) ),
inference(resolution,[],[f5877,f398]) ).
fof(f398,plain,
! [X0] :
( member(universal_class,X0)
| ~ subclass(universal_class,X0) ),
inference(resolution,[],[f396,f1]) ).
fof(f5877,plain,
! [X0,X1] :
( ~ member(X1,regular(X0))
| ~ member(X1,X0)
| null_class = X0 ),
inference(subsumption_resolution,[],[f846,f4451]) ).
fof(f846,plain,
! [X0,X1] :
( member(X1,null_class)
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| null_class = X0 ),
inference(superposition,[],[f23,f67]) ).
fof(f67,axiom,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f23,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X1)
| ~ member(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f124,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f9,f12]) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET505-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32 % Computer : n012.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue Apr 30 00:55:41 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.16/0.32 % (1299)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.35 % (1301)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.35 % (1306)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)
% 0.16/0.35 % (1303)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.35 % (1304)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)
% 0.16/0.36 % (1305)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)
% 0.16/0.36 % (1302)WARNING: value z3 for option sas not known
% 0.16/0.37 % (1302)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)
% 0.16/0.39 % (1300)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.49 TRYING [1]
% 0.16/0.50 TRYING [2]
% 1.10/0.62 TRYING [3]
% 1.64/0.74 TRYING [1]
% 1.64/0.75 TRYING [2]
% 1.90/0.79 % (1302)First to succeed.
% 1.90/0.79 % (1302)Refutation found. Thanks to Tanya!
% 1.90/0.79 % SZS status Unsatisfiable for theBenchmark
% 1.90/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 1.90/0.79 % (1302)------------------------------
% 1.90/0.79 % (1302)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.90/0.79 % (1302)Termination reason: Refutation
% 1.90/0.79
% 1.90/0.79 % (1302)Memory used [KB]: 4531
% 1.90/0.79 % (1302)Time elapsed: 0.430 s
% 1.90/0.79 % (1302)Instructions burned: 629 (million)
% 1.90/0.79 % (1302)------------------------------
% 1.90/0.79 % (1302)------------------------------
% 1.90/0.79 % (1299)Success in time 0.462 s
%------------------------------------------------------------------------------