TSTP Solution File: SET454-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET454-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 : 600s
% DateTime : Tue Jul 19 05:26:23 EDT 2022
% Result : Unsatisfiable 277.26s 277.42s
% Output : Refutation 277.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 16 unt; 12 nHn; 41 RR)
% Number of literals : 74 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
file('SET454-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET454-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET454-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET454-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET454-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET454-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET454-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET454-6.p',unknown),
[] ).
cnf(29,axiom,
equal(intersection(u,cross_product(v,w)),restrict(u,v,w)),
file('SET454-6.p',unknown),
[] ).
cnf(30,axiom,
equal(intersection(cross_product(u,v),w),restrict(w,u,v)),
file('SET454-6.p',unknown),
[] ).
cnf(75,axiom,
equal(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),subset_relation),
file('SET454-6.p',unknown),
[] ).
cnf(76,axiom,
equal(intersection(inverse(subset_relation),subset_relation),identity_relation),
file('SET454-6.p',unknown),
[] ).
cnf(115,plain,
equal(restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class),subset_relation),
inference(rew,[status(thm),theory(equality)],[30,75]),
[iquote('0:Rew:30.0,75.0,30.0,75.0')] ).
cnf(165,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),v) ),
inference(res,[status(thm),theory(equality)],[3,23]),
[iquote('0:Res:3.1,23.0')] ).
cnf(172,plain,
( subclass(intersection(u,v),w)
| member(not_subclass_element(intersection(u,v),w),u) ),
inference(res,[status(thm),theory(equality)],[3,22]),
[iquote('0:Res:3.1,22.0')] ).
cnf(1305,plain,
( ~ member(not_subclass_element(u,intersection(v,w)),w)
| ~ member(not_subclass_element(u,intersection(v,w)),v)
| subclass(u,intersection(v,w)) ),
inference(res,[status(thm),theory(equality)],[24,4]),
[iquote('0:Res:24.2,4.0')] ).
cnf(3606,plain,
( subclass(intersection(inverse(subset_relation),subset_relation),u)
| member(not_subclass_element(identity_relation,u),subset_relation) ),
inference(spr,[status(thm),theory(equality)],[76,165]),
[iquote('0:SpR:76.0,165.1')] ).
cnf(3618,plain,
( ~ subclass(u,v)
| subclass(intersection(w,u),x)
| member(not_subclass_element(intersection(w,u),x),v) ),
inference(res,[status(thm),theory(equality)],[165,2]),
[iquote('0:Res:165.1,2.0')] ).
cnf(3633,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[165,4]),
[iquote('0:Res:165.1,4.0')] ).
cnf(3636,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[3633]),
[iquote('0:Obv:3633.0')] ).
cnf(3638,plain,
( subclass(identity_relation,u)
| member(not_subclass_element(identity_relation,u),subset_relation) ),
inference(rew,[status(thm),theory(equality)],[76,3606]),
[iquote('0:Rew:76.0,3606.0')] ).
cnf(3653,plain,
subclass(restrict(u,v,w),cross_product(v,w)),
inference(spr,[status(thm),theory(equality)],[29,3636]),
[iquote('0:SpR:29.0,3636.0')] ).
cnf(5043,plain,
subclass(subset_relation,cross_product(universal_class,universal_class)),
inference(spr,[status(thm),theory(equality)],[115,3653]),
[iquote('0:SpR:115.0,3653.0')] ).
cnf(11367,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u))
| subclass(u,intersection(v,u)) ),
inference(res,[status(thm),theory(equality)],[3,1305]),
[iquote('0:Res:3.1,1305.0')] ).
cnf(11368,plain,
( ~ member(not_subclass_element(intersection(u,v),intersection(w,u)),w)
| subclass(intersection(u,v),intersection(w,u))
| subclass(intersection(u,v),intersection(w,u)) ),
inference(res,[status(thm),theory(equality)],[172,1305]),
[iquote('0:Res:172.1,1305.0')] ).
cnf(11387,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u)) ),
inference(obv,[status(thm),theory(equality)],[11367]),
[iquote('0:Obv:11367.1')] ).
cnf(11393,plain,
( ~ member(not_subclass_element(intersection(u,v),intersection(w,u)),w)
| subclass(intersection(u,v),intersection(w,u)) ),
inference(obv,[status(thm),theory(equality)],[11368]),
[iquote('0:Obv:11368.1')] ).
cnf(19907,plain,
( subclass(identity_relation,intersection(subset_relation,identity_relation))
| subclass(identity_relation,intersection(subset_relation,identity_relation)) ),
inference(res,[status(thm),theory(equality)],[3638,11387]),
[iquote('0:Res:3638.1,11387.0')] ).
cnf(19913,plain,
subclass(identity_relation,intersection(subset_relation,identity_relation)),
inference(obv,[status(thm),theory(equality)],[19907]),
[iquote('0:Obv:19907.0')] ).
cnf(19958,plain,
( ~ subclass(intersection(subset_relation,identity_relation),identity_relation)
| equal(intersection(subset_relation,identity_relation),identity_relation) ),
inference(res,[status(thm),theory(equality)],[19913,8]),
[iquote('0:Res:19913.0,8.0')] ).
cnf(19967,plain,
equal(intersection(subset_relation,identity_relation),identity_relation),
inference(mrr,[status(thm)],[19958,3636]),
[iquote('0:MRR:19958.0,3636.0')] ).
cnf(62498,plain,
( ~ subclass(u,v)
| subclass(intersection(w,u),v)
| subclass(intersection(w,u),v) ),
inference(res,[status(thm),theory(equality)],[3618,4]),
[iquote('0:Res:3618.2,4.0')] ).
cnf(62516,plain,
( ~ subclass(u,v)
| subclass(intersection(w,u),v) ),
inference(obv,[status(thm),theory(equality)],[62498]),
[iquote('0:Obv:62498.1')] ).
cnf(81670,plain,
( subclass(intersection(u,v),intersection(v,u))
| subclass(intersection(u,v),intersection(v,u)) ),
inference(res,[status(thm),theory(equality)],[165,11393]),
[iquote('0:Res:165.1,11393.0')] ).
cnf(81684,plain,
subclass(intersection(u,v),intersection(v,u)),
inference(obv,[status(thm),theory(equality)],[81670]),
[iquote('0:Obv:81670.0')] ).
cnf(82098,plain,
( ~ subclass(intersection(u,v),intersection(v,u))
| equal(intersection(u,v),intersection(v,u)) ),
inference(res,[status(thm),theory(equality)],[81684,8]),
[iquote('0:Res:81684.0,8.0')] ).
cnf(83563,plain,
equal(intersection(u,v),intersection(v,u)),
inference(mrr,[status(thm)],[82098,81684]),
[iquote('0:MRR:82098.0,81684.0')] ).
cnf(83582,plain,
equal(intersection(identity_relation,subset_relation),identity_relation),
inference(rew,[status(thm),theory(equality)],[83563,19967]),
[iquote('0:Rew:83563.0,19967.0')] ).
cnf(152910,plain,
( ~ subclass(subset_relation,u)
| subclass(identity_relation,u) ),
inference(spr,[status(thm),theory(equality)],[83582,62516]),
[iquote('0:SpR:83582.0,62516.1')] ).
cnf(153007,plain,
subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(res,[status(thm),theory(equality)],[5043,152910]),
[iquote('0:Res:5043.0,152910.0')] ).
cnf(153014,plain,
$false,
inference(mrr,[status(thm)],[153007,1]),
[iquote('0:MRR:153007.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET454-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 17:35:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 277.26/277.42
% 277.26/277.42 SPASS V 3.9
% 277.26/277.42 SPASS beiseite: Proof found.
% 277.26/277.42 % SZS status Theorem
% 277.26/277.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 277.26/277.42 SPASS derived 109926 clauses, backtracked 2454 clauses, performed 13 splits and kept 39436 clauses.
% 277.26/277.42 SPASS allocated 204375 KBytes.
% 277.26/277.42 SPASS spent 0:4:32.13 on the problem.
% 277.26/277.42 0:00:00.04 for the input.
% 277.26/277.42 0:00:00.00 for the FLOTTER CNF translation.
% 277.26/277.42 0:00:01.60 for inferences.
% 277.26/277.42 0:0:12.36 for the backtracking.
% 277.26/277.42 0:4:15.85 for the reduction.
% 277.26/277.42
% 277.26/277.42
% 277.26/277.42 Here is a proof with depth 6, length 41 :
% 277.26/277.42 % SZS output start Refutation
% See solution above
% 277.26/277.42 Formulae used in the proof : prove_identity_alternate_defn1_1 subclass_members not_subclass_members1 not_subclass_members2 subclass_implies_equal intersection1 intersection2 intersection3 restriction1 restriction2 subset_relation identity_relation
% 277.26/277.42
%------------------------------------------------------------------------------