TSTP Solution File: SET147-6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET147-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 05:24:30 EDT 2022
% Result : Unsatisfiable 11.25s 11.43s
% Output : Refutation 11.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 6 unt; 6 nHn; 23 RR)
% Number of literals : 48 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(intersection(universal_class,x__dfg),x__dfg),
file('SET147-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET147-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET147-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET147-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET147-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET147-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET147-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET147-6.p',unknown),
[] ).
cnf(117,plain,
( ~ subclass(x__dfg,intersection(universal_class,x__dfg))
| ~ subclass(intersection(universal_class,x__dfg),x__dfg) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.2,1.0')] ).
cnf(167,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(791,plain,
( ~ member(u,v)
| ~ member(u,w)
| ~ subclass(intersection(w,v),x)
| member(u,x) ),
inference(res,[status(thm),theory(equality)],[24,2]),
[iquote('0:Res:24.2,2.0')] ).
cnf(794,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(6499,plain,
( subclass(intersection(u,v),v)
| subclass(intersection(u,v),v) ),
inference(res,[status(thm),theory(equality)],[167,4]),
[iquote('0:Res:167.1,4.0')] ).
cnf(6501,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[6499]),
[iquote('0:Obv:6499.0')] ).
cnf(6502,plain,
~ subclass(x__dfg,intersection(universal_class,x__dfg)),
inference(mrr,[status(thm)],[117,6501]),
[iquote('0:MRR:117.1,6501.0')] ).
cnf(12453,plain,
( ~ member(u,v)
| ~ member(u,w)
| member(u,universal_class) ),
inference(res,[status(thm),theory(equality)],[5,791]),
[iquote('0:Res:5.0,791.2')] ).
cnf(12463,plain,
( ~ member(u,v)
| member(u,universal_class) ),
inference(con,[status(thm)],[12453]),
[iquote('0:Con:12453.1')] ).
cnf(12502,plain,
( subclass(u,v)
| member(not_subclass_element(u,v),universal_class) ),
inference(res,[status(thm),theory(equality)],[3,12463]),
[iquote('0:Res:3.1,12463.0')] ).
cnf(14593,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)],[3,794]),
[iquote('0:Res:3.1,794.0')] ).
cnf(14612,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u)) ),
inference(obv,[status(thm),theory(equality)],[14593]),
[iquote('0:Obv:14593.1')] ).
cnf(27803,plain,
( subclass(u,intersection(universal_class,u))
| subclass(u,intersection(universal_class,u)) ),
inference(res,[status(thm),theory(equality)],[12502,14612]),
[iquote('0:Res:12502.1,14612.0')] ).
cnf(27805,plain,
subclass(u,intersection(universal_class,u)),
inference(obv,[status(thm),theory(equality)],[27803]),
[iquote('0:Obv:27803.0')] ).
cnf(27806,plain,
$false,
inference(unc,[status(thm)],[27805,6502]),
[iquote('0:UnC:27805.0,6502.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET147-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 09:17:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 11.25/11.43
% 11.25/11.43 SPASS V 3.9
% 11.25/11.43 SPASS beiseite: Proof found.
% 11.25/11.43 % SZS status Theorem
% 11.25/11.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.25/11.43 SPASS derived 21669 clauses, backtracked 646 clauses, performed 7 splits and kept 9974 clauses.
% 11.25/11.43 SPASS allocated 99284 KBytes.
% 11.25/11.43 SPASS spent 0:0:10.86 on the problem.
% 11.25/11.43 0:00:00.04 for the input.
% 11.25/11.43 0:00:00.00 for the FLOTTER CNF translation.
% 11.25/11.43 0:00:00.26 for inferences.
% 11.25/11.43 0:00:01.03 for the backtracking.
% 11.25/11.43 0:00:09.33 for the reduction.
% 11.25/11.43
% 11.25/11.43
% 11.25/11.43 Here is a proof with depth 4, length 23 :
% 11.25/11.43 % SZS output start Refutation
% See solution above
% 11.25/11.43 Formulae used in the proof : prove_identity_for_intersection_1 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal intersection2 intersection3
% 11.25/11.43
%------------------------------------------------------------------------------