TSTP Solution File: SET149-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET149-6 : 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 05:24:32 EDT 2022
% Result : Unsatisfiable 10.14s 10.33s
% Output : Refutation 10.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 19 ( 5 unt; 6 nHn; 19 RR)
% Number of literals : 37 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(intersection(x__dfg,intersection(x__dfg,y__dfg)),intersection(x__dfg,y__dfg)),
file('SET149-6.p',unknown),
[] ).
cnf(3,axiom,
( subclass(u,v)
| member(not_subclass_element(u,v),u) ),
file('SET149-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(not_subclass_element(u,v),v)
| subclass(u,v) ),
file('SET149-6.p',unknown),
[] ).
cnf(8,axiom,
( ~ subclass(u,v)
| ~ subclass(v,u)
| equal(v,u) ),
file('SET149-6.p',unknown),
[] ).
cnf(22,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET149-6.p',unknown),
[] ).
cnf(23,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET149-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET149-6.p',unknown),
[] ).
cnf(120,plain,
( ~ subclass(intersection(x__dfg,y__dfg),intersection(x__dfg,intersection(x__dfg,y__dfg)))
| ~ subclass(intersection(x__dfg,intersection(x__dfg,y__dfg)),intersection(x__dfg,y__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(174,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(779,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(2757,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(2760,plain,
subclass(intersection(u,v),v),
inference(obv,[status(thm),theory(equality)],[2757]),
[iquote('0:Obv:2757.0')] ).
cnf(2761,plain,
~ subclass(intersection(x__dfg,y__dfg),intersection(x__dfg,intersection(x__dfg,y__dfg))),
inference(mrr,[status(thm)],[120,2760]),
[iquote('0:MRR:120.1,2760.0')] ).
cnf(11072,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)],[3,779]),
[iquote('0:Res:3.1,779.0')] ).
cnf(11089,plain,
( ~ member(not_subclass_element(u,intersection(v,u)),v)
| subclass(u,intersection(v,u)) ),
inference(obv,[status(thm),theory(equality)],[11072]),
[iquote('0:Obv:11072.1')] ).
cnf(24095,plain,
( subclass(intersection(u,v),intersection(u,intersection(u,v)))
| subclass(intersection(u,v),intersection(u,intersection(u,v))) ),
inference(res,[status(thm),theory(equality)],[174,11089]),
[iquote('0:Res:174.1,11089.0')] ).
cnf(24146,plain,
subclass(intersection(u,v),intersection(u,intersection(u,v))),
inference(obv,[status(thm),theory(equality)],[24095]),
[iquote('0:Obv:24095.0')] ).
cnf(24147,plain,
$false,
inference(unc,[status(thm)],[24146,2761]),
[iquote('0:UnC:24146.0,2761.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET149-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 9 18:51:17 EDT 2022
% 0.14/0.34 % CPUTime :
% 10.14/10.33
% 10.14/10.33 SPASS V 3.9
% 10.14/10.33 SPASS beiseite: Proof found.
% 10.14/10.33 % SZS status Theorem
% 10.14/10.33 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.14/10.33 SPASS derived 18819 clauses, backtracked 208 clauses, performed 5 splits and kept 8545 clauses.
% 10.14/10.33 SPASS allocated 97302 KBytes.
% 10.14/10.33 SPASS spent 0:00:09.78 on the problem.
% 10.14/10.33 0:00:00.04 for the input.
% 10.14/10.33 0:00:00.00 for the FLOTTER CNF translation.
% 10.14/10.33 0:00:00.23 for inferences.
% 10.14/10.33 0:00:00.82 for the backtracking.
% 10.14/10.33 0:00:08.50 for the reduction.
% 10.14/10.33
% 10.14/10.33
% 10.14/10.33 Here is a proof with depth 3, length 19 :
% 10.14/10.33 % SZS output start Refutation
% See solution above
% 10.14/10.33 Formulae used in the proof : prove_corollary_to_idempotency_of_intersection_1 not_subclass_members1 not_subclass_members2 subclass_implies_equal intersection1 intersection2 intersection3
% 10.14/10.33
%------------------------------------------------------------------------------