TSTP Solution File: SET138-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET138-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 05:24:25 EDT 2022
% Result : Unsatisfiable 21.42s 21.69s
% Output : Refutation 21.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 10 unt; 5 nHn; 18 RR)
% Number of literals : 27 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(union(singleton(u),v),set_builder(u,v)),
file('SET138-6.p',unknown),
[] ).
cnf(2,axiom,
member(u__dfg,universal_class),
file('SET138-6.p',unknown),
[] ).
cnf(5,axiom,
~ member(u__dfg,set_builder(u__dfg,set_builder(v__dfg,set_builder(w__dfg,null_class)))),
file('SET138-6.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET138-6.p',unknown),
[] ).
cnf(17,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET138-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET138-6.p',unknown),
[] ).
cnf(29,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET138-6.p',unknown),
[] ).
cnf(30,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET138-6.p',unknown),
[] ).
cnf(31,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET138-6.p',unknown),
[] ).
cnf(131,plain,
( member(u__dfg,u)
| member(u__dfg,complement(u)) ),
inference(res,[status(thm),theory(equality)],[2,30]),
[iquote('0:Res:2.0,30.0')] ).
cnf(132,plain,
member(u__dfg,unordered_pair(u__dfg,u)),
inference(res,[status(thm),theory(equality)],[2,14]),
[iquote('0:Res:2.0,14.0')] ).
cnf(201,plain,
member(u__dfg,singleton(u__dfg)),
inference(spr,[status(thm),theory(equality)],[17,132]),
[iquote('0:SpR:17.0,132.0')] ).
cnf(383,plain,
( member(u__dfg,intersection(complement(u),complement(v)))
| member(u__dfg,union(u,v)) ),
inference(spr,[status(thm),theory(equality)],[31,131]),
[iquote('0:SpR:31.0,131.1')] ).
cnf(18928,plain,
( member(u__dfg,union(u,v))
| member(u__dfg,complement(u)) ),
inference(res,[status(thm),theory(equality)],[383,26]),
[iquote('0:Res:383.0,26.0')] ).
cnf(19028,plain,
( member(u__dfg,set_builder(u,v))
| member(u__dfg,complement(singleton(u))) ),
inference(spr,[status(thm),theory(equality)],[1,18928]),
[iquote('0:SpR:1.0,18928.0')] ).
cnf(43209,plain,
member(u__dfg,complement(singleton(u__dfg))),
inference(res,[status(thm),theory(equality)],[19028,5]),
[iquote('0:Res:19028.0,5.0')] ).
cnf(43216,plain,
~ member(u__dfg,singleton(u__dfg)),
inference(res,[status(thm),theory(equality)],[43209,29]),
[iquote('0:Res:43209.0,29.1')] ).
cnf(43217,plain,
$false,
inference(mrr,[status(thm)],[43216,201]),
[iquote('0:MRR:43216.0,201.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET138-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 03:50:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 21.42/21.69
% 21.42/21.69 SPASS V 3.9
% 21.42/21.69 SPASS beiseite: Proof found.
% 21.42/21.69 % SZS status Theorem
% 21.42/21.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.42/21.69 SPASS derived 33390 clauses, backtracked 5550 clauses, performed 27 splits and kept 18371 clauses.
% 21.42/21.69 SPASS allocated 104527 KBytes.
% 21.42/21.69 SPASS spent 0:0:21.03 on the problem.
% 21.42/21.69 0:00:00.04 for the input.
% 21.42/21.69 0:00:00.00 for the FLOTTER CNF translation.
% 21.42/21.69 0:00:00.39 for inferences.
% 21.42/21.69 0:00:01.46 for the backtracking.
% 21.42/21.69 0:0:18.77 for the reduction.
% 21.42/21.69
% 21.42/21.69
% 21.42/21.69 Here is a proof with depth 6, length 18 :
% 21.42/21.69 % SZS output start Refutation
% See solution above
% 21.42/21.69 Formulae used in the proof : definition_of_set_builder prove_member_of_triple_kludge2_1 prove_member_of_triple_kludge2_4 unordered_pair2 singleton_set intersection1 complement1 complement2 union
% 21.42/21.69
%------------------------------------------------------------------------------