TSTP Solution File: SET130-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET130-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 05:24:22 EDT 2022
% Result : Unsatisfiable 8.45s 8.68s
% Output : Refutation 8.45s
% 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('SET130-6.p',unknown),
[] ).
cnf(2,axiom,
member(u__dfg,universal_class),
file('SET130-6.p',unknown),
[] ).
cnf(3,axiom,
~ member(u__dfg,set_builder(u__dfg,set_builder(y__dfg,set_builder(z__dfg,null_class)))),
file('SET130-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET130-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET130-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET130-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET130-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET130-6.p',unknown),
[] ).
cnf(29,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET130-6.p',unknown),
[] ).
cnf(99,plain,
( member(u__dfg,u)
| member(u__dfg,complement(u)) ),
inference(res,[status(thm),theory(equality)],[2,28]),
[iquote('0:Res:2.0,28.0')] ).
cnf(100,plain,
member(u__dfg,unordered_pair(u__dfg,u)),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(145,plain,
member(u__dfg,singleton(u__dfg)),
inference(spr,[status(thm),theory(equality)],[15,100]),
[iquote('0:SpR:15.0,100.0')] ).
cnf(247,plain,
( member(u__dfg,intersection(complement(u),complement(v)))
| member(u__dfg,union(u,v)) ),
inference(spr,[status(thm),theory(equality)],[29,99]),
[iquote('0:SpR:29.0,99.1')] ).
cnf(18713,plain,
( member(u__dfg,union(u,v))
| member(u__dfg,complement(u)) ),
inference(res,[status(thm),theory(equality)],[247,24]),
[iquote('0:Res:247.0,24.0')] ).
cnf(18729,plain,
( member(u__dfg,set_builder(u,v))
| member(u__dfg,complement(singleton(u))) ),
inference(spr,[status(thm),theory(equality)],[1,18713]),
[iquote('0:SpR:1.0,18713.0')] ).
cnf(21898,plain,
member(u__dfg,complement(singleton(u__dfg))),
inference(res,[status(thm),theory(equality)],[18729,3]),
[iquote('0:Res:18729.0,3.0')] ).
cnf(22187,plain,
~ member(u__dfg,singleton(u__dfg)),
inference(res,[status(thm),theory(equality)],[21898,27]),
[iquote('0:Res:21898.0,27.1')] ).
cnf(22188,plain,
$false,
inference(mrr,[status(thm)],[22187,145]),
[iquote('0:MRR:22187.0,145.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET130-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 05:25:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 8.45/8.68
% 8.45/8.68 SPASS V 3.9
% 8.45/8.68 SPASS beiseite: Proof found.
% 8.45/8.68 % SZS status Theorem
% 8.45/8.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.45/8.68 SPASS derived 18089 clauses, backtracked 961 clauses, performed 9 splits and kept 8863 clauses.
% 8.45/8.68 SPASS allocated 94072 KBytes.
% 8.45/8.68 SPASS spent 0:00:08.18 on the problem.
% 8.45/8.68 0:00:00.04 for the input.
% 8.45/8.68 0:00:00.00 for the FLOTTER CNF translation.
% 8.45/8.68 0:00:00.23 for inferences.
% 8.45/8.68 0:00:00.73 for the backtracking.
% 8.45/8.68 0:00:06.98 for the reduction.
% 8.45/8.68
% 8.45/8.68
% 8.45/8.68 Here is a proof with depth 6, length 18 :
% 8.45/8.68 % SZS output start Refutation
% See solution above
% 8.45/8.68 Formulae used in the proof : definition_of_set_builder prove_member_of_triple1_1 prove_member_of_triple1_2 unordered_pair2 singleton_set intersection1 complement1 complement2 union
% 8.45/8.68
%------------------------------------------------------------------------------