TSTP Solution File: SET131-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET131-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 05:24:23 EDT 2022
% Result : Unsatisfiable 8.30s 8.47s
% Output : Refutation 8.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 12 unt; 7 nHn; 23 RR)
% Number of literals : 35 ( 0 equ; 9 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('SET131-6.p',unknown),
[] ).
cnf(2,axiom,
member(u__dfg,universal_class),
file('SET131-6.p',unknown),
[] ).
cnf(3,axiom,
~ member(u__dfg,set_builder(x__dfg,set_builder(u__dfg,set_builder(z__dfg,null_class)))),
file('SET131-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(u,v)) ),
file('SET131-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET131-6.p',unknown),
[] ).
cnf(24,axiom,
( ~ member(u,intersection(v,w))
| member(u,v) ),
file('SET131-6.p',unknown),
[] ).
cnf(25,axiom,
( ~ member(u,intersection(v,w))
| member(u,w) ),
file('SET131-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET131-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET131-6.p',unknown),
[] ).
cnf(29,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET131-6.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(18714,plain,
( member(u__dfg,union(u,v))
| member(u__dfg,complement(v)) ),
inference(res,[status(thm),theory(equality)],[247,25]),
[iquote('0:Res:247.0,25.0')] ).
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(18866,plain,
( member(u__dfg,set_builder(u,v))
| member(u__dfg,complement(v)) ),
inference(spr,[status(thm),theory(equality)],[1,18714]),
[iquote('0:SpR:1.0,18714.0')] ).
cnf(21909,plain,
member(u__dfg,complement(set_builder(u__dfg,set_builder(z__dfg,null_class)))),
inference(res,[status(thm),theory(equality)],[18866,3]),
[iquote('0:Res:18866.0,3.0')] ).
cnf(23284,plain,
~ member(u__dfg,set_builder(u__dfg,set_builder(z__dfg,null_class))),
inference(res,[status(thm),theory(equality)],[21909,27]),
[iquote('0:Res:21909.0,27.1')] ).
cnf(23291,plain,
member(u__dfg,complement(singleton(u__dfg))),
inference(res,[status(thm),theory(equality)],[18729,23284]),
[iquote('0:Res:18729.0,23284.0')] ).
cnf(23298,plain,
~ member(u__dfg,singleton(u__dfg)),
inference(res,[status(thm),theory(equality)],[23291,27]),
[iquote('0:Res:23291.0,27.1')] ).
cnf(23299,plain,
$false,
inference(mrr,[status(thm)],[23298,145]),
[iquote('0:MRR:23298.0,145.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET131-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n010.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 : Mon Jul 11 06:18:45 EDT 2022
% 0.14/0.34 % CPUTime :
% 8.30/8.47
% 8.30/8.47 SPASS V 3.9
% 8.30/8.47 SPASS beiseite: Proof found.
% 8.30/8.47 % SZS status Theorem
% 8.30/8.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.30/8.47 SPASS derived 18955 clauses, backtracked 961 clauses, performed 9 splits and kept 9224 clauses.
% 8.30/8.47 SPASS allocated 94200 KBytes.
% 8.30/8.47 SPASS spent 0:00:07.96 on the problem.
% 8.30/8.47 0:00:00.04 for the input.
% 8.30/8.47 0:00:00.00 for the FLOTTER CNF translation.
% 8.30/8.47 0:00:00.22 for inferences.
% 8.30/8.47 0:00:00.71 for the backtracking.
% 8.30/8.47 0:00:06.80 for the reduction.
% 8.30/8.47
% 8.30/8.47
% 8.30/8.47 Here is a proof with depth 8, length 23 :
% 8.30/8.47 % SZS output start Refutation
% See solution above
% 8.30/8.47 Formulae used in the proof : definition_of_set_builder prove_member_of_triple2_1 prove_member_of_triple2_2 unordered_pair2 singleton_set intersection1 intersection2 complement1 complement2 union
% 8.30/8.47
%------------------------------------------------------------------------------