TSTP Solution File: SET166-6 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET166-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 05:24:41 EDT 2022
% Result : Unsatisfiable 35.64s 35.91s
% Output : Refutation 35.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of clauses : 19 ( 9 unt; 1 nHn; 19 RR)
% Number of literals : 33 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
member(x__dfg,union(y__dfg,z__dfg)),
file('SET166-6.p',unknown),
[] ).
cnf(2,axiom,
~ member(x__dfg,y__dfg),
file('SET166-6.p',unknown),
[] ).
cnf(3,axiom,
~ member(x__dfg,z__dfg),
file('SET166-6.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET166-6.p',unknown),
[] ).
cnf(7,axiom,
subclass(u,universal_class),
file('SET166-6.p',unknown),
[] ).
cnf(26,axiom,
( ~ member(u,v)
| ~ member(u,w)
| member(u,intersection(w,v)) ),
file('SET166-6.p',unknown),
[] ).
cnf(27,axiom,
( ~ member(u,v)
| ~ member(u,complement(v)) ),
file('SET166-6.p',unknown),
[] ).
cnf(28,axiom,
( ~ member(u,universal_class)
| member(u,v)
| member(u,complement(v)) ),
file('SET166-6.p',unknown),
[] ).
cnf(29,axiom,
equal(complement(intersection(complement(u),complement(v))),union(u,v)),
file('SET166-6.p',unknown),
[] ).
cnf(118,plain,
( ~ member(x__dfg,universal_class)
| member(x__dfg,complement(z__dfg)) ),
inference(res,[status(thm),theory(equality)],[28,3]),
[iquote('0:Res:28.2,3.0')] ).
cnf(125,plain,
( ~ member(x__dfg,universal_class)
| member(x__dfg,complement(y__dfg)) ),
inference(res,[status(thm),theory(equality)],[28,2]),
[iquote('0:Res:28.2,2.0')] ).
cnf(132,plain,
( ~ subclass(union(y__dfg,z__dfg),u)
| member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[1,4]),
[iquote('0:Res:1.0,4.1')] ).
cnf(169,plain,
member(x__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[7,132]),
[iquote('0:Res:7.0,132.0')] ).
cnf(172,plain,
member(x__dfg,complement(y__dfg)),
inference(mrr,[status(thm)],[125,169]),
[iquote('0:MRR:125.0,169.0')] ).
cnf(173,plain,
member(x__dfg,complement(z__dfg)),
inference(mrr,[status(thm)],[118,169]),
[iquote('0:MRR:118.0,169.0')] ).
cnf(284,plain,
( ~ member(u,intersection(complement(v),complement(w)))
| ~ member(u,union(v,w)) ),
inference(spl,[status(thm),theory(equality)],[29,27]),
[iquote('0:SpL:29.0,27.1')] ).
cnf(6800,plain,
( ~ member(u,complement(v))
| ~ member(u,complement(w))
| ~ member(u,union(w,v)) ),
inference(res,[status(thm),theory(equality)],[26,284]),
[iquote('0:Res:26.2,284.0')] ).
cnf(54987,plain,
( ~ member(x__dfg,complement(z__dfg))
| ~ member(x__dfg,complement(y__dfg)) ),
inference(res,[status(thm),theory(equality)],[1,6800]),
[iquote('0:Res:1.0,6800.2')] ).
cnf(55055,plain,
$false,
inference(mrr,[status(thm)],[54987,173,172]),
[iquote('0:MRR:54987.0,54987.1,173.0,172.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET166-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jul 11 07:36:28 EDT 2022
% 0.14/0.36 % CPUTime :
% 35.64/35.91
% 35.64/35.91 SPASS V 3.9
% 35.64/35.91 SPASS beiseite: Proof found.
% 35.64/35.91 % SZS status Theorem
% 35.64/35.91 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.64/35.91 SPASS derived 42812 clauses, backtracked 37 clauses, performed 7 splits and kept 16412 clauses.
% 35.64/35.91 SPASS allocated 121142 KBytes.
% 35.64/35.91 SPASS spent 0:0:34.96 on the problem.
% 35.64/35.91 0:00:00.04 for the input.
% 35.64/35.91 0:00:00.00 for the FLOTTER CNF translation.
% 35.64/35.91 0:00:00.53 for inferences.
% 35.64/35.91 0:00:02.06 for the backtracking.
% 35.64/35.91 0:0:31.82 for the reduction.
% 35.64/35.91
% 35.64/35.91
% 35.64/35.91 Here is a proof with depth 3, length 19 :
% 35.64/35.91 % SZS output start Refutation
% See solution above
% 35.64/35.91 Formulae used in the proof : prove_members_of_union1_1 prove_members_of_union1_2 prove_members_of_union1_3 subclass_members class_elements_are_sets intersection3 complement1 complement2 union
% 35.64/35.91
%------------------------------------------------------------------------------