TSTP Solution File: SET093-7 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET093-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 05:23:55 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 9 RR)
% Number of literals : 12 ( 0 equ; 6 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; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(29,axiom,
member(singleton(u),universal_class),
file('SET093-7.p',unknown),
[] ).
cnf(46,axiom,
equal(singleton(member_of(x__dfg)),x__dfg),
file('SET093-7.p',unknown),
[] ).
cnf(47,axiom,
~ member(x__dfg,universal_class),
file('SET093-7.p',unknown),
[] ).
cnf(48,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET093-7.p',unknown),
[] ).
cnf(51,axiom,
subclass(u,universal_class),
file('SET093-7.p',unknown),
[] ).
cnf(155,plain,
( ~ subclass(u,universal_class)
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[48,47]),
[iquote('0:Res:48.2,47.0')] ).
cnf(160,plain,
~ member(x__dfg,u),
inference(mrr,[status(thm)],[155,51]),
[iquote('0:MRR:155.0,51.0')] ).
cnf(163,plain,
member(x__dfg,universal_class),
inference(spr,[status(thm),theory(equality)],[46,29]),
[iquote('0:SpR:46.0,29.0')] ).
cnf(165,plain,
$false,
inference(mrr,[status(thm)],[163,160]),
[iquote('0:MRR:163.0,160.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET093-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 02:12:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 18 clauses, backtracked 0 clauses, performed 0 splits and kept 141 clauses.
% 0.19/0.43 SPASS allocated 75794 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.01 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 1, length 9 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : singletons_are_sets prove_corollary_2_to_singletons_are_sets_1 prove_corollary_2_to_singletons_are_sets_2 subclass_members class_elements_are_sets
% 0.19/0.43
%------------------------------------------------------------------------------