%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET093-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 05:23:54 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 11 RR)
% Number of literals : 14 ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(singleton(member_of(x__dfg)),x__dfg),
file('SET093-6.p',unknown),
[] ).
cnf(2,axiom,
~ member(x__dfg,universal_class),
file('SET093-6.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET093-6.p',unknown),
[] ).
cnf(6,axiom,
subclass(u,universal_class),
file('SET093-6.p',unknown),
[] ).
cnf(13,axiom,
member(unordered_pair(u,v),universal_class),
file('SET093-6.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET093-6.p',unknown),
[] ).
cnf(101,plain,
( ~ subclass(u,universal_class)
| ~ member(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[3,2]),
[iquote('0:Res:3.2,2.0')] ).
cnf(107,plain,
~ member(x__dfg,u),
inference(mrr,[status(thm)],[101,6]),
[iquote('0:MRR:101.0,6.0')] ).
cnf(111,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[14,13]),
[iquote('0:SpR:14.0,13.0')] ).
cnf(113,plain,
member(x__dfg,universal_class),
inference(spr,[status(thm),theory(equality)],[1,111]),
[iquote('0:SpR:1.0,111.0')] ).
cnf(114,plain,
$false,
inference(mrr,[status(thm)],[113,107]),
[iquote('0:MRR:113.0,107.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET093-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n003.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 : Sun Jul 10 15:25:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.42
% 0.20/0.42 SPASS V 3.9
% 0.20/0.42 SPASS beiseite: Proof found.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.42 SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 101 clauses.
% 0.20/0.42 SPASS allocated 75752 KBytes.
% 0.20/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.42 0:00:00.04 for the input.
% 0.20/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.42 0:00:00.00 for inferences.
% 0.20/0.42 0:00:00.00 for the backtracking.
% 0.20/0.42 0:00:00.01 for the reduction.
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42 Here is a proof with depth 2, length 11 :
% 0.20/0.42 % SZS output start Refutation
% See solution above
% 0.20/0.42 Formulae used in the proof : prove_corollary_2_to_singletons_are_sets_1 prove_corollary_2_to_singletons_are_sets_2 subclass_members class_elements_are_sets unordered_pairs_in_universal singleton_set
% 0.20/0.42
%------------------------------------------------------------------------------