TSTP Solution File: SET077-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET077-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 05:23:39 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% 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 : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ member(singleton(x__dfg),universal_class),
file('SET077-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET077-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET077-6.p',unknown),
[] ).
cnf(12,axiom,
member(unordered_pair(u,v),universal_class),
file('SET077-6.p',unknown),
[] ).
cnf(13,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET077-6.p',unknown),
[] ).
cnf(100,plain,
( ~ subclass(u,universal_class)
| ~ member(singleton(x__dfg),u) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.2,1.0')] ).
cnf(102,plain,
~ member(singleton(x__dfg),u),
inference(mrr,[status(thm)],[100,5]),
[iquote('0:MRR:100.0,5.0')] ).
cnf(105,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[13,12]),
[iquote('0:SpR:13.0,12.0')] ).
cnf(107,plain,
$false,
inference(unc,[status(thm)],[105,102]),
[iquote('0:UnC:105.0,102.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET077-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 11 07:26:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 95 clauses.
% 0.18/0.41 SPASS allocated 75743 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.41 0:00:00.04 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.01 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 1, length 9 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : prove_singletons_are_sets_1 subclass_members class_elements_are_sets unordered_pairs_in_universal singleton_set
% 0.18/0.41
%------------------------------------------------------------------------------