TSTP Solution File: SET077-7 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET077-7 : 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 05:23:40 EDT 2022
% Result : Unsatisfiable 0.11s 0.32s
% Output : Refutation 0.11s
% 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(29,axiom,
~ member(singleton(x__dfg),universal_class),
file('SET077-7.p',unknown),
[] ).
cnf(30,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET077-7.p',unknown),
[] ).
cnf(33,axiom,
subclass(u,universal_class),
file('SET077-7.p',unknown),
[] ).
cnf(40,axiom,
member(unordered_pair(u,v),universal_class),
file('SET077-7.p',unknown),
[] ).
cnf(41,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET077-7.p',unknown),
[] ).
cnf(136,plain,
( ~ subclass(u,universal_class)
| ~ member(singleton(x__dfg),u) ),
inference(res,[status(thm),theory(equality)],[30,29]),
[iquote('0:Res:30.2,29.0')] ).
cnf(137,plain,
~ member(singleton(x__dfg),u),
inference(mrr,[status(thm)],[136,33]),
[iquote('0:MRR:136.0,33.0')] ).
cnf(141,plain,
member(singleton(u),universal_class),
inference(spr,[status(thm),theory(equality)],[41,40]),
[iquote('0:SpR:41.0,40.0')] ).
cnf(143,plain,
$false,
inference(unc,[status(thm)],[141,137]),
[iquote('0:UnC:141.0,137.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET077-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.08 % Command : run_spass %d %s
% 0.07/0.26 % Computer : n028.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Sun Jul 10 04:29:11 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.11/0.32
% 0.11/0.32 SPASS V 3.9
% 0.11/0.32 SPASS beiseite: Proof found.
% 0.11/0.32 % SZS status Theorem
% 0.11/0.32 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.32 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 122 clauses.
% 0.11/0.32 SPASS allocated 75769 KBytes.
% 0.11/0.32 SPASS spent 0:00:00.05 on the problem.
% 0.11/0.32 0:00:00.03 for the input.
% 0.11/0.32 0:00:00.00 for the FLOTTER CNF translation.
% 0.11/0.32 0:00:00.00 for inferences.
% 0.11/0.32 0:00:00.00 for the backtracking.
% 0.11/0.32 0:00:00.00 for the reduction.
% 0.11/0.32
% 0.11/0.32
% 0.11/0.32 Here is a proof with depth 1, length 9 :
% 0.11/0.32 % SZS output start Refutation
% See solution above
% 0.11/0.32 Formulae used in the proof : prove_singletons_are_sets_1 subclass_members class_elements_are_sets unordered_pairs_in_universal singleton_set
% 0.11/0.32
%------------------------------------------------------------------------------