TSTP Solution File: SET083-7 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET083-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 05:23:46 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% 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 : 11 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(31,axiom,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
file('SET083-7.p',unknown),
[] ).
cnf(34,axiom,
( ~ member(u,singleton(v))
| equal(u,v) ),
file('SET083-7.p',unknown),
[] ).
cnf(36,axiom,
equal(singleton(y__dfg),singleton(x__dfg)),
file('SET083-7.p',unknown),
[] ).
cnf(37,axiom,
member(x__dfg,universal_class),
file('SET083-7.p',unknown),
[] ).
cnf(38,axiom,
~ equal(y__dfg,x__dfg),
file('SET083-7.p',unknown),
[] ).
cnf(141,plain,
member(x__dfg,singleton(x__dfg)),
inference(res,[status(thm),theory(equality)],[37,31]),
[iquote('0:Res:37.0,31.0')] ).
cnf(167,plain,
~ member(x__dfg,singleton(y__dfg)),
inference(res,[status(thm),theory(equality)],[34,38]),
[iquote('0:Res:34.1,38.0')] ).
cnf(174,plain,
~ member(x__dfg,singleton(x__dfg)),
inference(rew,[status(thm),theory(equality)],[36,167]),
[iquote('0:Rew:36.0,167.0')] ).
cnf(175,plain,
$false,
inference(mrr,[status(thm)],[174,141]),
[iquote('0:MRR:174.0,141.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET083-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 : Sun Jul 10 16:46:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 41 clauses, backtracked 0 clauses, performed 0 splits and kept 134 clauses.
% 0.18/0.42 SPASS allocated 75805 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.42 0:00:00.04 for the input.
% 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.01 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 1, length 9 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : set_in_its_singleton only_member_in_singleton prove_singleton_identified_by_element1_1 prove_singleton_identified_by_element1_2 prove_singleton_identified_by_element1_3
% 0.18/0.42
%------------------------------------------------------------------------------