TSTP Solution File: SET082-7 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET082-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 05:23:45 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 4 unt; 4 nHn; 8 RR)
% Number of literals : 14 ( 0 equ; 2 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 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(20,axiom,
( member(u,universal_class)
| equal(unordered_pair(v,u),singleton(v)) ),
file('SET082-7.p',unknown),
[] ).
cnf(22,axiom,
( equal(unordered_pair(u,v),null_class)
| member(u,universal_class)
| member(v,universal_class) ),
file('SET082-7.p',unknown),
[] ).
cnf(35,axiom,
~ member(x__dfg,universal_class),
file('SET082-7.p',unknown),
[] ).
cnf(36,axiom,
~ equal(singleton(x__dfg),null_class),
file('SET082-7.p',unknown),
[] ).
cnf(128,plain,
( equal(singleton(u),null_class)
| member(u,universal_class)
| member(v,universal_class) ),
inference(rew,[status(thm),theory(equality)],[20,22]),
[iquote('0:Rew:20.1,22.0')] ).
cnf(129,plain,
( member(u,universal_class)
| equal(singleton(u),null_class) ),
inference(con,[status(thm)],[128]),
[iquote('0:Con:128.2')] ).
cnf(144,plain,
member(x__dfg,universal_class),
inference(res,[status(thm),theory(equality)],[129,36]),
[iquote('0:Res:129.0,36.0')] ).
cnf(168,plain,
$false,
inference(mrr,[status(thm)],[144,35]),
[iquote('0:MRR:144.0,35.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET082-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 04:41:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.44
% 0.20/0.44 SPASS V 3.9
% 0.20/0.44 SPASS beiseite: Proof found.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 19 clauses, backtracked 0 clauses, performed 0 splits and kept 125 clauses.
% 0.20/0.44 SPASS allocated 75779 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.07 on the problem.
% 0.20/0.44 0:00:00.04 for the input.
% 0.20/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44 0:00:00.00 for inferences.
% 0.20/0.44 0:00:00.00 for the backtracking.
% 0.20/0.44 0:00:00.01 for the reduction.
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 Here is a proof with depth 1, length 8 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : unordered_pair_equals_singleton1 null_unordered_pair prove_singleton_is_null_class_1 prove_singleton_is_null_class_2
% 0.20/0.44
%------------------------------------------------------------------------------