TSTP Solution File: SET091+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET091+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 05:23:52 EDT 2022
% Result : Theorem 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 5 unt; 2 nHn; 8 RR)
% Number of literals : 11 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
~ equal(member_of(skc3),skc3),
file('SET091+1.p',unknown),
[] ).
cnf(22,axiom,
( equal(member_of(u),u)
| member(member_of(u),universal_class) ),
file('SET091+1.p',unknown),
[] ).
cnf(37,axiom,
( ~ member(u,universal_class)
| ~ equal(singleton(u),skc3) ),
file('SET091+1.p',unknown),
[] ).
cnf(39,axiom,
( equal(member_of(u),u)
| equal(singleton(member_of(u)),u) ),
file('SET091+1.p',unknown),
[] ).
cnf(96,plain,
equal(singleton(member_of(skc3)),skc3),
inference(res,[status(thm),theory(equality)],[39,8]),
[iquote('0:Res:39.1,8.0')] ).
cnf(97,plain,
member(member_of(skc3),universal_class),
inference(res,[status(thm),theory(equality)],[22,8]),
[iquote('0:Res:22.1,8.0')] ).
cnf(111,plain,
~ member(member_of(skc3),universal_class),
inference(res,[status(thm),theory(equality)],[96,37]),
[iquote('0:Res:96.0,37.1')] ).
cnf(112,plain,
$false,
inference(mrr,[status(thm)],[111,97]),
[iquote('0:MRR:111.0,97.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET091+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 10 09:58:56 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.50
% 0.21/0.50 SPASS V 3.9
% 0.21/0.50 SPASS beiseite: Proof found.
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.50 SPASS derived 10 clauses, backtracked 0 clauses, performed 0 splits and kept 101 clauses.
% 0.21/0.50 SPASS allocated 98337 KBytes.
% 0.21/0.50 SPASS spent 0:00:00.13 on the problem.
% 0.21/0.50 0:00:00.04 for the input.
% 0.21/0.50 0:00:00.06 for the FLOTTER CNF translation.
% 0.21/0.50 0:00:00.00 for inferences.
% 0.21/0.50 0:00:00.00 for the backtracking.
% 0.21/0.50 0:00:00.01 for the reduction.
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 Here is a proof with depth 2, length 8 :
% 0.21/0.50 % SZS output start Refutation
% See solution above
% 0.21/0.50 Formulae used in the proof : member_when_not_a_singleton member_universal_self singleton_self
% 0.21/0.50
%------------------------------------------------------------------------------