TSTP Solution File: SET084-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET084-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 05:23:47 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 10 unt; 1 nHn; 13 RR)
% Number of literals : 17 ( 0 equ; 6 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(singleton(y__dfg),singleton(x__dfg)),
file('SET084-6.p',unknown),
[] ).
cnf(2,axiom,
member(y__dfg,universal_class),
file('SET084-6.p',unknown),
[] ).
cnf(3,axiom,
~ equal(y__dfg,x__dfg),
file('SET084-6.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET084-6.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET084-6.p',unknown),
[] ).
cnf(15,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET084-6.p',unknown),
[] ).
cnf(101,plain,
member(y__dfg,unordered_pair(u,y__dfg)),
inference(res,[status(thm),theory(equality)],[2,13]),
[iquote('0:Res:2.0,13.0')] ).
cnf(114,plain,
( ~ member(y__dfg,unordered_pair(u,x__dfg))
| equal(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.2,3.0')] ).
cnf(127,plain,
~ member(y__dfg,unordered_pair(x__dfg,x__dfg)),
inference(res,[status(thm),theory(equality)],[114,3]),
[iquote('0:Res:114.1,3.0')] ).
cnf(131,plain,
~ member(y__dfg,singleton(x__dfg)),
inference(rew,[status(thm),theory(equality)],[15,127]),
[iquote('0:Rew:15.0,127.0')] ).
cnf(154,plain,
member(y__dfg,singleton(y__dfg)),
inference(spr,[status(thm),theory(equality)],[15,101]),
[iquote('0:SpR:15.0,101.0')] ).
cnf(159,plain,
member(y__dfg,singleton(x__dfg)),
inference(rew,[status(thm),theory(equality)],[1,154]),
[iquote('0:Rew:1.0,154.0')] ).
cnf(160,plain,
$false,
inference(mrr,[status(thm)],[159,131]),
[iquote('0:MRR:159.0,131.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET084-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 17:03:25 EDT 2022
% 0.12/0.34 % 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/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 SPASS derived 52 clauses, backtracked 0 clauses, performed 1 splits and kept 134 clauses.
% 0.20/0.44 SPASS allocated 75797 KBytes.
% 0.20/0.44 SPASS spent 0:00:00.08 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 2, length 13 :
% 0.20/0.44 % SZS output start Refutation
% See solution above
% 0.20/0.44 Formulae used in the proof : prove_singleton_identified_by_element2_1 prove_singleton_identified_by_element2_2 prove_singleton_identified_by_element2_3 unordered_pair_member unordered_pair3 singleton_set
% 0.20/0.44
%------------------------------------------------------------------------------