TSTP Solution File: SET085-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET085-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 10 unt; 1 nHn; 13 RR)
% Number of literals : 17 ( 0 equ; 7 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(unordered_pair(y__dfg,z__dfg),singleton(x__dfg)),
file('SET085-6.p',unknown),
[] ).
cnf(2,axiom,
member(x__dfg,universal_class),
file('SET085-6.p',unknown),
[] ).
cnf(3,axiom,
~ equal(x__dfg,y__dfg),
file('SET085-6.p',unknown),
[] ).
cnf(4,axiom,
~ equal(x__dfg,z__dfg),
file('SET085-6.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET085-6.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(u,universal_class)
| member(u,unordered_pair(v,u)) ),
file('SET085-6.p',unknown),
[] ).
cnf(16,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET085-6.p',unknown),
[] ).
cnf(102,plain,
member(x__dfg,unordered_pair(u,x__dfg)),
inference(res,[status(thm),theory(equality)],[2,14]),
[iquote('0:Res:2.0,14.0')] ).
cnf(115,plain,
( ~ member(x__dfg,unordered_pair(u,z__dfg))
| equal(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[12,4]),
[iquote('0:Res:12.2,4.0')] ).
cnf(135,plain,
~ member(x__dfg,unordered_pair(y__dfg,z__dfg)),
inference(res,[status(thm),theory(equality)],[115,3]),
[iquote('0:Res:115.1,3.0')] ).
cnf(147,plain,
~ member(x__dfg,singleton(x__dfg)),
inference(rew,[status(thm),theory(equality)],[1,135]),
[iquote('0:Rew:1.0,135.0')] ).
cnf(178,plain,
member(x__dfg,singleton(x__dfg)),
inference(spr,[status(thm),theory(equality)],[16,102]),
[iquote('0:SpR:16.0,102.0')] ).
cnf(182,plain,
$false,
inference(mrr,[status(thm)],[178,147]),
[iquote('0:MRR:178.0,147.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET085-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.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 11:17:38 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 70 clauses, backtracked 0 clauses, performed 1 splits and kept 148 clauses.
% 0.18/0.42 SPASS allocated 75814 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.08 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 2, length 13 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : prove_singleton_in_unordered_pair3_1 prove_singleton_in_unordered_pair3_2 prove_singleton_in_unordered_pair3_3 prove_singleton_in_unordered_pair3_4 unordered_pair_member unordered_pair3 singleton_set
% 0.18/0.43
%------------------------------------------------------------------------------