TSTP Solution File: SET081-6 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET081-6 : 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 05:23:43 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 6 unt; 1 nHn; 8 RR)
% Number of literals : 11 ( 0 equ; 5 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(1,axiom,
member(y__dfg,singleton(x__dfg)),
file('SET081-6.p',unknown),
[] ).
cnf(2,axiom,
~ equal(x__dfg,y__dfg),
file('SET081-6.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET081-6.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(u,u),singleton(u)),
file('SET081-6.p',unknown),
[] ).
cnf(101,plain,
( ~ member(y__dfg,unordered_pair(u,x__dfg))
| equal(y__dfg,u) ),
inference(res,[status(thm),theory(equality)],[10,2]),
[iquote('0:Res:10.2,2.0')] ).
cnf(111,plain,
~ member(y__dfg,unordered_pair(x__dfg,x__dfg)),
inference(res,[status(thm),theory(equality)],[101,2]),
[iquote('0:Res:101.1,2.0')] ).
cnf(115,plain,
~ member(y__dfg,singleton(x__dfg)),
inference(rew,[status(thm),theory(equality)],[14,111]),
[iquote('0:Rew:14.0,111.0')] ).
cnf(116,plain,
$false,
inference(mrr,[status(thm)],[115,1]),
[iquote('0:MRR:115.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET081-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.12 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 09:07:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 11 clauses, backtracked 0 clauses, performed 0 splits and kept 100 clauses.
% 0.19/0.42 SPASS allocated 75745 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.04 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 2, length 8 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : prove_only_member_in_singleton_1 prove_only_member_in_singleton_2 unordered_pair_member singleton_set
% 0.19/0.42
%------------------------------------------------------------------------------