%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET085-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 05:23:48 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 8 unt; 1 nHn; 11 RR)
% Number of literals : 15 ( 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(31,axiom,
( ~ member(u,universal_class)
| member(u,singleton(u)) ),
file('SET085-7.p',unknown),
[] ).
cnf(38,axiom,
equal(unordered_pair(y__dfg,z__dfg),singleton(x__dfg)),
file('SET085-7.p',unknown),
[] ).
cnf(39,axiom,
member(x__dfg,universal_class),
file('SET085-7.p',unknown),
[] ).
cnf(40,axiom,
~ equal(x__dfg,y__dfg),
file('SET085-7.p',unknown),
[] ).
cnf(41,axiom,
~ equal(x__dfg,z__dfg),
file('SET085-7.p',unknown),
[] ).
cnf(49,axiom,
( ~ member(u,unordered_pair(v,w))
| equal(u,w)
| equal(u,v) ),
file('SET085-7.p',unknown),
[] ).
cnf(144,plain,
member(x__dfg,singleton(x__dfg)),
inference(res,[status(thm),theory(equality)],[39,31]),
[iquote('0:Res:39.0,31.0')] ).
cnf(165,plain,
( ~ member(x__dfg,unordered_pair(u,z__dfg))
| equal(x__dfg,u) ),
inference(res,[status(thm),theory(equality)],[49,41]),
[iquote('0:Res:49.2,41.0')] ).
cnf(210,plain,
~ member(x__dfg,unordered_pair(y__dfg,z__dfg)),
inference(res,[status(thm),theory(equality)],[165,40]),
[iquote('0:Res:165.1,40.0')] ).
cnf(224,plain,
~ member(x__dfg,singleton(x__dfg)),
inference(rew,[status(thm),theory(equality)],[38,210]),
[iquote('0:Rew:38.0,210.0')] ).
cnf(225,plain,
$false,
inference(mrr,[status(thm)],[224,144]),
[iquote('0:MRR:224.0,144.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET085-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jul 10 06:51:25 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 82 clauses, backtracked 0 clauses, performed 0 splits and kept 183 clauses.
% 0.21/0.45 SPASS allocated 75844 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.08 on the problem.
% 0.21/0.45 0:00:00.04 for the input.
% 0.21/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.01 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 2, length 11 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : set_in_its_singleton 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
% 0.21/0.45
%------------------------------------------------------------------------------