%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET025-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 05:22:47 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 9 RR)
% Number of literals : 12 ( 0 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ member(ordered_pair(x__dfg,y__dfg),universal_class),
file('SET025-6.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET025-6.p',unknown),
[] ).
cnf(5,axiom,
subclass(u,universal_class),
file('SET025-6.p',unknown),
[] ).
cnf(12,axiom,
member(unordered_pair(u,v),universal_class),
file('SET025-6.p',unknown),
[] ).
cnf(14,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('SET025-6.p',unknown),
[] ).
cnf(100,plain,
( ~ subclass(u,universal_class)
| ~ member(ordered_pair(x__dfg,y__dfg),u) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.2,1.0')] ).
cnf(102,plain,
~ member(ordered_pair(x__dfg,y__dfg),u),
inference(mrr,[status(thm)],[100,5]),
[iquote('0:MRR:100.0,5.0')] ).
cnf(216,plain,
member(ordered_pair(u,v),universal_class),
inference(spr,[status(thm),theory(equality)],[14,12]),
[iquote('0:SpR:14.0,12.0')] ).
cnf(221,plain,
$false,
inference(unc,[status(thm)],[216,102]),
[iquote('0:UnC:216.0,102.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET025-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 05:53:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 110 clauses, backtracked 0 clauses, performed 0 splits and kept 168 clauses.
% 0.19/0.44 SPASS allocated 75931 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.09 on the problem.
% 0.19/0.44 0:00:00.04 for the input.
% 0.19/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.02 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 1, length 9 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : prove_ordered_pair_is_set_1 subclass_members class_elements_are_sets unordered_pairs_in_universal ordered_pair
% 0.19/0.44
%------------------------------------------------------------------------------