TSTP Solution File: SET117+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET117+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 05:24:14 EDT 2022
% Result : Theorem 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 11 RR)
% Number of literals : 14 ( 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
subclass(u,universal_class),
file('SET117+1.p',unknown),
[] ).
cnf(5,axiom,
~ member(skc3,universal_class),
file('SET117+1.p',unknown),
[] ).
cnf(9,axiom,
member(unordered_pair(u,v),universal_class),
file('SET117+1.p',unknown),
[] ).
cnf(17,axiom,
equal(ordered_pair(first(skc3),second(skc3)),skc3),
file('SET117+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ member(u,v)
| ~ subclass(v,w)
| member(u,w) ),
file('SET117+1.p',unknown),
[] ).
cnf(57,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('SET117+1.p',unknown),
[] ).
cnf(107,plain,
( ~ subclass(u,universal_class)
| ~ member(skc3,u) ),
inference(res,[status(thm),theory(equality)],[55,5]),
[iquote('0:Res:55.2,5.0')] ).
cnf(117,plain,
~ member(skc3,u),
inference(mrr,[status(thm)],[107,3]),
[iquote('0:MRR:107.0,3.0')] ).
cnf(315,plain,
member(ordered_pair(u,v),universal_class),
inference(spr,[status(thm),theory(equality)],[57,9]),
[iquote('0:SpR:57.0,9.0')] ).
cnf(320,plain,
member(skc3,universal_class),
inference(spr,[status(thm),theory(equality)],[17,315]),
[iquote('0:SpR:17.0,315.0')] ).
cnf(322,plain,
$false,
inference(mrr,[status(thm)],[320,117]),
[iquote('0:MRR:320.0,117.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET117+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.12 % 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 05:34:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.50
% 0.18/0.50 SPASS V 3.9
% 0.18/0.50 SPASS beiseite: Proof found.
% 0.18/0.50 % SZS status Theorem
% 0.18/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.50 SPASS derived 220 clauses, backtracked 0 clauses, performed 0 splits and kept 252 clauses.
% 0.18/0.50 SPASS allocated 98227 KBytes.
% 0.18/0.50 SPASS spent 0:00:00.16 on the problem.
% 0.18/0.50 0:00:00.04 for the input.
% 0.18/0.50 0:00:00.05 for the FLOTTER CNF translation.
% 0.18/0.50 0:00:00.01 for inferences.
% 0.18/0.50 0:00:00.00 for the backtracking.
% 0.18/0.50 0:00:00.03 for the reduction.
% 0.18/0.50
% 0.18/0.50
% 0.18/0.50 Here is a proof with depth 2, length 11 :
% 0.18/0.50 % SZS output start Refutation
% See solution above
% 0.18/0.50 Formulae used in the proof : class_elements_are_sets corollary_1_to_ordered_pairs_are_sets unordered_pair subclass_defn ordered_pair_defn
% 0.18/0.50
%------------------------------------------------------------------------------