%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET102+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 05:24:03 EDT 2022
% Result : Theorem 2.34s 2.54s
% Output : Refutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 5 unt; 0 nHn; 8 RR)
% Number of literals : 13 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 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(8,axiom,
member(unordered_pair(u,v),universal_class),
file('SET102+1.p',unknown),
[] ).
cnf(35,axiom,
~ member(unordered_pair(skc5,singleton(skc4)),ordered_pair(skc5,skc4)),
file('SET102+1.p',unknown),
[] ).
cnf(56,axiom,
equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
file('SET102+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ equal(u,v)
| ~ member(u,universal_class)
| member(u,unordered_pair(w,v)) ),
file('SET102+1.p',unknown),
[] ).
cnf(917,plain,
( ~ equal(u,unordered_pair(v,singleton(w)))
| ~ member(u,universal_class)
| member(u,ordered_pair(v,w)) ),
inference(spr,[status(thm),theory(equality)],[56,71]),
[iquote('0:SpR:56.0,71.2')] ).
cnf(9713,plain,
( ~ equal(unordered_pair(skc5,singleton(skc4)),unordered_pair(skc5,singleton(skc4)))
| ~ member(unordered_pair(skc5,singleton(skc4)),universal_class) ),
inference(res,[status(thm),theory(equality)],[917,35]),
[iquote('0:Res:917.2,35.0')] ).
cnf(9722,plain,
~ member(unordered_pair(skc5,singleton(skc4)),universal_class),
inference(obv,[status(thm),theory(equality)],[9713]),
[iquote('0:Obv:9713.0')] ).
cnf(9723,plain,
$false,
inference(mrr,[status(thm)],[9722,8]),
[iquote('0:MRR:9722.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET102+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 : Sat Jul 9 19:23:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.34/2.54
% 2.34/2.54 SPASS V 3.9
% 2.34/2.54 SPASS beiseite: Proof found.
% 2.34/2.54 % SZS status Theorem
% 2.34/2.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.34/2.54 SPASS derived 8416 clauses, backtracked 126 clauses, performed 5 splits and kept 4038 clauses.
% 2.34/2.54 SPASS allocated 104628 KBytes.
% 2.34/2.54 SPASS spent 0:00:02.16 on the problem.
% 2.34/2.54 0:00:00.04 for the input.
% 2.34/2.54 0:00:00.06 for the FLOTTER CNF translation.
% 2.34/2.54 0:00:00.08 for inferences.
% 2.34/2.54 0:00:00.05 for the backtracking.
% 2.34/2.54 0:00:01.87 for the reduction.
% 2.34/2.54
% 2.34/2.54
% 2.34/2.54 Here is a proof with depth 2, length 8 :
% 2.34/2.54 % SZS output start Refutation
% See solution above
% 2.34/2.54 Formulae used in the proof : unordered_pair unordered_pair_member_of_ordered_pair ordered_pair_defn unordered_pair_defn
% 2.34/2.54
%------------------------------------------------------------------------------