TSTP Solution File: SET891+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET891+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 05:29:37 EDT 2022
% Result : Theorem 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 6 RR)
% Number of literals : 6 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(unordered_pair(u,v),unordered_pair(v,u)),
file('SET891+1.p',unknown),
[] ).
cnf(8,axiom,
equal(union(unordered_pair(u,v)),set_union2(u,v)),
file('SET891+1.p',unknown),
[] ).
cnf(9,axiom,
equal(set_union2(singleton(u),singleton(v)),unordered_pair(u,v)),
file('SET891+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(union(unordered_pair(singleton(skc5),singleton(skc4))),unordered_pair(skc5,skc4)),
file('SET891+1.p',unknown),
[] ).
cnf(11,plain,
~ equal(unordered_pair(skc4,skc5),unordered_pair(skc4,skc5)),
inference(rew,[status(thm),theory(equality)],[9,10,8,4]),
[iquote('0:Rew:9.0,10.0,8.0,10.0,4.0,10.0,4.0,10.0')] ).
cnf(12,plain,
$false,
inference(obv,[status(thm),theory(equality)],[11]),
[iquote('0:Obv:11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET891+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 15:56:55 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 10 clauses.
% 0.18/0.42 SPASS allocated 85072 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.00 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 0, length 6 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : commutativity_k2_tarski l52_zfmisc_1 t41_enumset1 t32_zfmisc_1
% 0.18/0.42
%------------------------------------------------------------------------------