TSTP Solution File: SET979+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 05:30:11 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 9 RR)
% Number of literals : 11 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
equal(set_union2(singleton(u),singleton(v)),unordered_pair(u,v)),
file('SET979+1.p',unknown),
[] ).
cnf(9,axiom,
equal(cartesian_product2(set_union2(u,v),w),set_union2(cartesian_product2(u,w),cartesian_product2(v,w))),
file('SET979+1.p',unknown),
[] ).
cnf(10,axiom,
equal(cartesian_product2(u,set_union2(v,w)),set_union2(cartesian_product2(u,v),cartesian_product2(u,w))),
file('SET979+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ equal(cartesian_product2(skc11,unordered_pair(skc12,skc13)),set_union2(cartesian_product2(skc11,singleton(skc12)),cartesian_product2(skc11,singleton(skc13))))
| ~ equal(cartesian_product2(unordered_pair(skc8,skc9),skc10),set_union2(cartesian_product2(singleton(skc8),skc10),cartesian_product2(singleton(skc9),skc10))) ),
file('SET979+1.p',unknown),
[] ).
cnf(44,plain,
equal(cartesian_product2(unordered_pair(u,v),w),set_union2(cartesian_product2(singleton(u),w),cartesian_product2(singleton(v),w))),
inference(spr,[status(thm),theory(equality)],[8,9]),
[iquote('0:SpR:8.0,9.0')] ).
cnf(47,plain,
( ~ equal(cartesian_product2(skc11,unordered_pair(skc12,skc13)),set_union2(cartesian_product2(skc11,singleton(skc12)),cartesian_product2(skc11,singleton(skc13))))
| ~ equal(set_union2(cartesian_product2(singleton(skc8),skc10),cartesian_product2(singleton(skc9),skc10)),set_union2(cartesian_product2(singleton(skc8),skc10),cartesian_product2(singleton(skc9),skc10))) ),
inference(rew,[status(thm),theory(equality)],[44,11]),
[iquote('0:Rew:44.0,11.1')] ).
cnf(48,plain,
~ equal(cartesian_product2(skc11,unordered_pair(skc12,skc13)),set_union2(cartesian_product2(skc11,singleton(skc12)),cartesian_product2(skc11,singleton(skc13)))),
inference(obv,[status(thm),theory(equality)],[47]),
[iquote('0:Obv:47.1')] ).
cnf(60,plain,
equal(cartesian_product2(u,unordered_pair(v,w)),set_union2(cartesian_product2(u,singleton(v)),cartesian_product2(u,singleton(w)))),
inference(spr,[status(thm),theory(equality)],[8,10]),
[iquote('0:SpR:8.0,10.0')] ).
cnf(63,plain,
$false,
inference(unc,[status(thm)],[60,48]),
[iquote('0:UnC:60.0,48.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 9 20:33:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 44 clauses, backtracked 0 clauses, performed 0 splits and kept 18 clauses.
% 0.20/0.45 SPASS allocated 85127 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.45 0:00:00.04 for the input.
% 0.20/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.00 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 1, length 9 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : t41_enumset1 t120_zfmisc_1 t132_zfmisc_1
% 0.20/0.45
%------------------------------------------------------------------------------