TSTP Solution File: SET968+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:30:07 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 11 RR)
% Number of literals : 11 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(set_union2(u,v),set_union2(v,u)),
file('SET968+1.p',unknown),
[] ).
cnf(7,axiom,
equal(set_union2(set_union2(u,v),w),set_union2(u,set_union2(v,w))),
file('SET968+1.p',unknown),
[] ).
cnf(8,axiom,
equal(cartesian_product2(set_union2(u,v),w),set_union2(cartesian_product2(u,w),cartesian_product2(v,w))),
file('SET968+1.p',unknown),
[] ).
cnf(9,axiom,
equal(cartesian_product2(u,set_union2(v,w)),set_union2(cartesian_product2(u,v),cartesian_product2(u,w))),
file('SET968+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(cartesian_product2(set_union2(skc9,skc8),set_union2(skc7,skc6)),set_union2(set_union2(set_union2(cartesian_product2(skc9,skc7),cartesian_product2(skc9,skc6)),cartesian_product2(skc8,skc7)),cartesian_product2(skc8,skc6))),
file('SET968+1.p',unknown),
[] ).
cnf(11,plain,
~ equal(set_union2(cartesian_product2(skc9,skc6),set_union2(cartesian_product2(skc8,skc7),set_union2(cartesian_product2(skc8,skc6),cartesian_product2(skc9,skc7)))),set_union2(cartesian_product2(skc8,skc6),set_union2(cartesian_product2(skc8,skc7),set_union2(cartesian_product2(skc9,skc6),cartesian_product2(skc9,skc7))))),
inference(rew,[status(thm),theory(equality)],[7,10,9,8,4]),
[iquote('0:Rew:7.0,10.0,9.0,10.0,9.0,10.0,8.0,10.0,4.0,10.0,4.0,10.0,4.0,10.0,7.0,10.0,7.0,10.0,4.0,10.0,7.0,10.0,4.0,10.0')] ).
cnf(31,plain,
equal(set_union2(set_union2(u,v),w),set_union2(v,set_union2(u,w))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(35,plain,
equal(set_union2(u,set_union2(v,w)),set_union2(v,set_union2(u,w))),
inference(rew,[status(thm),theory(equality)],[7,31]),
[iquote('0:Rew:7.0,31.0')] ).
cnf(36,plain,
~ equal(set_union2(cartesian_product2(skc8,skc7),set_union2(cartesian_product2(skc9,skc6),set_union2(cartesian_product2(skc8,skc6),cartesian_product2(skc9,skc7)))),set_union2(cartesian_product2(skc8,skc6),set_union2(cartesian_product2(skc8,skc7),set_union2(cartesian_product2(skc9,skc6),cartesian_product2(skc9,skc7))))),
inference(rew,[status(thm),theory(equality)],[35,11]),
[iquote('0:Rew:35.0,11.0')] ).
cnf(39,plain,
~ equal(set_union2(cartesian_product2(skc8,skc6),set_union2(cartesian_product2(skc8,skc7),set_union2(cartesian_product2(skc9,skc6),cartesian_product2(skc9,skc7)))),set_union2(cartesian_product2(skc8,skc6),set_union2(cartesian_product2(skc8,skc7),set_union2(cartesian_product2(skc9,skc6),cartesian_product2(skc9,skc7))))),
inference(rew,[status(thm),theory(equality)],[35,36]),
[iquote('0:Rew:35.0,36.0,35.0,36.0')] ).
cnf(40,plain,
$false,
inference(obv,[status(thm),theory(equality)],[39]),
[iquote('0:Obv:39.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET968+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % 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 : Mon Jul 11 02:58:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 24 clauses, backtracked 0 clauses, performed 0 splits and kept 17 clauses.
% 0.18/0.43 SPASS allocated 85106 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 1, length 11 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : commutativity_k2_xboole_0 t4_xboole_1 t120_zfmisc_1 t121_zfmisc_1
% 0.18/0.43
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