TSTP Solution File: SET622+3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET622+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 05:27:34 EDT 2022
% Result : Theorem 0.20s 0.58s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 17 ( 0 equ; 6 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 : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(union(u,v),union(v,u)),
file('SET622+3.p',unknown),
[] ).
cnf(5,axiom,
equal(intersection(u,v),intersection(v,u)),
file('SET622+3.p',unknown),
[] ).
cnf(6,axiom,
equal(symmetric_difference(u,v),symmetric_difference(v,u)),
file('SET622+3.p',unknown),
[] ).
cnf(15,axiom,
equal(intersection(intersection(u,v),w),intersection(u,intersection(v,w))),
file('SET622+3.p',unknown),
[] ).
cnf(16,axiom,
equal(difference(union(u,v),intersection(u,v)),symmetric_difference(u,v)),
file('SET622+3.p',unknown),
[] ).
cnf(24,axiom,
equal(union(difference(u,v),intersection(u,w)),difference(u,difference(v,w))),
file('SET622+3.p',unknown),
[] ).
cnf(28,axiom,
~ equal(union(difference(skc5,union(skc4,skc3)),intersection(intersection(skc5,skc4),skc3)),difference(skc5,symmetric_difference(skc4,skc3))),
file('SET622+3.p',unknown),
[] ).
cnf(29,plain,
~ equal(union(intersection(skc4,intersection(skc3,skc5)),difference(skc5,union(skc3,skc4))),difference(skc5,symmetric_difference(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[4,28,5,15,6]),
[iquote('0:Rew:4.0,28.0,4.0,28.0,5.0,28.0,15.0,28.0,5.0,28.0,6.0,28.0')] ).
cnf(87,plain,
equal(intersection(u,intersection(v,w)),intersection(v,intersection(w,u))),
inference(spr,[status(thm),theory(equality)],[15,5]),
[iquote('0:SpR:15.0,5.0')] ).
cnf(96,plain,
~ equal(union(intersection(skc3,intersection(skc5,skc4)),difference(skc5,union(skc3,skc4))),difference(skc5,symmetric_difference(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[87,29]),
[iquote('0:Rew:87.0,29.0')] ).
cnf(101,plain,
~ equal(union(intersection(skc3,intersection(skc4,skc5)),difference(skc5,union(skc3,skc4))),difference(skc5,symmetric_difference(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[5,96]),
[iquote('0:Rew:5.0,96.0')] ).
cnf(169,plain,
equal(intersection(u,intersection(v,w)),intersection(w,intersection(v,u))),
inference(spr,[status(thm),theory(equality)],[5,87]),
[iquote('0:SpR:5.0,87.0')] ).
cnf(267,plain,
equal(union(intersection(u,v),difference(u,w)),difference(u,difference(w,v))),
inference(spr,[status(thm),theory(equality)],[24,4]),
[iquote('0:SpR:24.0,4.0')] ).
cnf(1575,plain,
equal(union(intersection(u,intersection(v,w)),difference(w,x)),difference(w,difference(x,intersection(v,u)))),
inference(spr,[status(thm),theory(equality)],[169,267]),
[iquote('0:SpR:169.0,267.0')] ).
cnf(1590,plain,
~ equal(difference(skc5,difference(union(skc3,skc4),intersection(skc4,skc3))),difference(skc5,symmetric_difference(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[1575,101]),
[iquote('0:Rew:1575.0,101.0')] ).
cnf(1592,plain,
~ equal(difference(skc5,symmetric_difference(skc3,skc4)),difference(skc5,symmetric_difference(skc3,skc4))),
inference(rew,[status(thm),theory(equality)],[16,1590,5]),
[iquote('0:Rew:16.0,1590.0,5.0,1590.0')] ).
cnf(1593,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1592]),
[iquote('0:Obv:1592.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET622+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.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 00:26:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.58
% 0.20/0.58 SPASS V 3.9
% 0.20/0.58 SPASS beiseite: Proof found.
% 0.20/0.58 % SZS status Theorem
% 0.20/0.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.58 SPASS derived 1289 clauses, backtracked 0 clauses, performed 0 splits and kept 493 clauses.
% 0.20/0.58 SPASS allocated 86293 KBytes.
% 0.20/0.58 SPASS spent 0:00:00.23 on the problem.
% 0.20/0.58 0:00:00.03 for the input.
% 0.20/0.58 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.58 0:00:00.01 for inferences.
% 0.20/0.58 0:00:00.00 for the backtracking.
% 0.20/0.58 0:00:00.13 for the reduction.
% 0.20/0.58
% 0.20/0.58
% 0.20/0.58 Here is a proof with depth 3, length 17 :
% 0.20/0.58 % SZS output start Refutation
% See solution above
% 0.20/0.58 Formulae used in the proof : commutativity_of_union commutativity_of_intersection commutativity_of_symmetric_difference associativity_of_intersection symmetric_difference_and_difference difference_difference_union2 prove_th98
% 0.20/0.58
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