TSTP Solution File: KLE128+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE128+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 02:28:39 EDT 2022
% Result : Theorem 57.11s 57.31s
% Output : Refutation 58.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of clauses : 76 ( 71 unt; 0 nHn; 76 RR)
% Number of literals : 81 ( 0 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divergence(skc2),zero),
file('KLE128+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(domain__dfg(skc3),zero),
file('KLE128+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,zero),u),
file('KLE128+1.p',unknown),
[] ).
cnf(4,axiom,
equal(addition(u,u),u),
file('KLE128+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(u,one),u),
file('KLE128+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(one,u),u),
file('KLE128+1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(zero,u),zero),
file('KLE128+1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE128+1.p',unknown),
[] ).
cnf(10,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE128+1.p',unknown),
[] ).
cnf(11,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE128+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE128+1.p',unknown),
[] ).
cnf(15,axiom,
equal(forward_diamond(u,divergence(u)),divergence(u)),
file('KLE128+1.p',unknown),
[] ).
cnf(16,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE128+1.p',unknown),
[] ).
cnf(21,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE128+1.p',unknown),
[] ).
cnf(25,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE128+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE128+1.p',unknown),
[] ).
cnf(27,axiom,
equal(addition(domain__dfg(skc3),forward_diamond(skc2,domain__dfg(skc3))),forward_diamond(skc2,domain__dfg(skc3))),
file('KLE128+1.p',unknown),
[] ).
cnf(28,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE128+1.p',unknown),
[] ).
cnf(29,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE128+1.p',unknown),
[] ).
cnf(30,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE128+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ equal(addition(domain__dfg(u),addition(forward_diamond(v,domain__dfg(u)),domain__dfg(w))),addition(forward_diamond(v,domain__dfg(u)),domain__dfg(w)))
| equal(addition(domain__dfg(u),addition(divergence(v),forward_diamond(star(v),domain__dfg(w)))),addition(divergence(v),forward_diamond(star(v),domain__dfg(w)))) ),
file('KLE128+1.p',unknown),
[] ).
cnf(34,plain,
~ equal(antidomain(antidomain(skc3)),zero),
inference(rew,[status(thm),theory(equality)],[10,2]),
[iquote('0:Rew:10.0,2.0')] ).
cnf(36,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[14,16]),
[iquote('0:Rew:14.0,16.0')] ).
cnf(41,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(antidomain(v))))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[10,21]),
[iquote('0:Rew:10.0,21.0,10.0,21.0')] ).
cnf(43,plain,
equal(addition(antidomain(antidomain(skc3)),forward_diamond(skc2,antidomain(antidomain(skc3)))),forward_diamond(skc2,antidomain(antidomain(skc3)))),
inference(rew,[status(thm),theory(equality)],[10,27]),
[iquote('0:Rew:10.0,27.0')] ).
cnf(44,plain,
( ~ equal(addition(antidomain(antidomain(u)),addition(forward_diamond(v,antidomain(antidomain(u))),antidomain(antidomain(w)))),addition(forward_diamond(v,antidomain(antidomain(u))),antidomain(antidomain(w))))
| equal(addition(antidomain(antidomain(u)),addition(divergence(v),forward_diamond(star(v),antidomain(antidomain(w))))),addition(divergence(v),forward_diamond(star(v),antidomain(antidomain(w))))) ),
inference(rew,[status(thm),theory(equality)],[10,32]),
[iquote('0:Rew:10.0,32.1,10.0,32.1,10.0,32.0,10.0,32.0')] ).
cnf(60,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(74,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[14,3]),
[iquote('0:SpR:14.0,3.0')] ).
cnf(97,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[60,36]),
[iquote('0:SpR:60.0,36.0')] ).
cnf(99,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[74,97]),
[iquote('0:Rew:74.0,97.0')] ).
cnf(175,plain,
equal(forward_diamond(zero,u),antidomain(antidomain(zero))),
inference(spr,[status(thm),theory(equality)],[8,41]),
[iquote('0:SpR:8.0,41.0')] ).
cnf(179,plain,
equal(forward_diamond(zero,u),zero),
inference(rew,[status(thm),theory(equality)],[60,175,99]),
[iquote('0:Rew:60.0,175.0,99.0,175.0')] ).
cnf(197,plain,
equal(antidomain(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w)))))),forward_diamond(multiplication(u,v),w)),
inference(spr,[status(thm),theory(equality)],[26,41]),
[iquote('0:SpR:26.0,41.0')] ).
cnf(271,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[4,25]),
[iquote('0:SpR:4.0,25.0')] ).
cnf(335,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[36,271]),
[iquote('0:SpR:36.0,271.0')] ).
cnf(341,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[14,335]),
[iquote('0:Rew:14.0,335.0')] ).
cnf(379,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[36,29]),
[iquote('0:SpR:36.0,29.0')] ).
cnf(390,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[6,379]),
[iquote('0:Rew:6.0,379.0')] ).
cnf(438,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[36,28]),
[iquote('0:SpR:36.0,28.0')] ).
cnf(450,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[5,438]),
[iquote('0:Rew:5.0,438.0')] ).
cnf(527,plain,
equal(addition(antidomain(antidomain(skc3)),addition(forward_diamond(skc2,antidomain(antidomain(skc3))),u)),addition(forward_diamond(skc2,antidomain(antidomain(skc3))),u)),
inference(spr,[status(thm),theory(equality)],[43,25]),
[iquote('0:SpR:43.0,25.0')] ).
cnf(779,plain,
equal(addition(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w))))),antidomain(multiplication(u,forward_diamond(v,w)))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(spr,[status(thm),theory(equality)],[41,30]),
[iquote('0:SpR:41.0,30.0')] ).
cnf(788,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[9,30]),
[iquote('0:SpR:9.0,30.0')] ).
cnf(810,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[341,788,99]),
[iquote('0:Rew:341.0,788.0,99.0,788.0')] ).
cnf(815,plain,
equal(addition(antidomain(multiplication(u,forward_diamond(v,w))),antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w)))))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[14,779]),
[iquote('0:Rew:14.0,779.0')] ).
cnf(1235,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[810,9]),
[iquote('0:SpR:810.0,9.0')] ).
cnf(1278,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[6,1235]),
[iquote('0:Rew:6.0,1235.0')] ).
cnf(4214,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1278,390]),
[iquote('0:SpR:1278.0,390.0')] ).
cnf(4256,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[74,4214,14]),
[iquote('0:Rew:74.0,4214.0,14.0,4214.0')] ).
cnf(4676,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1278,450]),
[iquote('0:SpR:1278.0,450.0')] ).
cnf(4700,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[74,4676]),
[iquote('0:Rew:74.0,4676.0')] ).
cnf(4701,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4256,4700]),
[iquote('0:Rew:4256.0,4700.0')] ).
cnf(4792,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(v)))),forward_diamond(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[4701,41]),
[iquote('0:SpR:4701.0,41.0')] ).
cnf(4851,plain,
equal(antidomain(multiplication(u,antidomain(antidomain(v)))),antidomain(forward_diamond(u,v))),
inference(spr,[status(thm),theory(equality)],[41,4701]),
[iquote('0:SpR:41.0,4701.0')] ).
cnf(4888,plain,
equal(forward_diamond(u,antidomain(antidomain(v))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[4792,41]),
[iquote('0:Rew:4792.0,41.0')] ).
cnf(4891,plain,
( ~ equal(addition(antidomain(antidomain(u)),addition(forward_diamond(v,antidomain(antidomain(u))),antidomain(antidomain(w)))),addition(forward_diamond(v,antidomain(antidomain(u))),antidomain(antidomain(w))))
| equal(addition(antidomain(antidomain(u)),addition(divergence(v),forward_diamond(star(v),w))),addition(divergence(v),forward_diamond(star(v),w))) ),
inference(rew,[status(thm),theory(equality)],[4888,44]),
[iquote('0:Rew:4888.0,44.1')] ).
cnf(4914,plain,
equal(addition(antidomain(antidomain(skc3)),addition(forward_diamond(skc2,skc3),u)),addition(forward_diamond(skc2,skc3),u)),
inference(rew,[status(thm),theory(equality)],[4888,527]),
[iquote('0:Rew:4888.0,527.0')] ).
cnf(4930,plain,
equal(addition(antidomain(multiplication(u,v)),antidomain(forward_diamond(u,v))),antidomain(forward_diamond(u,v))),
inference(rew,[status(thm),theory(equality)],[4851,30]),
[iquote('0:Rew:4851.0,30.0')] ).
cnf(5027,plain,
equal(addition(antidomain(forward_diamond(u,v)),antidomain(multiplication(u,v))),antidomain(forward_diamond(u,v))),
inference(rew,[status(thm),theory(equality)],[14,4930]),
[iquote('0:Rew:14.0,4930.0')] ).
cnf(5045,plain,
( ~ equal(addition(antidomain(antidomain(u)),addition(forward_diamond(v,u),antidomain(antidomain(w)))),addition(forward_diamond(v,u),antidomain(antidomain(w))))
| equal(addition(antidomain(antidomain(u)),addition(divergence(v),forward_diamond(star(v),w))),addition(divergence(v),forward_diamond(star(v),w))) ),
inference(rew,[status(thm),theory(equality)],[4888,4891]),
[iquote('0:Rew:4888.0,4891.0')] ).
cnf(7349,plain,
( ~ equal(addition(forward_diamond(skc2,skc3),antidomain(antidomain(u))),addition(forward_diamond(skc2,skc3),antidomain(antidomain(u))))
| equal(addition(antidomain(antidomain(skc3)),addition(divergence(skc2),forward_diamond(star(skc2),u))),addition(divergence(skc2),forward_diamond(star(skc2),u))) ),
inference(spl,[status(thm),theory(equality)],[4914,5045]),
[iquote('0:SpL:4914.0,5045.0')] ).
cnf(7367,plain,
equal(addition(antidomain(antidomain(skc3)),addition(divergence(skc2),forward_diamond(star(skc2),u))),addition(divergence(skc2),forward_diamond(star(skc2),u))),
inference(obv,[status(thm),theory(equality)],[7349]),
[iquote('0:Obv:7349.0')] ).
cnf(7368,plain,
equal(addition(antidomain(antidomain(skc3)),forward_diamond(star(skc2),u)),forward_diamond(star(skc2),u)),
inference(rew,[status(thm),theory(equality)],[74,7367,1]),
[iquote('0:Rew:74.0,7367.0,1.0,7367.0')] ).
cnf(7858,plain,
equal(antidomain(multiplication(u,multiplication(v,antidomain(antidomain(w))))),antidomain(forward_diamond(multiplication(u,v),w))),
inference(spr,[status(thm),theory(equality)],[197,4701]),
[iquote('0:SpR:197.0,4701.0')] ).
cnf(7979,plain,
equal(addition(antidomain(multiplication(u,forward_diamond(v,w))),antidomain(forward_diamond(multiplication(u,v),w))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[7858,815]),
[iquote('0:Rew:7858.0,815.0')] ).
cnf(8029,plain,
equal(addition(antidomain(forward_diamond(multiplication(u,v),w)),antidomain(multiplication(u,forward_diamond(v,w)))),antidomain(multiplication(u,forward_diamond(v,w)))),
inference(rew,[status(thm),theory(equality)],[14,7979]),
[iquote('0:Rew:14.0,7979.0')] ).
cnf(14210,plain,
equal(addition(antidomain(forward_diamond(zero,u)),antidomain(multiplication(v,forward_diamond(coantidomain(v),u)))),antidomain(multiplication(v,forward_diamond(coantidomain(v),u)))),
inference(spr,[status(thm),theory(equality)],[11,8029]),
[iquote('0:SpR:11.0,8029.0')] ).
cnf(14284,plain,
equal(antidomain(multiplication(u,forward_diamond(coantidomain(u),v))),one),
inference(rew,[status(thm),theory(equality)],[341,14210,99,179]),
[iquote('0:Rew:341.0,14210.0,99.0,14210.0,179.0,14210.0')] ).
cnf(30371,plain,
equal(antidomain(multiplication(u,divergence(coantidomain(u)))),one),
inference(spr,[status(thm),theory(equality)],[15,14284]),
[iquote('0:SpR:15.0,14284.0')] ).
cnf(30870,plain,
equal(addition(antidomain(forward_diamond(u,divergence(coantidomain(u)))),one),antidomain(forward_diamond(u,divergence(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[30371,5027]),
[iquote('0:SpR:30371.0,5027.0')] ).
cnf(30987,plain,
equal(antidomain(forward_diamond(u,divergence(coantidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[341,30870,14]),
[iquote('0:Rew:341.0,30870.0,14.0,30870.0')] ).
cnf(31176,plain,
equal(multiplication(one,forward_diamond(u,divergence(coantidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[30987,9]),
[iquote('0:SpR:30987.0,9.0')] ).
cnf(31311,plain,
equal(forward_diamond(u,divergence(coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[6,31176]),
[iquote('0:Rew:6.0,31176.0')] ).
cnf(109899,plain,
equal(addition(antidomain(antidomain(skc3)),zero),zero),
inference(spr,[status(thm),theory(equality)],[31311,7368]),
[iquote('0:SpR:31311.0,7368.0')] ).
cnf(109954,plain,
equal(antidomain(antidomain(skc3)),zero),
inference(rew,[status(thm),theory(equality)],[74,109899,14]),
[iquote('0:Rew:74.0,109899.0,14.0,109899.0')] ).
cnf(109955,plain,
$false,
inference(mrr,[status(thm)],[109954,34]),
[iquote('0:MRR:109954.0,34.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : KLE128+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.15 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 13:11:02 EDT 2022
% 0.15/0.36 % CPUTime :
% 57.11/57.31
% 57.11/57.31 SPASS V 3.9
% 57.11/57.31 SPASS beiseite: Proof found.
% 57.11/57.31 % SZS status Theorem
% 57.11/57.31 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 57.11/57.31 SPASS derived 71105 clauses, backtracked 0 clauses, performed 0 splits and kept 10420 clauses.
% 57.11/57.31 SPASS allocated 172788 KBytes.
% 57.11/57.31 SPASS spent 0:0:56.82 on the problem.
% 57.11/57.31 0:00:00.03 for the input.
% 57.11/57.31 0:00:00.03 for the FLOTTER CNF translation.
% 57.11/57.31 0:00:00.48 for inferences.
% 57.11/57.31 0:00:00.00 for the backtracking.
% 57.11/57.31 0:0:56.06 for the reduction.
% 57.11/57.31
% 57.11/57.31
% 57.11/57.31 Here is a proof with depth 6, length 76 :
% 57.11/57.31 % SZS output start Refutation
% See solution above
% 58.57/58.77 Formulae used in the proof : goals additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity left_annihilation domain1 domain4 codomain1 additive_commutativity divergence1 domain3 forward_diamond additive_associativity multiplicative_associativity right_distributivity left_distributivity domain2 divergence2
% 58.57/58.77
%------------------------------------------------------------------------------