TSTP Solution File: KLE131+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE131+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 0.77s 0.96s
% Output : Refutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 59 RR)
% Number of literals : 59 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(divergence(skc1),zero),
file('KLE131+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE131+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE131+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE131+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE131+1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiplication(u,zero),zero),
file('KLE131+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(zero,u),zero),
file('KLE131+1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE131+1.p',unknown),
[] ).
cnf(9,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE131+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE131+1.p',unknown),
[] ).
cnf(14,axiom,
equal(forward_diamond(u,divergence(u)),divergence(u)),
file('KLE131+1.p',unknown),
[] ).
cnf(15,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE131+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE131+1.p',unknown),
[] ).
cnf(20,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE131+1.p',unknown),
[] ).
cnf(24,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE131+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE131+1.p',unknown),
[] ).
cnf(27,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE131+1.p',unknown),
[] ).
cnf(28,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE131+1.p',unknown),
[] ).
cnf(30,axiom,
equal(addition(domain__dfg(u),forward_diamond(star(skc1),domain_difference(domain__dfg(u),forward_diamond(skc1,domain__dfg(u))))),forward_diamond(star(skc1),domain_difference(domain__dfg(u),forward_diamond(skc1,domain__dfg(u))))),
file('KLE131+1.p',unknown),
[] ).
cnf(34,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[13,15]),
[iquote('0:Rew:13.0,15.0')] ).
cnf(39,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(antidomain(v))))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[9,20]),
[iquote('0:Rew:9.0,20.0,9.0,20.0')] ).
cnf(40,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[9,19]),
[iquote('0:Rew:9.0,19.0')] ).
cnf(41,plain,
equal(addition(antidomain(antidomain(u)),forward_diamond(star(skc1),domain_difference(antidomain(antidomain(u)),forward_diamond(skc1,antidomain(antidomain(u)))))),forward_diamond(star(skc1),domain_difference(antidomain(antidomain(u)),forward_diamond(skc1,antidomain(antidomain(u)))))),
inference(rew,[status(thm),theory(equality)],[9,30]),
[iquote('0:Rew:9.0,30.0')] ).
cnf(57,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(69,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[13,2]),
[iquote('0:SpR:13.0,2.0')] ).
cnf(92,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[57,34]),
[iquote('0:SpR:57.0,34.0')] ).
cnf(94,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[69,92]),
[iquote('0:Rew:69.0,92.0')] ).
cnf(118,plain,
equal(domain_difference(u,u),zero),
inference(spr,[status(thm),theory(equality)],[40,8]),
[iquote('0:SpR:40.0,8.0')] ).
cnf(158,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(one)))),forward_diamond(u,zero)),
inference(spr,[status(thm),theory(equality)],[94,39]),
[iquote('0:SpR:94.0,39.0')] ).
cnf(165,plain,
equal(forward_diamond(u,zero),zero),
inference(rew,[status(thm),theory(equality)],[57,158,94,6]),
[iquote('0:Rew:57.0,158.0,94.0,158.0,6.0,158.0,57.0,158.0')] ).
cnf(249,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,24]),
[iquote('0:SpR:3.0,24.0')] ).
cnf(330,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[34,249]),
[iquote('0:SpR:34.0,249.0')] ).
cnf(336,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[13,330]),
[iquote('0:Rew:13.0,330.0')] ).
cnf(372,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[34,27]),
[iquote('0:SpR:34.0,27.0')] ).
cnf(383,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[5,372]),
[iquote('0:Rew:5.0,372.0')] ).
cnf(419,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[34,26]),
[iquote('0:SpR:34.0,26.0')] ).
cnf(431,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[4,419]),
[iquote('0:Rew:4.0,419.0')] ).
cnf(675,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)],[8,28]),
[iquote('0:SpR:8.0,28.0')] ).
cnf(697,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[336,675,94]),
[iquote('0:Rew:336.0,675.0,94.0,675.0')] ).
cnf(1220,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[697,8]),
[iquote('0:SpR:697.0,8.0')] ).
cnf(1264,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[5,1220]),
[iquote('0:Rew:5.0,1220.0')] ).
cnf(4137,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1264,383]),
[iquote('0:SpR:1264.0,383.0')] ).
cnf(4143,plain,
equal(addition(zero,multiplication(antidomain(antidomain(u)),u)),u),
inference(spr,[status(thm),theory(equality)],[8,383]),
[iquote('0:SpR:8.0,383.0')] ).
cnf(4160,plain,
equal(multiplication(antidomain(antidomain(u)),u),u),
inference(rew,[status(thm),theory(equality)],[69,4143]),
[iquote('0:Rew:69.0,4143.0')] ).
cnf(4178,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[69,4137,13]),
[iquote('0:Rew:69.0,4137.0,13.0,4137.0')] ).
cnf(4587,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1264,431]),
[iquote('0:SpR:1264.0,431.0')] ).
cnf(4610,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[69,4587]),
[iquote('0:Rew:69.0,4587.0')] ).
cnf(4611,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4178,4610]),
[iquote('0:Rew:4178.0,4610.0')] ).
cnf(4737,plain,
equal(multiplication(antidomain(u),antidomain(v)),domain_difference(antidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[4611,40]),
[iquote('0:SpR:4611.0,40.0')] ).
cnf(4748,plain,
equal(antidomain(antidomain(multiplication(u,antidomain(v)))),forward_diamond(u,antidomain(v))),
inference(spr,[status(thm),theory(equality)],[4611,39]),
[iquote('0:SpR:4611.0,39.0')] ).
cnf(4795,plain,
equal(domain_difference(antidomain(antidomain(u)),v),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[4737,40]),
[iquote('0:Rew:4737.0,40.0')] ).
cnf(4809,plain,
equal(addition(antidomain(antidomain(u)),forward_diamond(star(skc1),domain_difference(u,forward_diamond(skc1,antidomain(antidomain(u)))))),forward_diamond(star(skc1),domain_difference(u,forward_diamond(skc1,antidomain(antidomain(u)))))),
inference(rew,[status(thm),theory(equality)],[4795,41]),
[iquote('0:Rew:4795.0,41.0')] ).
cnf(4826,plain,
equal(forward_diamond(u,antidomain(antidomain(v))),forward_diamond(u,v)),
inference(rew,[status(thm),theory(equality)],[4748,39]),
[iquote('0:Rew:4748.0,39.0')] ).
cnf(4962,plain,
equal(addition(antidomain(antidomain(u)),forward_diamond(star(skc1),domain_difference(u,forward_diamond(skc1,u)))),forward_diamond(star(skc1),domain_difference(u,forward_diamond(skc1,u)))),
inference(rew,[status(thm),theory(equality)],[4826,4809]),
[iquote('0:Rew:4826.0,4809.0')] ).
cnf(5716,plain,
equal(addition(antidomain(antidomain(divergence(skc1))),forward_diamond(star(skc1),domain_difference(divergence(skc1),divergence(skc1)))),forward_diamond(star(skc1),domain_difference(divergence(skc1),divergence(skc1)))),
inference(spr,[status(thm),theory(equality)],[14,4962]),
[iquote('0:SpR:14.0,4962.0')] ).
cnf(5743,plain,
equal(antidomain(antidomain(divergence(skc1))),zero),
inference(rew,[status(thm),theory(equality)],[69,5716,13,165,118]),
[iquote('0:Rew:69.0,5716.0,13.0,5716.0,165.0,5716.0,118.0,5716.0')] ).
cnf(5796,plain,
equal(multiplication(zero,divergence(skc1)),divergence(skc1)),
inference(spr,[status(thm),theory(equality)],[5743,4160]),
[iquote('0:SpR:5743.0,4160.0')] ).
cnf(5837,plain,
equal(divergence(skc1),zero),
inference(rew,[status(thm),theory(equality)],[7,5796]),
[iquote('0:Rew:7.0,5796.0')] ).
cnf(5838,plain,
$false,
inference(mrr,[status(thm)],[5837,1]),
[iquote('0:MRR:5837.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : KLE131+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 09:46:47 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.77/0.96
% 0.77/0.96 SPASS V 3.9
% 0.77/0.96 SPASS beiseite: Proof found.
% 0.77/0.96 % SZS status Theorem
% 0.77/0.96 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/0.96 SPASS derived 4321 clauses, backtracked 0 clauses, performed 0 splits and kept 1061 clauses.
% 0.77/0.96 SPASS allocated 90002 KBytes.
% 0.77/0.96 SPASS spent 0:00:00.56 on the problem.
% 0.77/0.96 0:00:00.03 for the input.
% 0.77/0.96 0:00:00.03 for the FLOTTER CNF translation.
% 0.77/0.96 0:00:00.03 for inferences.
% 0.77/0.96 0:00:00.00 for the backtracking.
% 0.77/0.96 0:00:00.44 for the reduction.
% 0.77/0.96
% 0.77/0.96
% 0.77/0.96 Here is a proof with depth 4, length 59 :
% 0.77/0.96 % SZS output start Refutation
% See solution above
% 0.77/0.96 Formulae used in the proof : goals additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity right_annihilation left_annihilation domain1 domain4 additive_commutativity divergence1 domain3 domain_difference forward_diamond additive_associativity right_distributivity left_distributivity domain2
% 0.77/0.96
%------------------------------------------------------------------------------