TSTP Solution File: KLE091+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE091+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n003.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 02:28:28 EDT 2022
% Result : Theorem 2.84s 3.01s
% Output : Refutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 62 ( 62 unt; 0 nHn; 62 RR)
% Number of literals : 62 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(u,zero),u),
file('KLE091+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,u),u),
file('KLE091+1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiplication(u,one),u),
file('KLE091+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(one,u),u),
file('KLE091+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE091+1.p',unknown),
[] ).
cnf(8,axiom,
equal(antidomain(antidomain(u)),domain__dfg(u)),
file('KLE091+1.p',unknown),
[] ).
cnf(9,axiom,
equal(multiplication(u,coantidomain(u)),zero),
file('KLE091+1.p',unknown),
[] ).
cnf(10,axiom,
equal(coantidomain(coantidomain(u)),codomain(u)),
file('KLE091+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(domain__dfg(codomain(skc1)),codomain(skc1)),
file('KLE091+1.p',unknown),
[] ).
cnf(12,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE091+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE091+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(coantidomain(coantidomain(u)),coantidomain(u)),one),
file('KLE091+1.p',unknown),
[] ).
cnf(17,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE091+1.p',unknown),
[] ).
cnf(19,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE091+1.p',unknown),
[] ).
cnf(20,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE091+1.p',unknown),
[] ).
cnf(21,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE091+1.p',unknown),
[] ).
cnf(23,plain,
equal(addition(codomain(u),coantidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[10,14]),
[iquote('0:Rew:10.0,14.0')] ).
cnf(24,plain,
equal(addition(domain__dfg(u),antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[8,13]),
[iquote('0:Rew:8.0,13.0')] ).
cnf(26,plain,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,domain__dfg(v)))),antidomain(multiplication(u,domain__dfg(v)))),
inference(rew,[status(thm),theory(equality)],[8,21]),
[iquote('0:Rew:8.0,21.0')] ).
cnf(40,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(60,plain,
equal(antidomain(zero),domain__dfg(one)),
inference(spr,[status(thm),theory(equality)],[40,8]),
[iquote('0:SpR:40.0,8.0')] ).
cnf(88,plain,
equal(addition(domain__dfg(one),zero),one),
inference(spr,[status(thm),theory(equality)],[40,24]),
[iquote('0:SpR:40.0,24.0')] ).
cnf(91,plain,
equal(domain__dfg(one),one),
inference(rew,[status(thm),theory(equality)],[1,88]),
[iquote('0:Rew:1.0,88.0')] ).
cnf(92,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[91,60]),
[iquote('0:Rew:91.0,60.0')] ).
cnf(109,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[12,1]),
[iquote('0:SpR:12.0,1.0')] ).
cnf(302,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[2,17]),
[iquote('0:SpR:2.0,17.0')] ).
cnf(307,plain,
equal(addition(domain__dfg(u),addition(antidomain(u),v)),addition(one,v)),
inference(spr,[status(thm),theory(equality)],[24,17]),
[iquote('0:SpR:24.0,17.0')] ).
cnf(382,plain,
equal(addition(multiplication(codomain(u),v),multiplication(coantidomain(u),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[23,20]),
[iquote('0:SpR:23.0,20.0')] ).
cnf(385,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[24,20]),
[iquote('0:SpR:24.0,20.0')] ).
cnf(396,plain,
equal(addition(multiplication(codomain(u),v),multiplication(coantidomain(u),v)),v),
inference(rew,[status(thm),theory(equality)],[4,382]),
[iquote('0:Rew:4.0,382.0')] ).
cnf(397,plain,
equal(addition(multiplication(domain__dfg(u),v),multiplication(antidomain(u),v)),v),
inference(rew,[status(thm),theory(equality)],[4,385]),
[iquote('0:Rew:4.0,385.0')] ).
cnf(480,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),multiplication(antidomain(addition(u,v)),v)),zero),
inference(spr,[status(thm),theory(equality)],[19,7]),
[iquote('0:SpR:19.0,7.0')] ).
cnf(493,plain,
equal(addition(multiplication(u,codomain(v)),multiplication(u,coantidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[23,19]),
[iquote('0:SpR:23.0,19.0')] ).
cnf(496,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[24,19]),
[iquote('0:SpR:24.0,19.0')] ).
cnf(510,plain,
equal(addition(multiplication(u,codomain(v)),multiplication(u,coantidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,493]),
[iquote('0:Rew:3.0,493.0')] ).
cnf(511,plain,
equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,antidomain(v))),u),
inference(rew,[status(thm),theory(equality)],[3,496]),
[iquote('0:Rew:3.0,496.0')] ).
cnf(536,plain,
equal(addition(codomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[23,302]),
[iquote('0:SpR:23.0,302.0')] ).
cnf(548,plain,
equal(addition(one,codomain(u)),one),
inference(rew,[status(thm),theory(equality)],[12,536]),
[iquote('0:Rew:12.0,536.0')] ).
cnf(669,plain,
equal(addition(multiplication(one,u),multiplication(codomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[548,20]),
[iquote('0:SpR:548.0,20.0')] ).
cnf(681,plain,
equal(addition(u,multiplication(codomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[4,669]),
[iquote('0:Rew:4.0,669.0')] ).
cnf(706,plain,
equal(addition(antidomain(zero),antidomain(multiplication(u,domain__dfg(coantidomain(u))))),antidomain(multiplication(u,domain__dfg(coantidomain(u))))),
inference(spr,[status(thm),theory(equality)],[9,26]),
[iquote('0:SpR:9.0,26.0')] ).
cnf(732,plain,
equal(addition(one,antidomain(multiplication(u,domain__dfg(coantidomain(u))))),antidomain(multiplication(u,domain__dfg(coantidomain(u))))),
inference(rew,[status(thm),theory(equality)],[92,706]),
[iquote('0:Rew:92.0,706.0')] ).
cnf(1874,plain,
equal(addition(domain__dfg(u),antidomain(u)),addition(one,antidomain(u))),
inference(spr,[status(thm),theory(equality)],[2,307]),
[iquote('0:SpR:2.0,307.0')] ).
cnf(1891,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[24,1874]),
[iquote('0:Rew:24.0,1874.0')] ).
cnf(1903,plain,
equal(antidomain(multiplication(u,domain__dfg(coantidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[1891,732]),
[iquote('0:Rew:1891.0,732.0')] ).
cnf(1999,plain,
equal(multiplication(one,multiplication(u,domain__dfg(coantidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[1903,7]),
[iquote('0:SpR:1903.0,7.0')] ).
cnf(2042,plain,
equal(multiplication(u,domain__dfg(coantidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[4,1999]),
[iquote('0:Rew:4.0,1999.0')] ).
cnf(2405,plain,
equal(addition(multiplication(domain__dfg(u),u),zero),u),
inference(spr,[status(thm),theory(equality)],[7,397]),
[iquote('0:SpR:7.0,397.0')] ).
cnf(2433,plain,
equal(multiplication(domain__dfg(u),u),u),
inference(rew,[status(thm),theory(equality)],[109,2405,12]),
[iquote('0:Rew:109.0,2405.0,12.0,2405.0')] ).
cnf(2578,plain,
equal(addition(codomain(u),multiplication(domain__dfg(codomain(u)),coantidomain(u))),domain__dfg(codomain(u))),
inference(spr,[status(thm),theory(equality)],[2433,510]),
[iquote('0:SpR:2433.0,510.0')] ).
cnf(2865,plain,
equal(addition(zero,multiplication(u,antidomain(coantidomain(u)))),u),
inference(spr,[status(thm),theory(equality)],[2042,511]),
[iquote('0:SpR:2042.0,511.0')] ).
cnf(2881,plain,
equal(multiplication(u,antidomain(coantidomain(u))),u),
inference(rew,[status(thm),theory(equality)],[109,2865]),
[iquote('0:Rew:109.0,2865.0')] ).
cnf(4897,plain,
equal(addition(multiplication(antidomain(u),u),multiplication(antidomain(u),multiplication(codomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[681,480]),
[iquote('0:SpR:681.0,480.0')] ).
cnf(4908,plain,
equal(addition(multiplication(antidomain(u),multiplication(codomain(v),u)),multiplication(antidomain(u),multiplication(coantidomain(v),u))),zero),
inference(spr,[status(thm),theory(equality)],[396,480]),
[iquote('0:SpR:396.0,480.0')] ).
cnf(4995,plain,
equal(multiplication(antidomain(u),multiplication(codomain(v),u)),zero),
inference(rew,[status(thm),theory(equality)],[109,4897,7]),
[iquote('0:Rew:109.0,4897.0,7.0,4897.0')] ).
cnf(5011,plain,
equal(addition(zero,multiplication(antidomain(u),multiplication(coantidomain(v),u))),zero),
inference(rew,[status(thm),theory(equality)],[4995,4908]),
[iquote('0:Rew:4995.0,4908.0')] ).
cnf(5012,plain,
equal(multiplication(antidomain(u),multiplication(coantidomain(v),u)),zero),
inference(rew,[status(thm),theory(equality)],[109,5011]),
[iquote('0:Rew:109.0,5011.0')] ).
cnf(16264,plain,
equal(multiplication(antidomain(antidomain(coantidomain(coantidomain(u)))),coantidomain(u)),zero),
inference(spr,[status(thm),theory(equality)],[2881,5012]),
[iquote('0:SpR:2881.0,5012.0')] ).
cnf(16292,plain,
equal(multiplication(domain__dfg(codomain(u)),coantidomain(u)),zero),
inference(rew,[status(thm),theory(equality)],[8,16264,10]),
[iquote('0:Rew:8.0,16264.0,10.0,16264.0')] ).
cnf(16293,plain,
equal(addition(codomain(u),zero),domain__dfg(codomain(u))),
inference(rew,[status(thm),theory(equality)],[16292,2578]),
[iquote('0:Rew:16292.0,2578.0')] ).
cnf(16294,plain,
equal(domain__dfg(codomain(u)),codomain(u)),
inference(rew,[status(thm),theory(equality)],[109,16293,12]),
[iquote('0:Rew:109.0,16293.0,12.0,16293.0')] ).
cnf(16295,plain,
$false,
inference(unc,[status(thm)],[16294,11]),
[iquote('0:UnC:16294.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE091+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n003.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 : Thu Jun 16 14:18:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.84/3.01
% 2.84/3.01 SPASS V 3.9
% 2.84/3.01 SPASS beiseite: Proof found.
% 2.84/3.01 % SZS status Theorem
% 2.84/3.01 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.84/3.01 SPASS derived 10780 clauses, backtracked 0 clauses, performed 0 splits and kept 2156 clauses.
% 2.84/3.01 SPASS allocated 101961 KBytes.
% 2.84/3.01 SPASS spent 0:00:02.57 on the problem.
% 2.84/3.01 0:00:00.03 for the input.
% 2.84/3.01 0:00:00.03 for the FLOTTER CNF translation.
% 2.84/3.01 0:00:00.07 for inferences.
% 2.84/3.01 0:00:00.00 for the backtracking.
% 2.84/3.01 0:00:02.41 for the reduction.
% 2.84/3.01
% 2.84/3.01
% 2.84/3.01 Here is a proof with depth 4, length 62 :
% 2.84/3.01 % SZS output start Refutation
% See solution above
% 2.84/3.01 Formulae used in the proof : additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity domain1 domain4 codomain1 codomain4 goals additive_commutativity domain3 codomain3 additive_associativity right_distributivity left_distributivity domain2
% 2.84/3.01
%------------------------------------------------------------------------------