TSTP Solution File: KLE091+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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  
%------------------------------------------------------------------------------