TSTP Solution File: KLE064+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 02:28:20 EDT 2022

% Result   : Theorem 8.01s 8.18s
% Output   : Refutation 8.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   19 (  19 unt;   0 nHn;  19 RR)
%            Number of literals    :   19 (   0 equ;   2 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    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    equal(multiplication(one,u),u),
    file('KLE064+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(addition(domain__dfg(u),one),one),
    file('KLE064+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE064+1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(addition(domain__dfg(skc2),domain__dfg(skc3)),domain__dfg(skc3)),
    file('KLE064+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
    file('KLE064+1.p',unknown),
    [] ).

cnf(17,axiom,
    equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
    file('KLE064+1.p',unknown),
    [] ).

cnf(18,axiom,
    ~ equal(addition(skc2,multiplication(domain__dfg(skc3),skc2)),multiplication(domain__dfg(skc3),skc2)),
    file('KLE064+1.p',unknown),
    [] ).

cnf(20,axiom,
    equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
    file('KLE064+1.p',unknown),
    [] ).

cnf(21,plain,
    equal(addition(one,domain__dfg(u)),one),
    inference(rew,[status(thm),theory(equality)],[9,8]),
    [iquote('0:Rew:9.0,8.0')] ).

cnf(22,plain,
    equal(domain__dfg(addition(skc2,skc3)),domain__dfg(skc3)),
    inference(rew,[status(thm),theory(equality)],[14,10]),
    [iquote('0:Rew:14.0,10.0')] ).

cnf(719,plain,
    equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
    inference(spr,[status(thm),theory(equality)],[21,20]),
    [iquote('0:SpR:21.0,20.0')] ).

cnf(720,plain,
    equal(multiplication(domain__dfg(addition(u,v)),w),addition(multiplication(domain__dfg(u),w),multiplication(domain__dfg(v),w))),
    inference(spr,[status(thm),theory(equality)],[14,20]),
    [iquote('0:SpR:14.0,20.0')] ).

cnf(729,plain,
    equal(addition(u,multiplication(domain__dfg(v),u)),u),
    inference(rew,[status(thm),theory(equality)],[5,719]),
    [iquote('0:Rew:5.0,719.0')] ).

cnf(730,plain,
    ~ equal(multiplication(domain__dfg(skc3),skc2),skc2),
    inference(rew,[status(thm),theory(equality)],[729,18]),
    [iquote('0:Rew:729.0,18.0')] ).

cnf(731,plain,
    equal(multiplication(domain__dfg(u),u),u),
    inference(rew,[status(thm),theory(equality)],[729,17]),
    [iquote('0:Rew:729.0,17.0')] ).

cnf(6106,plain,
    equal(addition(multiplication(domain__dfg(skc2),u),multiplication(domain__dfg(skc3),u)),multiplication(domain__dfg(skc3),u)),
    inference(spr,[status(thm),theory(equality)],[22,720]),
    [iquote('0:SpR:22.0,720.0')] ).

cnf(38205,plain,
    equal(addition(skc2,multiplication(domain__dfg(skc3),skc2)),multiplication(domain__dfg(skc3),skc2)),
    inference(spr,[status(thm),theory(equality)],[731,6106]),
    [iquote('0:SpR:731.0,6106.0')] ).

cnf(38272,plain,
    equal(multiplication(domain__dfg(skc3),skc2),skc2),
    inference(rew,[status(thm),theory(equality)],[729,38205]),
    [iquote('0:Rew:729.0,38205.0')] ).

cnf(38273,plain,
    $false,
    inference(mrr,[status(thm)],[38272,730]),
    [iquote('0:MRR:38272.0,730.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 09:46:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 8.01/8.18  
% 8.01/8.18  SPASS V 3.9 
% 8.01/8.18  SPASS beiseite: Proof found.
% 8.01/8.18  % SZS status Theorem
% 8.01/8.18  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 8.01/8.18  SPASS derived 28613 clauses, backtracked 0 clauses, performed 0 splits and kept 4474 clauses.
% 8.01/8.18  SPASS allocated 110004 KBytes.
% 8.01/8.18  SPASS spent	0:00:07.63 on the problem.
% 8.01/8.18  		0:00:00.04 for the input.
% 8.01/8.18  		0:00:00.03 for the FLOTTER CNF translation.
% 8.01/8.18  		0:00:00.16 for inferences.
% 8.01/8.18  		0:00:00.00 for the backtracking.
% 8.01/8.18  		0:00:07.35 for the reduction.
% 8.01/8.18  
% 8.01/8.18  
% 8.01/8.18  Here is a proof with depth 3, length 19 :
% 8.01/8.18  % SZS output start Refutation
% See solution above
% 8.01/8.18  Formulae used in the proof : multiplicative_left_identity domain3 additive_commutativity goals domain5 domain1 left_distributivity
% 8.01/8.18  
%------------------------------------------------------------------------------