TSTP Solution File: KLE068+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE068+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n010.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 02:28:21 EDT 2022

% Result   : Theorem 108.03s 108.22s
% Output   : Refutation 108.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   46 (  46 unt;   0 nHn;  46 RR)
%            Number of literals    :   46 (   0 equ;   2 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    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    equal(multiplication(u,one),u),
    file('KLE068+1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(multiplication(one,u),u),
    file('KLE068+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(addition(domain__dfg(u),one),one),
    file('KLE068+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE068+1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
    file('KLE068+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
    file('KLE068+1.p',unknown),
    [] ).

cnf(16,axiom,
    equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
    file('KLE068+1.p',unknown),
    [] ).

cnf(17,axiom,
    ~ equal(domain__dfg(multiplication(domain__dfg(skc3),domain__dfg(skc2))),multiplication(domain__dfg(skc3),domain__dfg(skc2))),
    file('KLE068+1.p',unknown),
    [] ).

cnf(18,axiom,
    equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
    file('KLE068+1.p',unknown),
    [] ).

cnf(19,axiom,
    equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
    file('KLE068+1.p',unknown),
    [] ).

cnf(20,plain,
    equal(addition(one,domain__dfg(u)),one),
    inference(rew,[status(thm),theory(equality)],[9,8]),
    [iquote('0:Rew:9.0,8.0')] ).

cnf(21,plain,
    ~ equal(multiplication(domain__dfg(skc3),domain__dfg(skc2)),domain__dfg(multiplication(domain__dfg(skc3),skc2))),
    inference(rew,[status(thm),theory(equality)],[12,17]),
    [iquote('0:Rew:12.0,17.0')] ).

cnf(91,plain,
    equal(domain__dfg(multiplication(one,u)),domain__dfg(domain__dfg(u))),
    inference(spr,[status(thm),theory(equality)],[5,12]),
    [iquote('0:SpR:5.0,12.0')] ).

cnf(94,plain,
    equal(domain__dfg(domain__dfg(u)),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[5,91]),
    [iquote('0:Rew:5.0,91.0')] ).

cnf(100,plain,
    equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(domain__dfg(u),v))),
    inference(spr,[status(thm),theory(equality)],[94,13]),
    [iquote('0:SpR:94.0,13.0')] ).

cnf(109,plain,
    equal(domain__dfg(addition(domain__dfg(u),v)),domain__dfg(addition(u,v))),
    inference(rew,[status(thm),theory(equality)],[13,100]),
    [iquote('0:Rew:13.0,100.0')] ).

cnf(191,plain,
    equal(addition(multiplication(u,domain__dfg(v)),multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v)))),multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v)))),
    inference(spr,[status(thm),theory(equality)],[12,16]),
    [iquote('0:SpR:12.0,16.0')] ).

cnf(192,plain,
    equal(addition(domain__dfg(u),multiplication(domain__dfg(u),domain__dfg(u))),multiplication(domain__dfg(u),domain__dfg(u))),
    inference(spr,[status(thm),theory(equality)],[94,16]),
    [iquote('0:SpR:94.0,16.0')] ).

cnf(194,plain,
    equal(addition(one,domain__dfg(one)),domain__dfg(one)),
    inference(spr,[status(thm),theory(equality)],[4,16]),
    [iquote('0:SpR:4.0,16.0')] ).

cnf(196,plain,
    equal(domain__dfg(one),one),
    inference(rew,[status(thm),theory(equality)],[20,194]),
    [iquote('0:Rew:20.0,194.0')] ).

cnf(202,plain,
    equal(addition(one,domain__dfg(u)),domain__dfg(addition(one,u))),
    inference(spr,[status(thm),theory(equality)],[196,13]),
    [iquote('0:SpR:196.0,13.0')] ).

cnf(209,plain,
    equal(domain__dfg(addition(one,u)),one),
    inference(rew,[status(thm),theory(equality)],[20,202]),
    [iquote('0:Rew:20.0,202.0')] ).

cnf(221,plain,
    equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(multiplication(u,one))),
    inference(spr,[status(thm),theory(equality)],[209,12]),
    [iquote('0:SpR:209.0,12.0')] ).

cnf(235,plain,
    equal(domain__dfg(multiplication(u,addition(one,v))),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[4,221]),
    [iquote('0:Rew:4.0,221.0')] ).

cnf(236,plain,
    equal(domain__dfg(addition(multiplication(u,one),multiplication(u,v))),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[18,235]),
    [iquote('0:Rew:18.0,235.0')] ).

cnf(237,plain,
    equal(domain__dfg(addition(u,multiplication(u,v))),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[4,236]),
    [iquote('0:Rew:4.0,236.0')] ).

cnf(622,plain,
    equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
    inference(spr,[status(thm),theory(equality)],[20,19]),
    [iquote('0:SpR:20.0,19.0')] ).

cnf(623,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)],[13,19]),
    [iquote('0:SpR:13.0,19.0')] ).

cnf(632,plain,
    equal(addition(u,multiplication(domain__dfg(v),u)),u),
    inference(rew,[status(thm),theory(equality)],[5,622]),
    [iquote('0:Rew:5.0,622.0')] ).

cnf(634,plain,
    equal(multiplication(domain__dfg(multiplication(u,v)),multiplication(u,domain__dfg(v))),multiplication(u,domain__dfg(v))),
    inference(rew,[status(thm),theory(equality)],[632,191]),
    [iquote('0:Rew:632.0,191.0')] ).

cnf(635,plain,
    equal(multiplication(domain__dfg(u),domain__dfg(u)),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[632,192]),
    [iquote('0:Rew:632.0,192.0')] ).

cnf(825,plain,
    equal(addition(multiplication(u,one),multiplication(u,domain__dfg(v))),multiplication(u,one)),
    inference(spr,[status(thm),theory(equality)],[20,18]),
    [iquote('0:SpR:20.0,18.0')] ).

cnf(826,plain,
    equal(multiplication(u,domain__dfg(addition(v,w))),addition(multiplication(u,domain__dfg(v)),multiplication(u,domain__dfg(w)))),
    inference(spr,[status(thm),theory(equality)],[13,18]),
    [iquote('0:SpR:13.0,18.0')] ).

cnf(835,plain,
    equal(addition(u,multiplication(u,domain__dfg(v))),u),
    inference(rew,[status(thm),theory(equality)],[4,825]),
    [iquote('0:Rew:4.0,825.0')] ).

cnf(945,plain,
    equal(addition(multiplication(u,v),multiplication(u,multiplication(domain__dfg(w),v))),multiplication(u,v)),
    inference(spr,[status(thm),theory(equality)],[632,18]),
    [iquote('0:SpR:632.0,18.0')] ).

cnf(6024,plain,
    equal(addition(multiplication(u,domain__dfg(v)),multiplication(u,domain__dfg(multiplication(domain__dfg(w),v)))),multiplication(u,domain__dfg(v))),
    inference(spr,[status(thm),theory(equality)],[632,826]),
    [iquote('0:SpR:632.0,826.0')] ).

cnf(8169,plain,
    equal(domain__dfg(addition(u,multiplication(domain__dfg(u),v))),domain__dfg(domain__dfg(u))),
    inference(spr,[status(thm),theory(equality)],[109,237]),
    [iquote('0:SpR:109.0,237.0')] ).

cnf(8263,plain,
    equal(domain__dfg(addition(u,multiplication(domain__dfg(u),v))),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[94,8169]),
    [iquote('0:Rew:94.0,8169.0')] ).

cnf(18658,plain,
    equal(addition(multiplication(domain__dfg(u),v),multiplication(domain__dfg(multiplication(domain__dfg(u),w)),v)),multiplication(domain__dfg(u),v)),
    inference(spr,[status(thm),theory(equality)],[8263,623]),
    [iquote('0:SpR:8263.0,623.0')] ).

cnf(56082,plain,
    equal(addition(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),multiplication(domain__dfg(u),domain__dfg(v))),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),
    inference(spr,[status(thm),theory(equality)],[634,945]),
    [iquote('0:SpR:634.0,945.0')] ).

cnf(56257,plain,
    equal(addition(multiplication(domain__dfg(u),domain__dfg(v)),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),
    inference(rew,[status(thm),theory(equality)],[9,56082]),
    [iquote('0:Rew:9.0,56082.0')] ).

cnf(56258,plain,
    equal(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),multiplication(domain__dfg(u),domain__dfg(v))),
    inference(rew,[status(thm),theory(equality)],[18658,56257]),
    [iquote('0:Rew:18658.0,56257.0')] ).

cnf(128018,plain,
    equal(addition(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),domain__dfg(multiplication(domain__dfg(u),v))),multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v))),
    inference(spr,[status(thm),theory(equality)],[635,6024]),
    [iquote('0:SpR:635.0,6024.0')] ).

cnf(128358,plain,
    equal(multiplication(domain__dfg(multiplication(domain__dfg(u),v)),domain__dfg(v)),domain__dfg(multiplication(domain__dfg(u),v))),
    inference(rew,[status(thm),theory(equality)],[835,128018,9]),
    [iquote('0:Rew:835.0,128018.0,9.0,128018.0')] ).

cnf(128359,plain,
    equal(multiplication(domain__dfg(u),domain__dfg(v)),domain__dfg(multiplication(domain__dfg(u),v))),
    inference(rew,[status(thm),theory(equality)],[56258,128358]),
    [iquote('0:Rew:56258.0,128358.0')] ).

cnf(128360,plain,
    $false,
    inference(unc,[status(thm)],[128359,21]),
    [iquote('0:UnC:128359.0,21.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KLE068+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n010.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun 16 11:44:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 108.03/108.22  
% 108.03/108.22  SPASS V 3.9 
% 108.03/108.22  SPASS beiseite: Proof found.
% 108.03/108.22  % SZS status Theorem
% 108.03/108.22  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 108.03/108.22  SPASS derived 88867 clauses, backtracked 0 clauses, performed 0 splits and kept 14906 clauses.
% 108.03/108.22  SPASS allocated 165531 KBytes.
% 108.03/108.22  SPASS spent	0:1:45.00 on the problem.
% 108.03/108.22  		0:00:00.04 for the input.
% 108.03/108.22  		0:00:00.03 for the FLOTTER CNF translation.
% 108.03/108.22  		0:00:00.58 for inferences.
% 108.03/108.22  		0:00:00.00 for the backtracking.
% 108.03/108.22  		0:1:44.22 for the reduction.
% 108.03/108.22  
% 108.03/108.22  
% 108.03/108.22  Here is a proof with depth 5, length 46 :
% 108.03/108.22  % SZS output start Refutation
% See solution above
% 108.03/108.22  Formulae used in the proof : multiplicative_right_identity multiplicative_left_identity domain3 additive_commutativity domain2 domain5 domain1 goals right_distributivity left_distributivity
% 108.03/108.22  
%------------------------------------------------------------------------------