TSTP Solution File: KLE071+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KLE071+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n004.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 02:28:22 EDT 2022

% Result   : Theorem 2.65s 2.91s
% Output   : Refutation 2.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   35 (  35 unt;   0 nHn;  35 RR)
%            Number of literals    :   35 (   0 equ;   8 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    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    equal(multiplication(u,one),u),
    file('KLE071+1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(multiplication(one,u),u),
    file('KLE071+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(addition(domain__dfg(u),one),one),
    file('KLE071+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(addition(u,v),addition(v,u)),
    file('KLE071+1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(domain__dfg(multiplication(u,domain__dfg(v))),domain__dfg(multiplication(u,v))),
    file('KLE071+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(addition(domain__dfg(u),domain__dfg(v)),domain__dfg(addition(u,v))),
    file('KLE071+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(addition(addition(u,v),w),addition(u,addition(v,w))),
    file('KLE071+1.p',unknown),
    [] ).

cnf(16,axiom,
    equal(addition(u,multiplication(domain__dfg(u),u)),multiplication(domain__dfg(u),u)),
    file('KLE071+1.p',unknown),
    [] ).

cnf(17,axiom,
    equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
    file('KLE071+1.p',unknown),
    [] ).

cnf(18,axiom,
    equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
    file('KLE071+1.p',unknown),
    [] ).

cnf(19,axiom,
    ~ equal(multiplication(addition(domain__dfg(skc5),domain__dfg(skc4)),addition(domain__dfg(skc5),domain__dfg(skc3))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
    file('KLE071+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(addition(skc4,skc5)),domain__dfg(addition(skc3,skc5))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
    inference(rew,[status(thm),theory(equality)],[9,19,13]),
    [iquote('0:Rew:9.0,19.0,13.0,19.0,9.0,19.0,13.0,19.0')] ).

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(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(454,plain,
    equal(addition(u,addition(v,w)),addition(w,addition(u,v))),
    inference(spr,[status(thm),theory(equality)],[14,9]),
    [iquote('0:SpR:14.0,9.0')] ).

cnf(470,plain,
    equal(addition(addition(u,v),w),addition(v,addition(u,w))),
    inference(spr,[status(thm),theory(equality)],[9,14]),
    [iquote('0:SpR:9.0,14.0')] ).

cnf(480,plain,
    equal(addition(u,addition(v,w)),addition(v,addition(u,w))),
    inference(rew,[status(thm),theory(equality)],[14,470]),
    [iquote('0:Rew:14.0,470.0')] ).

cnf(590,plain,
    equal(addition(multiplication(one,u),multiplication(domain__dfg(v),u)),multiplication(one,u)),
    inference(spr,[status(thm),theory(equality)],[20,18]),
    [iquote('0:SpR:20.0,18.0')] ).

cnf(591,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)],[13,18]),
    [iquote('0:SpR:13.0,18.0')] ).

cnf(600,plain,
    equal(addition(u,multiplication(domain__dfg(v),u)),u),
    inference(rew,[status(thm),theory(equality)],[5,590]),
    [iquote('0:Rew:5.0,590.0')] ).

cnf(602,plain,
    equal(multiplication(domain__dfg(u),domain__dfg(u)),domain__dfg(u)),
    inference(rew,[status(thm),theory(equality)],[600,192]),
    [iquote('0:Rew:600.0,192.0')] ).

cnf(617,plain,
    ~ equal(addition(multiplication(domain__dfg(skc4),domain__dfg(addition(skc3,skc5))),multiplication(domain__dfg(skc5),domain__dfg(addition(skc3,skc5)))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
    inference(rew,[status(thm),theory(equality)],[591,21]),
    [iquote('0:Rew:591.0,21.0')] ).

cnf(743,plain,
    equal(addition(multiplication(u,one),multiplication(u,domain__dfg(v))),multiplication(u,one)),
    inference(spr,[status(thm),theory(equality)],[20,17]),
    [iquote('0:SpR:20.0,17.0')] ).

cnf(744,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)],[13,17]),
    [iquote('0:SpR:13.0,17.0')] ).

cnf(753,plain,
    equal(addition(u,multiplication(u,domain__dfg(v))),u),
    inference(rew,[status(thm),theory(equality)],[4,743]),
    [iquote('0:Rew:4.0,743.0')] ).

cnf(758,plain,
    ~ equal(addition(addition(multiplication(domain__dfg(skc4),domain__dfg(skc3)),multiplication(domain__dfg(skc4),domain__dfg(skc5))),multiplication(domain__dfg(skc5),domain__dfg(addition(skc3,skc5)))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
    inference(rew,[status(thm),theory(equality)],[744,617]),
    [iquote('0:Rew:744.0,617.0')] ).

cnf(766,plain,
    ~ equal(addition(multiplication(domain__dfg(skc4),domain__dfg(skc3)),addition(multiplication(domain__dfg(skc4),domain__dfg(skc5)),multiplication(domain__dfg(skc5),domain__dfg(addition(skc3,skc5))))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
    inference(rew,[status(thm),theory(equality)],[14,758]),
    [iquote('0:Rew:14.0,758.0')] ).

cnf(767,plain,
    ~ equal(addition(domain__dfg(skc5),addition(multiplication(domain__dfg(skc4),domain__dfg(skc3)),addition(multiplication(domain__dfg(skc4),domain__dfg(skc5)),multiplication(domain__dfg(skc5),domain__dfg(skc3))))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
    inference(rew,[status(thm),theory(equality)],[480,766,454,602,744]),
    [iquote('0:Rew:480.0,766.0,454.0,766.0,602.0,766.0,744.0,766.0')] ).

cnf(928,plain,
    equal(addition(u,addition(multiplication(domain__dfg(v),u),w)),addition(u,w)),
    inference(spr,[status(thm),theory(equality)],[600,14]),
    [iquote('0:SpR:600.0,14.0')] ).

cnf(18533,plain,
    equal(addition(u,addition(v,addition(multiplication(domain__dfg(w),u),x))),addition(v,addition(u,x))),
    inference(spr,[status(thm),theory(equality)],[928,480]),
    [iquote('0:SpR:928.0,480.0')] ).

cnf(18825,plain,
    ~ equal(addition(multiplication(domain__dfg(skc4),domain__dfg(skc3)),addition(domain__dfg(skc5),multiplication(domain__dfg(skc5),domain__dfg(skc3)))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
    inference(rew,[status(thm),theory(equality)],[18533,767]),
    [iquote('0:Rew:18533.0,767.0')] ).

cnf(18877,plain,
    ~ equal(addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3))),addition(domain__dfg(skc5),multiplication(domain__dfg(skc4),domain__dfg(skc3)))),
    inference(rew,[status(thm),theory(equality)],[9,18825,753]),
    [iquote('0:Rew:9.0,18825.0,753.0,18825.0')] ).

cnf(18878,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[18877]),
    [iquote('0:Obv:18877.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : KLE071+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n004.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Thu Jun 16 12:29:23 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.65/2.91  
% 2.65/2.91  SPASS V 3.9 
% 2.65/2.91  SPASS beiseite: Proof found.
% 2.65/2.91  % SZS status Theorem
% 2.65/2.91  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 2.65/2.91  SPASS derived 13777 clauses, backtracked 0 clauses, performed 0 splits and kept 2179 clauses.
% 2.65/2.91  SPASS allocated 97890 KBytes.
% 2.65/2.91  SPASS spent	0:00:02.48 on the problem.
% 2.65/2.91  		0:00:00.04 for the input.
% 2.65/2.91  		0:00:00.03 for the FLOTTER CNF translation.
% 2.65/2.91  		0:00:00.08 for inferences.
% 2.65/2.91  		0:00:00.00 for the backtracking.
% 2.65/2.91  		0:00:02.31 for the reduction.
% 2.65/2.91  
% 2.65/2.91  
% 2.65/2.91  Here is a proof with depth 3, length 35 :
% 2.65/2.91  % SZS output start Refutation
% See solution above
% 2.65/2.91  Formulae used in the proof : multiplicative_right_identity multiplicative_left_identity domain3 additive_commutativity domain2 domain5 additive_associativity domain1 right_distributivity left_distributivity goals
% 2.65/2.91  
%------------------------------------------------------------------------------