TSTP Solution File: GRP580-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP580-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 : Sat Jul 16 11:48:08 EDT 2022

% Result   : Unsatisfiable 0.19s 0.44s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   45 (  45 unt;   0 nHn;  45 RR)
%            Number of literals    :   45 (   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    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(v,u),w),double_divide(v,identity))),double_divide(identity,identity)),w),
    file('GRP580-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
    file('GRP580-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(double_divide(u,identity),inverse(u)),
    file('GRP580-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(double_divide(u,inverse(u)),identity),
    file('GRP580-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(b,a),multiply(a,b)),
    file('GRP580-1.p',unknown),
    [] ).

cnf(6,plain,
    equal(inverse(double_divide(u,v)),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[3,2]),
    [iquote('0:Rew:3.0,2.0')] ).

cnf(7,plain,
    equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(v,u),w),inverse(v))),inverse(identity)),w),
    inference(rew,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Rew:3.0,1.0,3.0,1.0')] ).

cnf(12,plain,
    equal(multiply(inverse(u),u),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[4,6]),
    [iquote('0:SpR:4.0,6.0')] ).

cnf(13,plain,
    equal(multiply(identity,u),inverse(inverse(u))),
    inference(spr,[status(thm),theory(equality)],[3,6]),
    [iquote('0:SpR:3.0,6.0')] ).

cnf(20,plain,
    equal(double_divide(double_divide(inverse(u),double_divide(double_divide(identity,v),inverse(u))),inverse(identity)),v),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

cnf(22,plain,
    equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),inverse(double_divide(v,u))),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

cnf(23,plain,
    equal(double_divide(double_divide(u,double_divide(inverse(double_divide(v,u)),inverse(v))),inverse(identity)),identity),
    inference(spr,[status(thm),theory(equality)],[3,7]),
    [iquote('0:SpR:3.0,7.0')] ).

cnf(24,plain,
    equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),multiply(u,v)),
    inference(rew,[status(thm),theory(equality)],[6,22]),
    [iquote('0:Rew:6.0,22.0')] ).

cnf(25,plain,
    equal(double_divide(double_divide(u,double_divide(multiply(u,v),inverse(v))),inverse(identity)),identity),
    inference(rew,[status(thm),theory(equality)],[6,23]),
    [iquote('0:Rew:6.0,23.0')] ).

cnf(72,plain,
    equal(double_divide(double_divide(u,identity),inverse(identity)),multiply(u,identity)),
    inference(spr,[status(thm),theory(equality)],[4,24]),
    [iquote('0:SpR:4.0,24.0')] ).

cnf(73,plain,
    equal(double_divide(inverse(u),inverse(identity)),multiply(u,identity)),
    inference(rew,[status(thm),theory(equality)],[3,72]),
    [iquote('0:Rew:3.0,72.0')] ).

cnf(82,plain,
    equal(double_divide(multiply(u,v),inverse(identity)),multiply(double_divide(v,u),identity)),
    inference(spr,[status(thm),theory(equality)],[6,73]),
    [iquote('0:SpR:6.0,73.0')] ).

cnf(136,plain,
    equal(double_divide(double_divide(inverse(double_divide(identity,u)),identity),inverse(identity)),u),
    inference(spr,[status(thm),theory(equality)],[4,20]),
    [iquote('0:SpR:4.0,20.0')] ).

cnf(138,plain,
    equal(double_divide(double_divide(inverse(identity),multiply(identity,u)),inverse(identity)),double_divide(identity,inverse(u))),
    inference(spr,[status(thm),theory(equality)],[24,20]),
    [iquote('0:SpR:24.0,20.0')] ).

cnf(139,plain,
    equal(double_divide(double_divide(inverse(identity),identity),inverse(identity)),double_divide(multiply(identity,u),inverse(u))),
    inference(spr,[status(thm),theory(equality)],[25,20]),
    [iquote('0:SpR:25.0,20.0')] ).

cnf(141,plain,
    equal(multiply(multiply(u,identity),identity),u),
    inference(rew,[status(thm),theory(equality)],[73,136,3,6]),
    [iquote('0:Rew:73.0,136.0,3.0,136.0,6.0,136.0')] ).

cnf(143,plain,
    equal(double_divide(double_divide(inverse(identity),inverse(inverse(u))),inverse(identity)),double_divide(identity,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[13,138]),
    [iquote('0:Rew:13.0,138.0')] ).

cnf(144,plain,
    equal(double_divide(inverse(inverse(u)),inverse(u)),inverse(identity)),
    inference(rew,[status(thm),theory(equality)],[12,139,73,3,13]),
    [iquote('0:Rew:12.0,139.0,73.0,139.0,3.0,139.0,13.0,139.0')] ).

cnf(158,plain,
    equal(multiply(inverse(inverse(identity)),identity),identity),
    inference(spr,[status(thm),theory(equality)],[13,141]),
    [iquote('0:SpR:13.0,141.0')] ).

cnf(161,plain,
    equal(multiply(double_divide(identity,inverse(inverse(identity))),identity),double_divide(identity,inverse(identity))),
    inference(spr,[status(thm),theory(equality)],[158,82]),
    [iquote('0:SpR:158.0,82.0')] ).

cnf(167,plain,
    equal(multiply(double_divide(identity,inverse(inverse(identity))),identity),identity),
    inference(rew,[status(thm),theory(equality)],[4,161]),
    [iquote('0:Rew:4.0,161.0')] ).

cnf(173,plain,
    equal(double_divide(identity,inverse(inverse(identity))),multiply(identity,identity)),
    inference(spr,[status(thm),theory(equality)],[167,141]),
    [iquote('0:SpR:167.0,141.0')] ).

cnf(175,plain,
    equal(double_divide(identity,inverse(inverse(identity))),inverse(inverse(identity))),
    inference(rew,[status(thm),theory(equality)],[13,173]),
    [iquote('0:Rew:13.0,173.0')] ).

cnf(185,plain,
    equal(multiply(inverse(inverse(identity)),identity),inverse(inverse(inverse(identity)))),
    inference(spr,[status(thm),theory(equality)],[175,6]),
    [iquote('0:SpR:175.0,6.0')] ).

cnf(192,plain,
    equal(inverse(inverse(inverse(identity))),identity),
    inference(rew,[status(thm),theory(equality)],[158,185]),
    [iquote('0:Rew:158.0,185.0')] ).

cnf(246,plain,
    equal(double_divide(inverse(identity),identity),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[192,144]),
    [iquote('0:SpR:192.0,144.0')] ).

cnf(250,plain,
    equal(inverse(inverse(identity)),inverse(identity)),
    inference(rew,[status(thm),theory(equality)],[3,246]),
    [iquote('0:Rew:3.0,246.0')] ).

cnf(253,plain,
    equal(inverse(inverse(identity)),identity),
    inference(rew,[status(thm),theory(equality)],[250,192]),
    [iquote('0:Rew:250.0,192.0')] ).

cnf(261,plain,
    equal(inverse(identity),identity),
    inference(rew,[status(thm),theory(equality)],[250,253]),
    [iquote('0:Rew:250.0,253.0')] ).

cnf(265,plain,
    equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),identity),multiply(u,v)),
    inference(rew,[status(thm),theory(equality)],[261,24]),
    [iquote('0:Rew:261.0,24.0')] ).

cnf(266,plain,
    equal(double_divide(inverse(u),identity),multiply(u,identity)),
    inference(rew,[status(thm),theory(equality)],[261,73]),
    [iquote('0:Rew:261.0,73.0')] ).

cnf(293,plain,
    equal(double_divide(double_divide(identity,inverse(inverse(u))),identity),double_divide(identity,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[261,143]),
    [iquote('0:Rew:261.0,143.0')] ).

cnf(318,plain,
    equal(multiply(u,identity),inverse(inverse(u))),
    inference(rew,[status(thm),theory(equality)],[3,266]),
    [iquote('0:Rew:3.0,266.0')] ).

cnf(319,plain,
    equal(inverse(inverse(multiply(u,identity))),u),
    inference(rew,[status(thm),theory(equality)],[318,141]),
    [iquote('0:Rew:318.0,141.0')] ).

cnf(322,plain,
    equal(inverse(inverse(inverse(inverse(u)))),u),
    inference(rew,[status(thm),theory(equality)],[318,319]),
    [iquote('0:Rew:318.0,319.0')] ).

cnf(352,plain,
    equal(multiply(double_divide(identity,inverse(u)),v),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[6,265,3]),
    [iquote('0:Rew:6.0,265.0,3.0,265.0')] ).

cnf(360,plain,
    equal(multiply(inverse(inverse(u)),identity),double_divide(identity,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[6,293,3]),
    [iquote('0:Rew:6.0,293.0,3.0,293.0')] ).

cnf(361,plain,
    equal(double_divide(identity,inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[322,360,318]),
    [iquote('0:Rew:322.0,360.0,318.0,360.0')] ).

cnf(362,plain,
    equal(multiply(u,v),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[361,352]),
    [iquote('0:Rew:361.0,352.0')] ).

cnf(365,plain,
    $false,
    inference(unc,[status(thm)],[362,5]),
    [iquote('0:UnC:362.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP580-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n004.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 : Mon Jun 13 20:08:54 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.44  
% 0.19/0.44  SPASS V 3.9 
% 0.19/0.44  SPASS beiseite: Proof found.
% 0.19/0.44  % SZS status Theorem
% 0.19/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.44  SPASS derived 226 clauses, backtracked 0 clauses, performed 0 splits and kept 108 clauses.
% 0.19/0.44  SPASS allocated 63652 KBytes.
% 0.19/0.44  SPASS spent	0:00:00.09 on the problem.
% 0.19/0.44  		0:00:00.03 for the input.
% 0.19/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44  		0:00:00.00 for inferences.
% 0.19/0.44  		0:00:00.00 for the backtracking.
% 0.19/0.44  		0:00:00.03 for the reduction.
% 0.19/0.44  
% 0.19/0.44  
% 0.19/0.44  Here is a proof with depth 7, length 45 :
% 0.19/0.44  % SZS output start Refutation
% See solution above
% 0.19/0.44  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.19/0.44  
%------------------------------------------------------------------------------