TSTP Solution File: GRP565-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP565-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 11:48:04 EDT 2022

% Result   : Unsatisfiable 0.22s 0.45s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   22 (  22 unt;   0 nHn;  22 RR)
%            Number of literals    :   22 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,w)),double_divide(identity,w))),double_divide(identity,identity)),v),
    file('GRP565-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
    file('GRP565-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(double_divide(u,identity),inverse(u)),
    file('GRP565-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(double_divide(u,inverse(u)),identity),
    file('GRP565-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(inverse(a1),a1),identity),
    file('GRP565-1.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(v,double_divide(u,w)),double_divide(identity,w))),inverse(identity)),v),
    inference(rew,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Rew: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(14,plain,
    ~ equal(inverse(identity),identity),
    inference(rew,[status(thm),theory(equality)],[12,5]),
    [iquote('0:Rew:12.0,5.0')] ).

cnf(50,plain,
    equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,inverse(identity))),identity)),inverse(identity)),v),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

cnf(51,plain,
    equal(double_divide(double_divide(u,double_divide(double_divide(v,double_divide(u,identity)),inverse(identity))),inverse(identity)),v),
    inference(spr,[status(thm),theory(equality)],[3,7]),
    [iquote('0:SpR:3.0,7.0')] ).

cnf(55,plain,
    equal(double_divide(double_divide(u,multiply(double_divide(u,inverse(identity)),v)),inverse(identity)),v),
    inference(rew,[status(thm),theory(equality)],[6,50,3]),
    [iquote('0:Rew:6.0,50.0,3.0,50.0')] ).

cnf(56,plain,
    equal(double_divide(double_divide(u,double_divide(double_divide(v,inverse(u)),inverse(identity))),inverse(identity)),v),
    inference(rew,[status(thm),theory(equality)],[3,51]),
    [iquote('0:Rew:3.0,51.0')] ).

cnf(69,plain,
    equal(double_divide(double_divide(identity,multiply(identity,u)),inverse(identity)),u),
    inference(spr,[status(thm),theory(equality)],[4,55]),
    [iquote('0:SpR:4.0,55.0')] ).

cnf(71,plain,
    equal(double_divide(double_divide(identity,inverse(inverse(u))),inverse(identity)),u),
    inference(rew,[status(thm),theory(equality)],[13,69]),
    [iquote('0:Rew:13.0,69.0')] ).

cnf(116,plain,
    equal(double_divide(double_divide(u,double_divide(identity,inverse(identity))),inverse(identity)),u),
    inference(spr,[status(thm),theory(equality)],[4,56]),
    [iquote('0:SpR:4.0,56.0')] ).

cnf(121,plain,
    equal(double_divide(double_divide(inverse(u),u),inverse(identity)),identity),
    inference(spr,[status(thm),theory(equality)],[71,56]),
    [iquote('0:SpR:71.0,56.0')] ).

cnf(123,plain,
    equal(double_divide(inverse(u),inverse(identity)),u),
    inference(rew,[status(thm),theory(equality)],[3,116,4]),
    [iquote('0:Rew:3.0,116.0,4.0,116.0')] ).

cnf(162,plain,
    equal(double_divide(inverse(inverse(identity)),inverse(identity)),identity),
    inference(spr,[status(thm),theory(equality)],[3,121]),
    [iquote('0:SpR:3.0,121.0')] ).

cnf(164,plain,
    equal(inverse(identity),identity),
    inference(rew,[status(thm),theory(equality)],[123,162]),
    [iquote('0:Rew:123.0,162.0')] ).

cnf(165,plain,
    $false,
    inference(mrr,[status(thm)],[164,14]),
    [iquote('0:MRR:164.0,14.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : GRP565-1 : TPTP v8.1.0. Released v2.6.0.
% 0.13/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n027.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Tue Jun 14 09:29:18 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.22/0.45  
% 0.22/0.45  SPASS V 3.9 
% 0.22/0.45  SPASS beiseite: Proof found.
% 0.22/0.45  % SZS status Theorem
% 0.22/0.45  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.22/0.45  SPASS derived 105 clauses, backtracked 0 clauses, performed 0 splits and kept 39 clauses.
% 0.22/0.45  SPASS allocated 63301 KBytes.
% 0.22/0.45  SPASS spent	0:00:00.07 on the problem.
% 0.22/0.45  		0:00:00.04 for the input.
% 0.22/0.45  		0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.45  		0:00:00.00 for inferences.
% 0.22/0.45  		0:00:00.00 for the backtracking.
% 0.22/0.45  		0:00:00.01 for the reduction.
% 0.22/0.45  
% 0.22/0.45  
% 0.22/0.45  Here is a proof with depth 4, length 22 :
% 0.22/0.45  % SZS output start Refutation
% See solution above
% 0.22/0.45  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_1
% 0.22/0.45  
%------------------------------------------------------------------------------