TSTP Solution File: GRP577-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP577-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n032.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 11:48:07 EDT 2022

% Result   : Unsatisfiable 0.11s 0.35s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   36 (  36 unt;   0 nHn;  36 RR)
%            Number of literals    :   36 (   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    :    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(double_divide(v,u),w),double_divide(v,identity))),double_divide(identity,identity)),w),
    file('GRP577-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
    file('GRP577-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(double_divide(u,identity),inverse(u)),
    file('GRP577-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(double_divide(u,inverse(u)),identity),
    file('GRP577-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(inverse(a1),a1),identity),
    file('GRP577-1.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(10,plain,
    equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
    inference(spr,[status(thm),theory(equality)],[6,4]),
    [iquote('0:SpR:6.0,4.0')] ).

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(53,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(57,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(58,plain,
    equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),multiply(u,v)),
    inference(spr,[status(thm),theory(equality)],[10,7]),
    [iquote('0:SpR:10.0,7.0')] ).

cnf(60,plain,
    equal(double_divide(double_divide(u,double_divide(multiply(u,v),inverse(v))),inverse(identity)),identity),
    inference(rew,[status(thm),theory(equality)],[6,57]),
    [iquote('0:Rew:6.0,57.0')] ).

cnf(73,plain,
    equal(double_divide(double_divide(u,identity),inverse(identity)),multiply(u,identity)),
    inference(spr,[status(thm),theory(equality)],[4,58]),
    [iquote('0:SpR:4.0,58.0')] ).

cnf(74,plain,
    equal(double_divide(inverse(u),inverse(identity)),multiply(u,identity)),
    inference(rew,[status(thm),theory(equality)],[3,73]),
    [iquote('0:Rew:3.0,73.0')] ).

cnf(83,plain,
    equal(double_divide(multiply(u,v),inverse(identity)),multiply(double_divide(v,u),identity)),
    inference(spr,[status(thm),theory(equality)],[6,74]),
    [iquote('0:SpR:6.0,74.0')] ).

cnf(109,plain,
    equal(double_divide(double_divide(double_divide(multiply(u,v),inverse(v)),double_divide(identity,inverse(u))),inverse(identity)),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[60,7]),
    [iquote('0:SpR:60.0,7.0')] ).

cnf(125,plain,
    equal(multiply(double_divide(multiply(u,v),inverse(v)),u),inverse(identity)),
    inference(rew,[status(thm),theory(equality)],[58,109]),
    [iquote('0:Rew:58.0,109.0')] ).

cnf(135,plain,
    equal(multiply(double_divide(inverse(identity),inverse(u)),inverse(u)),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[12,125]),
    [iquote('0:SpR:12.0,125.0')] ).

cnf(162,plain,
    equal(multiply(identity,inverse(inverse(identity))),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[4,135]),
    [iquote('0:SpR:4.0,135.0')] ).

cnf(164,plain,
    equal(inverse(inverse(inverse(inverse(identity)))),inverse(identity)),
    inference(rew,[status(thm),theory(equality)],[13,162]),
    [iquote('0:Rew:13.0,162.0')] ).

cnf(167,plain,
    equal(double_divide(inverse(inverse(inverse(identity))),inverse(identity)),identity),
    inference(spr,[status(thm),theory(equality)],[164,4]),
    [iquote('0:SpR:164.0,4.0')] ).

cnf(177,plain,
    equal(multiply(inverse(inverse(identity)),identity),identity),
    inference(rew,[status(thm),theory(equality)],[74,167]),
    [iquote('0:Rew:74.0,167.0')] ).

cnf(196,plain,
    equal(double_divide(double_divide(inverse(double_divide(identity,u)),identity),inverse(identity)),u),
    inference(spr,[status(thm),theory(equality)],[4,53]),
    [iquote('0:SpR:4.0,53.0')] ).

cnf(202,plain,
    equal(multiply(multiply(u,identity),identity),u),
    inference(rew,[status(thm),theory(equality)],[74,196,3,6]),
    [iquote('0:Rew:74.0,196.0,3.0,196.0,6.0,196.0')] ).

cnf(215,plain,
    equal(multiply(double_divide(identity,inverse(inverse(identity))),identity),double_divide(identity,inverse(identity))),
    inference(spr,[status(thm),theory(equality)],[177,83]),
    [iquote('0:SpR:177.0,83.0')] ).

cnf(222,plain,
    equal(multiply(double_divide(identity,inverse(inverse(identity))),identity),identity),
    inference(rew,[status(thm),theory(equality)],[4,215]),
    [iquote('0:Rew:4.0,215.0')] ).

cnf(244,plain,
    equal(double_divide(identity,inverse(inverse(identity))),multiply(identity,identity)),
    inference(spr,[status(thm),theory(equality)],[222,202]),
    [iquote('0:SpR:222.0,202.0')] ).

cnf(248,plain,
    equal(double_divide(identity,inverse(inverse(identity))),inverse(inverse(identity))),
    inference(rew,[status(thm),theory(equality)],[13,244]),
    [iquote('0:Rew:13.0,244.0')] ).

cnf(259,plain,
    equal(multiply(inverse(inverse(identity)),identity),inverse(inverse(inverse(identity)))),
    inference(spr,[status(thm),theory(equality)],[248,6]),
    [iquote('0:SpR:248.0,6.0')] ).

cnf(267,plain,
    equal(inverse(inverse(inverse(identity))),identity),
    inference(rew,[status(thm),theory(equality)],[177,259]),
    [iquote('0:Rew:177.0,259.0')] ).

cnf(307,plain,
    equal(multiply(double_divide(inverse(identity),identity),identity),inverse(identity)),
    inference(spr,[status(thm),theory(equality)],[267,135]),
    [iquote('0:SpR:267.0,135.0')] ).

cnf(317,plain,
    equal(inverse(identity),identity),
    inference(rew,[status(thm),theory(equality)],[177,307,3]),
    [iquote('0:Rew:177.0,307.0,3.0,307.0')] ).

cnf(318,plain,
    $false,
    inference(mrr,[status(thm)],[317,14]),
    [iquote('0:MRR:317.0,14.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08  % Problem  : GRP577-1 : TPTP v8.1.0. Released v2.6.0.
% 0.02/0.08  % Command  : run_spass %d %s
% 0.07/0.27  % Computer : n032.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 600
% 0.07/0.27  % DateTime : Mon Jun 13 06:15:26 EDT 2022
% 0.07/0.27  % CPUTime  : 
% 0.11/0.35  
% 0.11/0.35  SPASS V 3.9 
% 0.11/0.35  SPASS beiseite: Proof found.
% 0.11/0.35  % SZS status Theorem
% 0.11/0.35  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.11/0.35  SPASS derived 208 clauses, backtracked 0 clauses, performed 0 splits and kept 95 clauses.
% 0.11/0.35  SPASS allocated 63548 KBytes.
% 0.11/0.35  SPASS spent	0:00:00.06 on the problem.
% 0.11/0.35  		0:00:00.03 for the input.
% 0.11/0.35  		0:00:00.00 for the FLOTTER CNF translation.
% 0.11/0.35  		0:00:00.00 for inferences.
% 0.11/0.35  		0:00:00.00 for the backtracking.
% 0.11/0.35  		0:00:00.02 for the reduction.
% 0.11/0.35  
% 0.11/0.35  
% 0.11/0.35  Here is a proof with depth 9, length 36 :
% 0.11/0.35  % SZS output start Refutation
% See solution above
% 0.11/0.35  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_1
% 0.11/0.35  
%------------------------------------------------------------------------------