TSTP Solution File: GRP548-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP548-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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 11:47:59 EDT 2022

% Result   : Unsatisfiable 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   26 (  26 unt;   0 nHn;  26 RR)
%            Number of literals    :   26 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   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(divide(divide(identity,divide(u,v)),divide(divide(v,w),u)),w),
    file('GRP548-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(u,divide(identity,v)),multiply(u,v)),
    file('GRP548-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(identity,u),inverse(u)),
    file('GRP548-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(divide(u,u),identity),
    file('GRP548-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(b,a),multiply(a,b)),
    file('GRP548-1.p',unknown),
    [] ).

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

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

cnf(9,plain,
    equal(inverse(identity),identity),
    inference(spr,[status(thm),theory(equality)],[3,4]),
    [iquote('0:SpR:3.0,4.0')] ).

cnf(15,plain,
    equal(divide(u,identity),multiply(u,identity)),
    inference(spr,[status(thm),theory(equality)],[9,6]),
    [iquote('0:SpR:9.0,6.0')] ).

cnf(29,plain,
    equal(divide(inverse(divide(u,v)),divide(identity,u)),v),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

cnf(33,plain,
    equal(divide(inverse(divide(divide(u,v),u)),identity),v),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

cnf(36,plain,
    equal(divide(inverse(identity),divide(divide(u,v),u)),v),
    inference(spr,[status(thm),theory(equality)],[4,7]),
    [iquote('0:SpR:4.0,7.0')] ).

cnf(37,plain,
    equal(divide(inverse(inverse(u)),divide(divide(u,v),identity)),v),
    inference(spr,[status(thm),theory(equality)],[3,7]),
    [iquote('0:SpR:3.0,7.0')] ).

cnf(40,plain,
    equal(multiply(inverse(divide(u,v)),u),v),
    inference(rew,[status(thm),theory(equality)],[6,29,3]),
    [iquote('0:Rew:6.0,29.0,3.0,29.0')] ).

cnf(41,plain,
    equal(multiply(inverse(divide(divide(u,v),u)),identity),v),
    inference(rew,[status(thm),theory(equality)],[15,33]),
    [iquote('0:Rew:15.0,33.0')] ).

cnf(42,plain,
    equal(inverse(divide(divide(u,v),u)),v),
    inference(rew,[status(thm),theory(equality)],[3,36,9]),
    [iquote('0:Rew:3.0,36.0,9.0,36.0')] ).

cnf(43,plain,
    equal(multiply(u,identity),u),
    inference(rew,[status(thm),theory(equality)],[42,41]),
    [iquote('0:Rew:42.0,41.0')] ).

cnf(44,plain,
    equal(divide(u,identity),u),
    inference(rew,[status(thm),theory(equality)],[43,15]),
    [iquote('0:Rew:43.0,15.0')] ).

cnf(46,plain,
    equal(divide(inverse(inverse(u)),divide(u,v)),v),
    inference(rew,[status(thm),theory(equality)],[44,37]),
    [iquote('0:Rew:44.0,37.0')] ).

cnf(66,plain,
    equal(inverse(divide(identity,u)),u),
    inference(spr,[status(thm),theory(equality)],[40,43]),
    [iquote('0:SpR:40.0,43.0')] ).

cnf(73,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[3,66]),
    [iquote('0:Rew:3.0,66.0')] ).

cnf(75,plain,
    equal(divide(u,divide(u,v)),v),
    inference(rew,[status(thm),theory(equality)],[73,46]),
    [iquote('0:Rew:73.0,46.0')] ).

cnf(102,plain,
    equal(multiply(inverse(u),v),divide(v,u)),
    inference(spr,[status(thm),theory(equality)],[75,40]),
    [iquote('0:SpR:75.0,40.0')] ).

cnf(151,plain,
    equal(divide(u,inverse(v)),multiply(v,u)),
    inference(spr,[status(thm),theory(equality)],[73,102]),
    [iquote('0:SpR:73.0,102.0')] ).

cnf(153,plain,
    equal(multiply(u,v),multiply(v,u)),
    inference(rew,[status(thm),theory(equality)],[6,151]),
    [iquote('0:Rew:6.0,151.0')] ).

cnf(154,plain,
    $false,
    inference(unc,[status(thm)],[153,5]),
    [iquote('0:UnC:153.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP548-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n008.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 : Tue Jun 14 09:27:52 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.41  
% 0.20/0.41  SPASS V 3.9 
% 0.20/0.41  SPASS beiseite: Proof found.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.41  SPASS derived 104 clauses, backtracked 0 clauses, performed 0 splits and kept 41 clauses.
% 0.20/0.41  SPASS allocated 63224 KBytes.
% 0.20/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.41  		0:00:00.03 for the input.
% 0.20/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41  		0:00:00.00 for inferences.
% 0.20/0.41  		0:00:00.00 for the backtracking.
% 0.20/0.41  		0:00:00.01 for the reduction.
% 0.20/0.41  
% 0.20/0.41  
% 0.20/0.41  Here is a proof with depth 3, length 26 :
% 0.20/0.41  % SZS output start Refutation
% See solution above
% 0.20/0.41  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.20/0.41  
%------------------------------------------------------------------------------