TSTP Solution File: GRP538-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP538-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 11:47:56 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   16 (  16 unt;   0 nHn;  16 RR)
%            Number of literals    :   16 (   0 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   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(u,v),divide(divide(u,w),v)),w),
    file('GRP538-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
    file('GRP538-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(divide(u,u),v),inverse(v)),
    file('GRP538-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(divide(u,u),identity),
    file('GRP538-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
    file('GRP538-1.p',unknown),
    [] ).

cnf(6,plain,
    equal(divide(identity,u),inverse(u)),
    inference(rew,[status(thm),theory(equality)],[4,3]),
    [iquote('0:Rew:4.0,3.0')] ).

cnf(7,plain,
    equal(divide(u,inverse(v)),multiply(u,v)),
    inference(rew,[status(thm),theory(equality)],[6,2,4]),
    [iquote('0:Rew:6.0,2.0,4.0,2.0')] ).

cnf(12,plain,
    equal(multiply(inverse(u),u),identity),
    inference(spr,[status(thm),theory(equality)],[7,4]),
    [iquote('0:SpR:7.0,4.0')] ).

cnf(13,plain,
    equal(multiply(identity,u),inverse(inverse(u))),
    inference(spr,[status(thm),theory(equality)],[7,6]),
    [iquote('0:SpR:7.0,6.0')] ).

cnf(16,plain,
    ~ equal(multiply(identity,a2),a2),
    inference(rew,[status(thm),theory(equality)],[12,5]),
    [iquote('0:Rew:12.0,5.0')] ).

cnf(17,plain,
    ~ equal(inverse(inverse(a2)),a2),
    inference(rew,[status(thm),theory(equality)],[13,16]),
    [iquote('0:Rew:13.0,16.0')] ).

cnf(32,plain,
    equal(divide(divide(u,v),divide(identity,v)),u),
    inference(spr,[status(thm),theory(equality)],[4,1]),
    [iquote('0:SpR:4.0,1.0')] ).

cnf(43,plain,
    equal(multiply(divide(u,v),v),u),
    inference(rew,[status(thm),theory(equality)],[7,32,6]),
    [iquote('0:Rew:7.0,32.0,6.0,32.0')] ).

cnf(54,plain,
    equal(multiply(identity,u),u),
    inference(spr,[status(thm),theory(equality)],[4,43]),
    [iquote('0:SpR:4.0,43.0')] ).

cnf(59,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[13,54]),
    [iquote('0:Rew:13.0,54.0')] ).

cnf(60,plain,
    $false,
    inference(unc,[status(thm)],[59,17]),
    [iquote('0:UnC:59.0,17.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP538-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n014.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 : Mon Jun 13 15:04:07 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.41  
% 0.19/0.41  SPASS V 3.9 
% 0.19/0.41  SPASS beiseite: Proof found.
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.41  SPASS derived 38 clauses, backtracked 0 clauses, performed 0 splits and kept 26 clauses.
% 0.19/0.41  SPASS allocated 63155 KBytes.
% 0.19/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.41  		0:00:00.03 for the input.
% 0.19/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41  		0:00:00.00 for inferences.
% 0.19/0.41  		0:00:00.00 for the backtracking.
% 0.19/0.41  		0:00:00.00 for the reduction.
% 0.19/0.41  
% 0.19/0.41  
% 0.19/0.41  Here is a proof with depth 2, length 16 :
% 0.19/0.41  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.19/0.41  
%------------------------------------------------------------------------------