TSTP Solution File: GRP540-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP540-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n023.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 11:47:57 EDT 2022

% Result   : Unsatisfiable 0.22s 0.44s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   29 (  29 unt;   0 nHn;  29 RR)
%            Number of literals    :   29 (   0 equ;   1 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('GRP540-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
    file('GRP540-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(divide(u,u),v),inverse(v)),
    file('GRP540-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(divide(u,u),identity),
    file('GRP540-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(multiply(b,a),multiply(a,b)),
    file('GRP540-1.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(9,plain,
    equal(inverse(identity),identity),
    inference(spr,[status(thm),theory(equality)],[6,4]),
    [iquote('0:SpR:6.0,4.0')] ).

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(15,plain,
    equal(divide(u,identity),multiply(u,identity)),
    inference(spr,[status(thm),theory(equality)],[9,7]),
    [iquote('0:SpR:9.0,7.0')] ).

cnf(30,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(34,plain,
    equal(divide(divide(u,divide(u,v)),identity),v),
    inference(spr,[status(thm),theory(equality)],[4,1]),
    [iquote('0:SpR:4.0,1.0')] ).

cnf(37,plain,
    equal(divide(identity,divide(divide(u,v),u)),v),
    inference(spr,[status(thm),theory(equality)],[4,1]),
    [iquote('0:SpR:4.0,1.0')] ).

cnf(41,plain,
    equal(multiply(divide(u,v),v),u),
    inference(rew,[status(thm),theory(equality)],[7,30,6]),
    [iquote('0:Rew:7.0,30.0,6.0,30.0')] ).

cnf(42,plain,
    equal(multiply(divide(u,divide(u,v)),identity),v),
    inference(rew,[status(thm),theory(equality)],[15,34]),
    [iquote('0:Rew:15.0,34.0')] ).

cnf(43,plain,
    equal(inverse(divide(divide(u,v),u)),v),
    inference(rew,[status(thm),theory(equality)],[6,37]),
    [iquote('0:Rew:6.0,37.0')] ).

cnf(52,plain,
    equal(multiply(identity,u),u),
    inference(spr,[status(thm),theory(equality)],[4,41]),
    [iquote('0:SpR:4.0,41.0')] ).

cnf(54,plain,
    equal(multiply(multiply(u,v),inverse(v)),u),
    inference(spr,[status(thm),theory(equality)],[7,41]),
    [iquote('0:SpR:7.0,41.0')] ).

cnf(57,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[13,52]),
    [iquote('0:Rew:13.0,52.0')] ).

cnf(61,plain,
    equal(multiply(u,inverse(v)),divide(u,v)),
    inference(spr,[status(thm),theory(equality)],[57,7]),
    [iquote('0:SpR:57.0,7.0')] ).

cnf(64,plain,
    equal(divide(multiply(u,v),v),u),
    inference(rew,[status(thm),theory(equality)],[61,54]),
    [iquote('0:Rew:61.0,54.0')] ).

cnf(89,plain,
    equal(inverse(divide(inverse(u),identity)),u),
    inference(spr,[status(thm),theory(equality)],[6,43]),
    [iquote('0:SpR:6.0,43.0')] ).

cnf(97,plain,
    equal(inverse(multiply(inverse(u),identity)),u),
    inference(rew,[status(thm),theory(equality)],[15,89]),
    [iquote('0:Rew:15.0,89.0')] ).

cnf(104,plain,
    equal(multiply(inverse(u),identity),inverse(u)),
    inference(spr,[status(thm),theory(equality)],[97,57]),
    [iquote('0:SpR:97.0,57.0')] ).

cnf(121,plain,
    equal(multiply(u,identity),u),
    inference(spr,[status(thm),theory(equality)],[57,104]),
    [iquote('0:SpR:57.0,104.0')] ).

cnf(125,plain,
    equal(divide(u,divide(u,v)),v),
    inference(rew,[status(thm),theory(equality)],[121,42]),
    [iquote('0:Rew:121.0,42.0')] ).

cnf(144,plain,
    equal(multiply(u,divide(v,u)),v),
    inference(spr,[status(thm),theory(equality)],[125,41]),
    [iquote('0:SpR:125.0,41.0')] ).

cnf(174,plain,
    equal(multiply(u,v),multiply(v,u)),
    inference(spr,[status(thm),theory(equality)],[64,144]),
    [iquote('0:SpR:64.0,144.0')] ).

cnf(176,plain,
    $false,
    inference(unc,[status(thm)],[174,5]),
    [iquote('0:UnC:174.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRP540-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.14/0.14  % Command  : run_spass %d %s
% 0.14/0.36  % Computer : n023.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 12:43:20 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.22/0.44  
% 0.22/0.44  SPASS V 3.9 
% 0.22/0.44  SPASS beiseite: Proof found.
% 0.22/0.44  % SZS status Theorem
% 0.22/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.22/0.44  SPASS derived 137 clauses, backtracked 0 clauses, performed 0 splits and kept 51 clauses.
% 0.22/0.44  SPASS allocated 63227 KBytes.
% 0.22/0.44  SPASS spent	0:00:00.06 on the problem.
% 0.22/0.44  		0:00:00.03 for the input.
% 0.22/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.44  		0:00:00.00 for inferences.
% 0.22/0.44  		0:00:00.00 for the backtracking.
% 0.22/0.44  		0:00:00.01 for the reduction.
% 0.22/0.44  
% 0.22/0.44  
% 0.22/0.44  Here is a proof with depth 4, length 29 :
% 0.22/0.44  % SZS output start Refutation
% See solution above
% 0.22/0.44  Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_4
% 0.22/0.44  
%------------------------------------------------------------------------------