TSTP Solution File: GRP451-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP451-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 11:47:32 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   19 (  19 unt;   0 nHn;  19 RR)
%            Number of literals    :   19 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   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(divide(divide(divide(u,u),divide(u,divide(v,divide(divide(divide(u,u),u),w)))),w),v),
    file('GRP451-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
    file('GRP451-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(divide(divide(u,u),v),inverse(v)),
    file('GRP451-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
    file('GRP451-1.p',unknown),
    [] ).

cnf(5,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(6,plain,
    equal(divide(inverse(divide(u,divide(v,divide(inverse(u),w)))),w),v),
    inference(rew,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Rew:3.0,1.0,3.0,1.0')] ).

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

cnf(9,plain,
    equal(divide(multiply(inverse(u),u),v),inverse(v)),
    inference(spr,[status(thm),theory(equality)],[5,3]),
    [iquote('0:SpR:5.0,3.0')] ).

cnf(11,plain,
    equal(multiply(divide(u,u),v),inverse(inverse(v))),
    inference(spr,[status(thm),theory(equality)],[5,3]),
    [iquote('0:SpR:5.0,3.0')] ).

cnf(20,plain,
    equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
    inference(spr,[status(thm),theory(equality)],[9,5]),
    [iquote('0:SpR:9.0,5.0')] ).

cnf(57,plain,
    equal(divide(inverse(divide(divide(u,u),divide(v,inverse(w)))),w),v),
    inference(spr,[status(thm),theory(equality)],[7,6]),
    [iquote('0:SpR:7.0,6.0')] ).

cnf(70,plain,
    equal(divide(inverse(inverse(multiply(u,v))),v),u),
    inference(rew,[status(thm),theory(equality)],[3,57,5]),
    [iquote('0:Rew:3.0,57.0,5.0,57.0')] ).

cnf(87,plain,
    equal(multiply(inverse(inverse(multiply(u,inverse(v)))),v),u),
    inference(spr,[status(thm),theory(equality)],[70,5]),
    [iquote('0:SpR:70.0,5.0')] ).

cnf(96,plain,
    equal(inverse(inverse(multiply(u,inverse(v)))),divide(inverse(inverse(u)),v)),
    inference(spr,[status(thm),theory(equality)],[87,70]),
    [iquote('0:SpR:87.0,70.0')] ).

cnf(100,plain,
    equal(multiply(inverse(inverse(inverse(inverse(inverse(u))))),u),multiply(inverse(v),v)),
    inference(spr,[status(thm),theory(equality)],[20,87]),
    [iquote('0:SpR:20.0,87.0')] ).

cnf(102,plain,
    equal(multiply(divide(inverse(inverse(u)),v),v),u),
    inference(rew,[status(thm),theory(equality)],[96,87]),
    [iquote('0:Rew:96.0,87.0')] ).

cnf(105,plain,
    equal(inverse(inverse(inverse(inverse(u)))),u),
    inference(spr,[status(thm),theory(equality)],[102,11]),
    [iquote('0:SpR:102.0,11.0')] ).

cnf(114,plain,
    equal(multiply(inverse(u),u),multiply(inverse(v),v)),
    inference(rew,[status(thm),theory(equality)],[105,100]),
    [iquote('0:Rew:105.0,100.0')] ).

cnf(120,plain,
    $false,
    inference(unc,[status(thm)],[114,4]),
    [iquote('0:UnC:114.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRP451-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jun 13 22:42:10 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.43  
% 0.20/0.43  SPASS V 3.9 
% 0.20/0.43  SPASS beiseite: Proof found.
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.43  SPASS derived 95 clauses, backtracked 0 clauses, performed 0 splits and kept 50 clauses.
% 0.20/0.43  SPASS allocated 63256 KBytes.
% 0.20/0.43  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.43  		0:00:00.03 for the input.
% 0.20/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43  		0:00:00.00 for inferences.
% 0.20/0.43  		0:00:00.00 for the backtracking.
% 0.20/0.43  		0:00:00.01 for the reduction.
% 0.20/0.43  
% 0.20/0.43  
% 0.20/0.43  Here is a proof with depth 4, length 19 :
% 0.20/0.43  % SZS output start Refutation
% See solution above
% 0.20/0.43  Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_1
% 0.20/0.43  
%------------------------------------------------------------------------------