TSTP Solution File: BOO013-2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : Thu Jul 14 23:49:26 EDT 2022

% Result   : Unsatisfiable 0.18s 0.43s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   10
% 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    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(add(a,b),multiplicative_identity),
    file('BOO013-2.p',unknown),
    [] ).

cnf(2,axiom,
    equal(add(a,c),multiplicative_identity),
    file('BOO013-2.p',unknown),
    [] ).

cnf(3,axiom,
    equal(multiply(a,b),additive_identity),
    file('BOO013-2.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiply(a,c),additive_identity),
    file('BOO013-2.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(c,b),
    file('BOO013-2.p',unknown),
    [] ).

cnf(7,axiom,
    equal(multiply(u,v),multiply(v,u)),
    file('BOO013-2.p',unknown),
    [] ).

cnf(10,axiom,
    equal(add(multiply(u,v),multiply(w,v)),multiply(add(u,w),v)),
    file('BOO013-2.p',unknown),
    [] ).

cnf(16,axiom,
    equal(multiply(u,multiplicative_identity),u),
    file('BOO013-2.p',unknown),
    [] ).

cnf(17,axiom,
    equal(multiply(multiplicative_identity,u),u),
    file('BOO013-2.p',unknown),
    [] ).

cnf(19,axiom,
    equal(add(additive_identity,u),u),
    file('BOO013-2.p',unknown),
    [] ).

cnf(68,plain,
    equal(add(additive_identity,multiply(u,c)),multiply(add(a,u),c)),
    inference(spr,[status(thm),theory(equality)],[4,10]),
    [iquote('0:SpR:4.0,10.0')] ).

cnf(69,plain,
    equal(add(additive_identity,multiply(u,b)),multiply(add(a,u),b)),
    inference(spr,[status(thm),theory(equality)],[3,10]),
    [iquote('0:SpR:3.0,10.0')] ).

cnf(79,plain,
    equal(multiply(c,add(a,u)),multiply(u,c)),
    inference(rew,[status(thm),theory(equality)],[19,68,7]),
    [iquote('0:Rew:19.0,68.0,7.0,68.0')] ).

cnf(80,plain,
    equal(multiply(b,add(a,u)),multiply(u,b)),
    inference(rew,[status(thm),theory(equality)],[19,69,7]),
    [iquote('0:Rew:19.0,69.0,7.0,69.0')] ).

cnf(152,plain,
    equal(multiply(c,multiplicative_identity),multiply(b,c)),
    inference(spr,[status(thm),theory(equality)],[1,79]),
    [iquote('0:SpR:1.0,79.0')] ).

cnf(158,plain,
    equal(multiply(b,c),c),
    inference(rew,[status(thm),theory(equality)],[17,152,7]),
    [iquote('0:Rew:17.0,152.0,7.0,152.0')] ).

cnf(276,plain,
    equal(multiply(c,b),multiply(b,multiplicative_identity)),
    inference(spr,[status(thm),theory(equality)],[2,80]),
    [iquote('0:SpR:2.0,80.0')] ).

cnf(282,plain,
    equal(c,b),
    inference(rew,[status(thm),theory(equality)],[158,276,7,16]),
    [iquote('0:Rew:158.0,276.0,7.0,276.0,16.0,276.0')] ).

cnf(283,plain,
    $false,
    inference(mrr,[status(thm)],[282,5]),
    [iquote('0:MRR:282.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun  1 15:32:41 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.43  
% 0.18/0.43  SPASS V 3.9 
% 0.18/0.43  SPASS beiseite: Proof found.
% 0.18/0.43  % SZS status Theorem
% 0.18/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.43  SPASS derived 168 clauses, backtracked 0 clauses, performed 0 splits and kept 97 clauses.
% 0.18/0.43  SPASS allocated 63420 KBytes.
% 0.18/0.43  SPASS spent	0:00:00.09 on the problem.
% 0.18/0.43  		0:00:00.04 for the input.
% 0.18/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43  		0:00:00.00 for inferences.
% 0.18/0.43  		0:00:00.00 for the backtracking.
% 0.18/0.43  		0:00:00.03 for the reduction.
% 0.18/0.43  
% 0.18/0.43  
% 0.18/0.43  Here is a proof with depth 2, length 19 :
% 0.18/0.43  % SZS output start Refutation
% See solution above
% 0.18/0.43  Formulae used in the proof : b_and_multiplicative_identity c_and_multiplicative_identity b_a_additive_identity c_a_additive_identity prove_b_is_a commutativity_of_multiply distributivity3 multiplicative_id1 multiplicative_id2 additive_id2
% 0.18/0.43  
%------------------------------------------------------------------------------