TSTP Solution File: GRP191-2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP191-2 : 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 : Sat Jul 16 11:46:16 EDT 2022

% Result   : Unsatisfiable 0.21s 0.52s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% 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    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(greatest_lower_bound(a,b),b),
    file('GRP191-2.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(least_upper_bound(inverse(a),inverse(b)),inverse(b)),
    file('GRP191-2.p',unknown),
    [] ).

cnf(3,axiom,
    equal(multiply(identity,u),u),
    file('GRP191-2.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiply(inverse(u),u),identity),
    file('GRP191-2.p',unknown),
    [] ).

cnf(5,axiom,
    equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
    file('GRP191-2.p',unknown),
    [] ).

cnf(6,axiom,
    equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
    file('GRP191-2.p',unknown),
    [] ).

cnf(7,axiom,
    equal(least_upper_bound(u,v),least_upper_bound(v,u)),
    file('GRP191-2.p',unknown),
    [] ).

cnf(12,axiom,
    equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
    file('GRP191-2.p',unknown),
    [] ).

cnf(15,axiom,
    equal(multiply(u,greatest_lower_bound(v,w)),greatest_lower_bound(multiply(u,v),multiply(u,w))),
    file('GRP191-2.p',unknown),
    [] ).

cnf(17,axiom,
    equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
    file('GRP191-2.p',unknown),
    [] ).

cnf(41,plain,
    equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[6,12]),
    [iquote('0:SpR:6.0,12.0')] ).

cnf(247,plain,
    equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
    inference(spr,[status(thm),theory(equality)],[4,5]),
    [iquote('0:SpR:4.0,5.0')] ).

cnf(248,plain,
    equal(multiply(inverse(u),multiply(u,v)),v),
    inference(rew,[status(thm),theory(equality)],[3,247]),
    [iquote('0:Rew:3.0,247.0')] ).

cnf(251,plain,
    equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
    inference(spr,[status(thm),theory(equality)],[248]),
    [iquote('0:SpR:248.0,248.0')] ).

cnf(254,plain,
    equal(multiply(inverse(inverse(u)),identity),u),
    inference(spr,[status(thm),theory(equality)],[4,248]),
    [iquote('0:SpR:4.0,248.0')] ).

cnf(256,plain,
    equal(multiply(u,identity),u),
    inference(rew,[status(thm),theory(equality)],[251,254]),
    [iquote('0:Rew:251.0,254.0')] ).

cnf(271,plain,
    equal(multiply(u,inverse(u)),identity),
    inference(spr,[status(thm),theory(equality)],[251,4]),
    [iquote('0:SpR:251.0,4.0')] ).

cnf(288,plain,
    equal(greatest_lower_bound(multiply(a,u),multiply(b,u)),multiply(b,u)),
    inference(spr,[status(thm),theory(equality)],[1,17]),
    [iquote('0:SpR:1.0,17.0')] ).

cnf(998,plain,
    equal(greatest_lower_bound(multiply(a,inverse(b)),identity),identity),
    inference(spr,[status(thm),theory(equality)],[271,288]),
    [iquote('0:SpR:271.0,288.0')] ).

cnf(1009,plain,
    equal(greatest_lower_bound(identity,multiply(a,inverse(b))),identity),
    inference(rew,[status(thm),theory(equality)],[6,998]),
    [iquote('0:Rew:6.0,998.0')] ).

cnf(1026,plain,
    equal(greatest_lower_bound(multiply(u,identity),multiply(u,multiply(a,inverse(b)))),multiply(u,identity)),
    inference(spr,[status(thm),theory(equality)],[1009,15]),
    [iquote('0:SpR:1009.0,15.0')] ).

cnf(1032,plain,
    equal(greatest_lower_bound(u,multiply(u,multiply(a,inverse(b)))),u),
    inference(rew,[status(thm),theory(equality)],[256,1026]),
    [iquote('0:Rew:256.0,1026.0')] ).

cnf(1143,plain,
    equal(greatest_lower_bound(inverse(a),inverse(b)),inverse(a)),
    inference(spr,[status(thm),theory(equality)],[248,1032]),
    [iquote('0:SpR:248.0,1032.0')] ).

cnf(1185,plain,
    equal(least_upper_bound(inverse(b),inverse(a)),inverse(b)),
    inference(spr,[status(thm),theory(equality)],[1143,41]),
    [iquote('0:SpR:1143.0,41.0')] ).

cnf(1191,plain,
    equal(least_upper_bound(inverse(a),inverse(b)),inverse(b)),
    inference(rew,[status(thm),theory(equality)],[7,1185]),
    [iquote('0:Rew:7.0,1185.0')] ).

cnf(1192,plain,
    $false,
    inference(mrr,[status(thm)],[1191,2]),
    [iquote('0:MRR:1191.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GRP191-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n023.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 : Tue Jun 14 00:21:06 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.21/0.52  
% 0.21/0.52  SPASS V 3.9 
% 0.21/0.52  SPASS beiseite: Proof found.
% 0.21/0.52  % SZS status Theorem
% 0.21/0.52  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.21/0.52  SPASS derived 844 clauses, backtracked 0 clauses, performed 0 splits and kept 215 clauses.
% 0.21/0.52  SPASS allocated 64434 KBytes.
% 0.21/0.52  SPASS spent	0:00:00.15 on the problem.
% 0.21/0.52  		0:00:00.04 for the input.
% 0.21/0.52  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.52  		0:00:00.01 for inferences.
% 0.21/0.52  		0:00:00.00 for the backtracking.
% 0.21/0.52  		0:00:00.08 for the reduction.
% 0.21/0.52  
% 0.21/0.52  
% 0.21/0.52  Here is a proof with depth 7, length 26 :
% 0.21/0.52  % SZS output start Refutation
% See solution above
% 0.21/0.52  Formulae used in the proof : p39d_1 prove_p39d left_identity left_inverse associativity symmetry_of_glb symmetry_of_lub lub_absorbtion monotony_glb1 monotony_glb2
% 0.21/0.52  
%------------------------------------------------------------------------------