TSTP Solution File: GRP185-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP185-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 11:46:12 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% 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    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),least_upper_bound(multiply(a,b),identity)),
    file('GRP185-3.p',unknown),
    [] ).

cnf(2,axiom,
    equal(multiply(identity,u),u),
    file('GRP185-3.p',unknown),
    [] ).

cnf(6,axiom,
    equal(least_upper_bound(u,v),least_upper_bound(v,u)),
    file('GRP185-3.p',unknown),
    [] ).

cnf(8,axiom,
    equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(u,least_upper_bound(v,w))),
    file('GRP185-3.p',unknown),
    [] ).

cnf(12,axiom,
    equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
    file('GRP185-3.p',unknown),
    [] ).

cnf(13,axiom,
    equal(multiply(u,least_upper_bound(v,w)),least_upper_bound(multiply(u,v),multiply(u,w))),
    file('GRP185-3.p',unknown),
    [] ).

cnf(15,axiom,
    equal(multiply(least_upper_bound(u,v),w),least_upper_bound(multiply(u,w),multiply(v,w))),
    file('GRP185-3.p',unknown),
    [] ).

cnf(17,plain,
    ~ equal(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(b,least_upper_bound(multiply(a,b),least_upper_bound(identity,multiply(a,identity))))),least_upper_bound(identity,multiply(a,b))),
    inference(rew,[status(thm),theory(equality)],[8,1,6,2,15,13]),
    [iquote('0:Rew:8.0,1.0,6.0,1.0,2.0,1.0,15.0,1.0,6.0,1.0,2.0,1.0,15.0,1.0,13.0,1.0,6.0,1.0')] ).

cnf(29,plain,
    equal(greatest_lower_bound(u,least_upper_bound(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[6,12]),
    [iquote('0:SpR:6.0,12.0')] ).

cnf(58,plain,
    equal(greatest_lower_bound(u,least_upper_bound(v,least_upper_bound(w,u))),u),
    inference(spr,[status(thm),theory(equality)],[8,29]),
    [iquote('0:SpR:8.0,29.0')] ).

cnf(61,plain,
    equal(least_upper_bound(least_upper_bound(u,v),w),least_upper_bound(v,least_upper_bound(u,w))),
    inference(spr,[status(thm),theory(equality)],[6,8]),
    [iquote('0:SpR:6.0,8.0')] ).

cnf(64,plain,
    equal(least_upper_bound(u,least_upper_bound(v,w)),least_upper_bound(v,least_upper_bound(u,w))),
    inference(rew,[status(thm),theory(equality)],[8,61]),
    [iquote('0:Rew:8.0,61.0')] ).

cnf(65,plain,
    ~ equal(greatest_lower_bound(least_upper_bound(identity,multiply(a,b)),least_upper_bound(b,least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(a,identity))))),least_upper_bound(identity,multiply(a,b))),
    inference(rew,[status(thm),theory(equality)],[64,17]),
    [iquote('0:Rew:64.0,17.0')] ).

cnf(98,plain,
    equal(greatest_lower_bound(u,least_upper_bound(v,least_upper_bound(u,w))),u),
    inference(spr,[status(thm),theory(equality)],[6,58]),
    [iquote('0:SpR:6.0,58.0')] ).

cnf(219,plain,
    equal(greatest_lower_bound(least_upper_bound(u,v),least_upper_bound(w,least_upper_bound(u,least_upper_bound(v,x)))),least_upper_bound(u,v)),
    inference(spr,[status(thm),theory(equality)],[8,98]),
    [iquote('0:SpR:8.0,98.0')] ).

cnf(230,plain,
    $false,
    inference(unc,[status(thm)],[219,65]),
    [iquote('0:UnC:219.0,65.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP185-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n013.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 : Mon Jun 13 06:02:29 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 173 clauses, backtracked 0 clauses, performed 0 splits and kept 57 clauses.
% 0.19/0.42  SPASS allocated 63302 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.19/0.42  		0:00:00.03 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.01 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 4, length 16 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : prove_p22b left_identity symmetry_of_lub associativity_of_lub glb_absorbtion monotony_lub1 monotony_lub2
% 0.19/0.42  
%------------------------------------------------------------------------------