TSTP Solution File: LAT028-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LAT028-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 : Sun Jul 17 06:48:40 EDT 2022

% Result   : Unsatisfiable 0.84s 1.01s
% Output   : Refutation 0.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   35 (  35 unt;   0 nHn;  35 RR)
%            Number of literals    :   35 (   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    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(meet2(u,u),u),
    file('LAT028-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(meet2(u,v),meet2(v,u)),
    file('LAT028-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(meet2(meet2(join(u,v),join(w,v)),v),v),
    file('LAT028-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(join(join(meet2(u,v),meet2(w,v)),v),v),
    file('LAT028-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(meet(a,b),meet2(a,b)),
    file('LAT028-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(join(u,u),u),
    file('LAT028-1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(meet(u,v),meet(v,u)),
    file('LAT028-1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(join(u,v),join(v,u)),
    file('LAT028-1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(meet(meet(join(u,v),join(w,v)),v),v),
    file('LAT028-1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(join(join(meet(u,v),meet(w,v)),v),v),
    file('LAT028-1.p',unknown),
    [] ).

cnf(12,plain,
    equal(join(u,join(meet(v,u),meet(w,u))),u),
    inference(rew,[status(thm),theory(equality)],[9,11]),
    [iquote('0:Rew:9.0,11.0')] ).

cnf(13,plain,
    equal(meet(u,meet(join(v,u),join(w,u))),u),
    inference(rew,[status(thm),theory(equality)],[8,10]),
    [iquote('0:Rew:8.0,10.0')] ).

cnf(14,plain,
    equal(join(u,join(meet2(v,u),meet2(w,u))),u),
    inference(rew,[status(thm),theory(equality)],[9,4]),
    [iquote('0:Rew:9.0,4.0')] ).

cnf(15,plain,
    equal(meet2(u,meet2(join(v,u),join(w,u))),u),
    inference(rew,[status(thm),theory(equality)],[2,3]),
    [iquote('0:Rew:2.0,3.0')] ).

cnf(39,plain,
    equal(join(u,join(meet(v,u),meet(u,w))),u),
    inference(spr,[status(thm),theory(equality)],[8,12]),
    [iquote('0:SpR:8.0,12.0')] ).

cnf(44,plain,
    equal(join(u,meet(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[7,12]),
    [iquote('0:SpR:7.0,12.0')] ).

cnf(139,plain,
    equal(meet(join(meet2(u,v),meet2(w,v)),meet(join(x,join(meet2(u,v),meet2(w,v))),v)),join(meet2(u,v),meet2(w,v))),
    inference(spr,[status(thm),theory(equality)],[14,13]),
    [iquote('0:SpR:14.0,13.0')] ).

cnf(143,plain,
    equal(join(u,join(meet2(v,u),meet2(u,w))),u),
    inference(spr,[status(thm),theory(equality)],[2,14]),
    [iquote('0:SpR:2.0,14.0')] ).

cnf(156,plain,
    equal(meet(join(meet2(u,v),meet2(w,v)),meet(v,join(x,join(meet2(u,v),meet2(w,v))))),join(meet2(u,v),meet2(w,v))),
    inference(rew,[status(thm),theory(equality)],[8,139]),
    [iquote('0:Rew:8.0,139.0')] ).

cnf(235,plain,
    equal(meet2(join(meet(u,v),meet(w,v)),meet2(v,join(x,join(meet(u,v),meet(w,v))))),join(meet(u,v),meet(w,v))),
    inference(spr,[status(thm),theory(equality)],[12,15]),
    [iquote('0:SpR:12.0,15.0')] ).

cnf(242,plain,
    equal(meet2(u,join(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[1,15]),
    [iquote('0:SpR:1.0,15.0')] ).

cnf(270,plain,
    equal(meet2(meet(u,v),v),meet(u,v)),
    inference(spr,[status(thm),theory(equality)],[44,242]),
    [iquote('0:SpR:44.0,242.0')] ).

cnf(275,plain,
    equal(meet2(u,meet(v,u)),meet(v,u)),
    inference(rew,[status(thm),theory(equality)],[2,270]),
    [iquote('0:Rew:2.0,270.0')] ).

cnf(367,plain,
    equal(join(u,join(meet(u,v),meet(u,w))),u),
    inference(spr,[status(thm),theory(equality)],[8,39]),
    [iquote('0:SpR:8.0,39.0')] ).

cnf(711,plain,
    equal(join(u,join(meet2(u,v),meet2(u,w))),u),
    inference(spr,[status(thm),theory(equality)],[2,143]),
    [iquote('0:SpR:2.0,143.0')] ).

cnf(2432,plain,
    equal(meet(join(meet2(u,v),meet2(u,v)),meet(v,u)),join(meet2(u,v),meet2(u,v))),
    inference(spr,[status(thm),theory(equality)],[711,156]),
    [iquote('0:SpR:711.0,156.0')] ).

cnf(2498,plain,
    equal(meet(meet2(u,v),meet(v,u)),meet2(u,v)),
    inference(rew,[status(thm),theory(equality)],[7,2432]),
    [iquote('0:Rew:7.0,2432.0')] ).

cnf(3482,plain,
    equal(meet2(join(meet(u,v),meet(u,v)),meet2(v,u)),join(meet(u,v),meet(u,v))),
    inference(spr,[status(thm),theory(equality)],[367,235]),
    [iquote('0:SpR:367.0,235.0')] ).

cnf(3530,plain,
    equal(meet2(meet2(u,v),meet(v,u)),meet(v,u)),
    inference(rew,[status(thm),theory(equality)],[2,3482,7]),
    [iquote('0:Rew:2.0,3482.0,7.0,3482.0')] ).

cnf(4045,plain,
    equal(meet2(meet(u,v),meet2(v,u)),meet2(v,u)),
    inference(spr,[status(thm),theory(equality)],[2498,275]),
    [iquote('0:SpR:2498.0,275.0')] ).

cnf(4116,plain,
    equal(meet2(meet2(u,v),meet(v,u)),meet2(u,v)),
    inference(rew,[status(thm),theory(equality)],[2,4045]),
    [iquote('0:Rew:2.0,4045.0')] ).

cnf(4117,plain,
    equal(meet(u,v),meet2(v,u)),
    inference(rew,[status(thm),theory(equality)],[3530,4116]),
    [iquote('0:Rew:3530.0,4116.0')] ).

cnf(4132,plain,
    ~ equal(meet2(b,a),meet2(a,b)),
    inference(rew,[status(thm),theory(equality)],[4117,5]),
    [iquote('0:Rew:4117.0,5.0')] ).

cnf(4469,plain,
    ~ equal(meet2(a,b),meet2(a,b)),
    inference(rew,[status(thm),theory(equality)],[2,4132]),
    [iquote('0:Rew:2.0,4132.0')] ).

cnf(4470,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[4469]),
    [iquote('0:Obv:4469.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LAT028-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n017.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 29 23:14:38 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.84/1.01  
% 0.84/1.01  SPASS V 3.9 
% 0.84/1.01  SPASS beiseite: Proof found.
% 0.84/1.01  % SZS status Theorem
% 0.84/1.01  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.84/1.01  SPASS derived 3031 clauses, backtracked 0 clauses, performed 0 splits and kept 441 clauses.
% 0.84/1.01  SPASS allocated 68368 KBytes.
% 0.84/1.01  SPASS spent	0:00:00.64 on the problem.
% 0.84/1.01  		0:00:00.04 for the input.
% 0.84/1.01  		0:00:00.00 for the FLOTTER CNF translation.
% 0.84/1.01  		0:00:00.03 for inferences.
% 0.84/1.01  		0:00:00.00 for the backtracking.
% 0.84/1.01  		0:00:00.55 for the reduction.
% 0.84/1.01  
% 0.84/1.01  
% 0.84/1.01  Here is a proof with depth 4, length 35 :
% 0.84/1.01  % SZS output start Refutation
% See solution above
% 0.84/1.01  Formulae used in the proof : idempotence_of_meet2 commutativity_of_meet2 wal_1_2 wal_2_2 name__dfg idempotence_of_join commutativity_of_meet commutativity_of_join wal_1 wal_2
% 0.84/1.01  
%------------------------------------------------------------------------------