TSTP Solution File: LAT143-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LAT143-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 06:49:14 EDT 2022

% Result   : Unsatisfiable 3.20s 3.39s
% Output   : Refutation 3.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   49 (  49 unt;   0 nHn;  49 RR)
%            Number of literals    :   49 (   0 equ;   4 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    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(join(meet(u,v),meet(v,join(meet(u,v),meet(w,join(u,v))))),join(meet(u,v),meet(v,w))),
    file('LAT143-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),meet(a,join(meet(a,b),meet(a,c)))),
    file('LAT143-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(meet(u,join(u,v)),u),
    file('LAT143-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(join(u,meet(u,v)),u),
    file('LAT143-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(meet(u,v),meet(v,u)),
    file('LAT143-1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(join(u,v),join(v,u)),
    file('LAT143-1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(meet(meet(u,v),w),meet(u,meet(v,w))),
    file('LAT143-1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(join(join(u,v),w),join(u,join(v,w))),
    file('LAT143-1.p',unknown),
    [] ).

cnf(20,plain,
    equal(meet(u,join(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[8,5]),
    [iquote('0:SpR:8.0,5.0')] ).

cnf(28,plain,
    equal(join(u,meet(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[7,6]),
    [iquote('0:SpR:7.0,6.0')] ).

cnf(39,plain,
    equal(meet(meet(u,v),u),meet(u,v)),
    inference(spr,[status(thm),theory(equality)],[6,20]),
    [iquote('0:SpR:6.0,20.0')] ).

cnf(42,plain,
    equal(meet(u,meet(u,v)),meet(u,v)),
    inference(rew,[status(thm),theory(equality)],[7,39]),
    [iquote('0:Rew:7.0,39.0')] ).

cnf(46,plain,
    equal(meet(meet(u,v),v),meet(u,v)),
    inference(spr,[status(thm),theory(equality)],[28,20]),
    [iquote('0:SpR:28.0,20.0')] ).

cnf(50,plain,
    equal(join(join(u,v),v),join(u,v)),
    inference(spr,[status(thm),theory(equality)],[20,28]),
    [iquote('0:SpR:20.0,28.0')] ).

cnf(52,plain,
    equal(meet(u,meet(v,u)),meet(v,u)),
    inference(rew,[status(thm),theory(equality)],[7,46]),
    [iquote('0:Rew:7.0,46.0')] ).

cnf(54,plain,
    equal(join(u,join(v,u)),join(v,u)),
    inference(rew,[status(thm),theory(equality)],[8,50]),
    [iquote('0:Rew:8.0,50.0')] ).

cnf(67,plain,
    equal(meet(join(u,v),join(u,join(v,w))),join(u,v)),
    inference(spr,[status(thm),theory(equality)],[10,5]),
    [iquote('0:SpR:10.0,5.0')] ).

cnf(68,plain,
    equal(join(u,join(v,w)),join(w,join(u,v))),
    inference(spr,[status(thm),theory(equality)],[10,8]),
    [iquote('0:SpR:10.0,8.0')] ).

cnf(71,plain,
    equal(meet(u,join(v,join(w,u))),u),
    inference(spr,[status(thm),theory(equality)],[10,20]),
    [iquote('0:SpR:10.0,20.0')] ).

cnf(74,plain,
    equal(join(u,join(meet(u,v),w)),join(u,w)),
    inference(spr,[status(thm),theory(equality)],[6,10]),
    [iquote('0:SpR:6.0,10.0')] ).

cnf(140,plain,
    equal(meet(u,join(v,join(u,w))),u),
    inference(spr,[status(thm),theory(equality)],[8,71]),
    [iquote('0:SpR:8.0,71.0')] ).

cnf(159,plain,
    equal(join(meet(u,v),meet(u,meet(v,w))),meet(u,v)),
    inference(spr,[status(thm),theory(equality)],[9,6]),
    [iquote('0:SpR:9.0,6.0')] ).

cnf(160,plain,
    equal(meet(u,meet(v,w)),meet(w,meet(u,v))),
    inference(spr,[status(thm),theory(equality)],[9,7]),
    [iquote('0:SpR:9.0,7.0')] ).

cnf(164,plain,
    equal(meet(u,meet(v,join(w,meet(u,v)))),meet(u,v)),
    inference(spr,[status(thm),theory(equality)],[9,20]),
    [iquote('0:SpR:9.0,20.0')] ).

cnf(340,plain,
    equal(join(u,join(v,w)),join(w,join(v,u))),
    inference(spr,[status(thm),theory(equality)],[8,68]),
    [iquote('0:SpR:8.0,68.0')] ).

cnf(493,plain,
    equal(meet(meet(u,v),join(u,w)),meet(u,v)),
    inference(spr,[status(thm),theory(equality)],[74,140]),
    [iquote('0:SpR:74.0,140.0')] ).

cnf(521,plain,
    equal(meet(u,meet(v,join(u,w))),meet(u,v)),
    inference(rew,[status(thm),theory(equality)],[9,493]),
    [iquote('0:Rew:9.0,493.0')] ).

cnf(915,plain,
    equal(meet(u,meet(v,w)),meet(w,meet(v,u))),
    inference(spr,[status(thm),theory(equality)],[7,160]),
    [iquote('0:SpR:7.0,160.0')] ).

cnf(1765,plain,
    equal(meet(join(u,v),join(v,u)),join(u,v)),
    inference(spr,[status(thm),theory(equality)],[54,67]),
    [iquote('0:SpR:54.0,67.0')] ).

cnf(2479,plain,
    equal(join(meet(u,v),meet(v,u)),meet(u,v)),
    inference(spr,[status(thm),theory(equality)],[52,159]),
    [iquote('0:SpR:52.0,159.0')] ).

cnf(2574,plain,
    equal(join(meet(u,join(v,w)),meet(v,u)),meet(u,join(v,w))),
    inference(spr,[status(thm),theory(equality)],[521,28]),
    [iquote('0:SpR:521.0,28.0')] ).

cnf(2655,plain,
    equal(join(meet(u,v),meet(v,join(u,w))),meet(v,join(u,w))),
    inference(rew,[status(thm),theory(equality)],[8,2574]),
    [iquote('0:Rew:8.0,2574.0')] ).

cnf(2656,plain,
    ~ equal(meet(a,join(meet(a,b),meet(c,join(a,b)))),meet(a,join(meet(a,b),meet(a,c)))),
    inference(rew,[status(thm),theory(equality)],[2655,2]),
    [iquote('0:Rew:2655.0,2.0')] ).

cnf(3038,plain,
    equal(meet(join(u,v),meet(join(v,u),w)),meet(join(u,v),w)),
    inference(spr,[status(thm),theory(equality)],[1765,9]),
    [iquote('0:SpR:1765.0,9.0')] ).

cnf(3051,plain,
    equal(meet(join(u,v),meet(join(v,u),w)),meet(w,join(v,u))),
    inference(spr,[status(thm),theory(equality)],[1765,915]),
    [iquote('0:SpR:1765.0,915.0')] ).

cnf(3139,plain,
    equal(meet(join(u,v),w),meet(w,join(v,u))),
    inference(rew,[status(thm),theory(equality)],[3038,3051]),
    [iquote('0:Rew:3038.0,3051.0')] ).

cnf(3189,plain,
    equal(join(meet(u,v),join(meet(v,u),w)),join(meet(u,v),w)),
    inference(spr,[status(thm),theory(equality)],[2479,10]),
    [iquote('0:SpR:2479.0,10.0')] ).

cnf(3205,plain,
    equal(join(meet(u,v),join(meet(v,u),w)),join(w,meet(v,u))),
    inference(spr,[status(thm),theory(equality)],[2479,340]),
    [iquote('0:SpR:2479.0,340.0')] ).

cnf(3289,plain,
    equal(join(meet(u,v),w),join(w,meet(v,u))),
    inference(rew,[status(thm),theory(equality)],[3189,3205]),
    [iquote('0:Rew:3189.0,3205.0')] ).

cnf(5713,plain,
    equal(join(meet(u,join(v,meet(w,u))),meet(w,u)),meet(u,join(v,meet(w,u)))),
    inference(spr,[status(thm),theory(equality)],[164,28]),
    [iquote('0:SpR:164.0,28.0')] ).

cnf(5852,plain,
    equal(join(meet(u,v),meet(v,join(meet(u,v),w))),meet(v,join(w,meet(u,v)))),
    inference(rew,[status(thm),theory(equality)],[3139,5713,3289]),
    [iquote('0:Rew:3139.0,5713.0,3289.0,5713.0')] ).

cnf(5853,plain,
    equal(meet(u,join(meet(v,join(w,u)),meet(w,u))),join(meet(w,u),meet(u,v))),
    inference(rew,[status(thm),theory(equality)],[5852,1]),
    [iquote('0:Rew:5852.0,1.0')] ).

cnf(5886,plain,
    equal(meet(u,join(meet(v,u),meet(join(v,u),w))),join(meet(v,u),meet(u,w))),
    inference(rew,[status(thm),theory(equality)],[3289,5853]),
    [iquote('0:Rew:3289.0,5853.0')] ).

cnf(6220,plain,
    equal(meet(u,join(meet(u,v),meet(join(v,u),w))),join(meet(u,v),meet(u,w))),
    inference(spr,[status(thm),theory(equality)],[7,5886]),
    [iquote('0:SpR:7.0,5886.0')] ).

cnf(10130,plain,
    equal(meet(u,join(meet(u,v),meet(u,w))),join(meet(u,v),meet(u,w))),
    inference(spr,[status(thm),theory(equality)],[6220,42]),
    [iquote('0:SpR:6220.0,42.0')] ).

cnf(10259,plain,
    equal(meet(u,join(meet(u,v),meet(w,join(u,v)))),join(meet(u,v),meet(u,w))),
    inference(spr,[status(thm),theory(equality)],[3139,6220]),
    [iquote('0:SpR:3139.0,6220.0')] ).

cnf(10333,plain,
    ~ equal(meet(a,join(meet(a,b),meet(c,join(a,b)))),join(meet(a,b),meet(a,c))),
    inference(rew,[status(thm),theory(equality)],[10130,2656]),
    [iquote('0:Rew:10130.0,2656.0')] ).

cnf(10349,plain,
    ~ equal(join(meet(a,b),meet(a,c)),join(meet(a,b),meet(a,c))),
    inference(rew,[status(thm),theory(equality)],[10259,10333]),
    [iquote('0:Rew:10259.0,10333.0')] ).

cnf(10350,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[10349]),
    [iquote('0:Obv:10349.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LAT143-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n020.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Thu Jun 30 13:08:45 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 3.20/3.39  
% 3.20/3.39  SPASS V 3.9 
% 3.20/3.39  SPASS beiseite: Proof found.
% 3.20/3.39  % SZS status Theorem
% 3.20/3.39  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 3.20/3.39  SPASS derived 6647 clauses, backtracked 0 clauses, performed 0 splits and kept 1093 clauses.
% 3.20/3.39  SPASS allocated 73059 KBytes.
% 3.20/3.39  SPASS spent	0:00:02.99 on the problem.
% 3.20/3.39  		0:00:00.04 for the input.
% 3.20/3.39  		0:00:00.00 for the FLOTTER CNF translation.
% 3.20/3.39  		0:00:00.06 for inferences.
% 3.20/3.39  		0:00:00.00 for the backtracking.
% 3.20/3.39  		0:00:02.87 for the reduction.
% 3.20/3.39  
% 3.20/3.39  
% 3.20/3.39  Here is a proof with depth 5, length 49 :
% 3.20/3.39  % SZS output start Refutation
% See solution above
% 3.20/3.39  Formulae used in the proof : equation_H24 prove_H15 absorption1 absorption2 commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join
% 3.20/3.39  
%------------------------------------------------------------------------------