TSTP Solution File: LAT037-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LAT037-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 06:48:43 EDT 2022

% Result   : Unsatisfiable 1.18s 1.36s
% Output   : Refutation 1.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of clauses     :   46 (  32 unt;   0 nHn;  46 RR)
%            Number of literals    :   62 (   0 equ;  18 neg)
%            Maximal clause size   :    3 (   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(2,axiom,
    equal(join(meet(u,v),meet(u,w)),meet(u,join(v,w))),
    file('LAT037-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(join(u,n0),u),
    file('LAT037-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(meet(u,n1),u),
    file('LAT037-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(join(u,n1),n1),
    file('LAT037-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ equal(meet(u,v),u)
    | equal(join(u,meet(w,v)),meet(v,join(u,w))) ),
    file('LAT037-1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(join(xx,yy),n1),
    file('LAT037-1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(join(xx,zz),n1),
    file('LAT037-1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(meet(xx,yy),n0),
    file('LAT037-1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(meet(xx,zz),n0),
    file('LAT037-1.p',unknown),
    [] ).

cnf(12,axiom,
    ~ equal(zz,yy),
    file('LAT037-1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(meet(u,u),u),
    file('LAT037-1.p',unknown),
    [] ).

cnf(15,axiom,
    equal(meet(u,join(u,v)),u),
    file('LAT037-1.p',unknown),
    [] ).

cnf(17,axiom,
    equal(meet(u,v),meet(v,u)),
    file('LAT037-1.p',unknown),
    [] ).

cnf(18,axiom,
    equal(join(u,v),join(v,u)),
    file('LAT037-1.p',unknown),
    [] ).

cnf(20,axiom,
    equal(join(join(u,v),w),join(u,join(v,w))),
    file('LAT037-1.p',unknown),
    [] ).

cnf(49,plain,
    equal(join(n1,u),n1),
    inference(spr,[status(thm),theory(equality)],[18,6]),
    [iquote('0:SpR:18.0,6.0')] ).

cnf(50,plain,
    equal(join(n0,u),u),
    inference(spr,[status(thm),theory(equality)],[18,4]),
    [iquote('0:SpR:18.0,4.0')] ).

cnf(52,plain,
    equal(meet(u,join(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[18,15]),
    [iquote('0:SpR:18.0,15.0')] ).

cnf(62,plain,
    equal(meet(n1,u),u),
    inference(spr,[status(thm),theory(equality)],[17,5]),
    [iquote('0:SpR:17.0,5.0')] ).

cnf(114,plain,
    equal(join(xx,join(zz,u)),join(n1,u)),
    inference(spr,[status(thm),theory(equality)],[9,20]),
    [iquote('0:SpR:9.0,20.0')] ).

cnf(115,plain,
    equal(join(xx,join(yy,u)),join(n1,u)),
    inference(spr,[status(thm),theory(equality)],[8,20]),
    [iquote('0:SpR:8.0,20.0')] ).

cnf(126,plain,
    equal(join(xx,join(zz,u)),n1),
    inference(rew,[status(thm),theory(equality)],[49,114]),
    [iquote('0:Rew:49.0,114.0')] ).

cnf(127,plain,
    equal(join(xx,join(yy,u)),n1),
    inference(rew,[status(thm),theory(equality)],[49,115]),
    [iquote('0:Rew:49.0,115.0')] ).

cnf(274,plain,
    equal(join(meet(u,v),meet(w,u)),meet(u,join(v,w))),
    inference(spr,[status(thm),theory(equality)],[17,2]),
    [iquote('0:SpR:17.0,2.0')] ).

cnf(280,plain,
    equal(join(n0,meet(xx,u)),meet(xx,join(zz,u))),
    inference(spr,[status(thm),theory(equality)],[11,2]),
    [iquote('0:SpR:11.0,2.0')] ).

cnf(281,plain,
    equal(join(n0,meet(xx,u)),meet(xx,join(yy,u))),
    inference(spr,[status(thm),theory(equality)],[10,2]),
    [iquote('0:SpR:10.0,2.0')] ).

cnf(303,plain,
    equal(meet(xx,join(zz,u)),meet(xx,u)),
    inference(rew,[status(thm),theory(equality)],[50,280]),
    [iquote('0:Rew:50.0,280.0')] ).

cnf(304,plain,
    equal(meet(xx,join(yy,u)),meet(xx,u)),
    inference(rew,[status(thm),theory(equality)],[50,281]),
    [iquote('0:Rew:50.0,281.0')] ).

cnf(689,plain,
    ( ~ equal(meet(u,yy),u)
    | equal(meet(yy,join(u,xx)),join(u,n0)) ),
    inference(spr,[status(thm),theory(equality)],[10,7]),
    [iquote('0:SpR:10.0,7.1')] ).

cnf(698,plain,
    ( ~ equal(meet(u,v),u)
    | equal(meet(v,join(u,v)),join(u,v)) ),
    inference(spr,[status(thm),theory(equality)],[13,7]),
    [iquote('0:SpR:13.0,7.1')] ).

cnf(714,plain,
    ( ~ equal(meet(u,yy),u)
    | equal(meet(yy,join(u,xx)),u) ),
    inference(rew,[status(thm),theory(equality)],[4,689]),
    [iquote('0:Rew:4.0,689.1')] ).

cnf(716,plain,
    ( ~ equal(meet(u,v),u)
    | equal(join(u,v),v) ),
    inference(rew,[status(thm),theory(equality)],[52,698]),
    [iquote('0:Rew:52.0,698.1')] ).

cnf(6072,plain,
    ( ~ equal(meet(xx,join(zz,u)),xx)
    | equal(join(zz,u),n1) ),
    inference(spr,[status(thm),theory(equality)],[716,126]),
    [iquote('0:SpR:716.1,126.0')] ).

cnf(6073,plain,
    ( ~ equal(meet(xx,join(yy,u)),xx)
    | equal(join(yy,u),n1) ),
    inference(spr,[status(thm),theory(equality)],[716,127]),
    [iquote('0:SpR:716.1,127.0')] ).

cnf(6195,plain,
    ( ~ equal(meet(xx,u),xx)
    | equal(join(zz,u),n1) ),
    inference(rew,[status(thm),theory(equality)],[303,6072]),
    [iquote('0:Rew:303.0,6072.0')] ).

cnf(6197,plain,
    ( ~ equal(meet(xx,u),xx)
    | equal(join(yy,u),n1) ),
    inference(rew,[status(thm),theory(equality)],[304,6073]),
    [iquote('0:Rew:304.0,6073.0')] ).

cnf(8346,plain,
    ( ~ equal(meet(xx,xx),xx)
    | ~ equal(meet(zz,yy),zz)
    | equal(meet(yy,n1),zz) ),
    inference(spr,[status(thm),theory(equality)],[6195,714]),
    [iquote('0:SpR:6195.1,714.1')] ).

cnf(8367,plain,
    ( ~ equal(xx,xx)
    | ~ equal(meet(yy,zz),zz)
    | equal(zz,yy) ),
    inference(rew,[status(thm),theory(equality)],[62,8346,17,13]),
    [iquote('0:Rew:62.0,8346.2,17.0,8346.2,17.0,8346.1,13.0,8346.0')] ).

cnf(8368,plain,
    ( ~ equal(meet(yy,zz),zz)
    | equal(zz,yy) ),
    inference(obv,[status(thm),theory(equality)],[8367]),
    [iquote('0:Obv:8367.0')] ).

cnf(8369,plain,
    ~ equal(meet(yy,zz),zz),
    inference(mrr,[status(thm)],[8368,12]),
    [iquote('0:MRR:8368.1,12.0')] ).

cnf(9209,plain,
    equal(join(meet(zz,u),n0),meet(zz,join(u,xx))),
    inference(spr,[status(thm),theory(equality)],[11,274]),
    [iquote('0:SpR:11.0,274.0')] ).

cnf(9321,plain,
    equal(meet(zz,join(u,xx)),meet(zz,u)),
    inference(rew,[status(thm),theory(equality)],[50,9209,18]),
    [iquote('0:Rew:50.0,9209.0,18.0,9209.0')] ).

cnf(9573,plain,
    ( ~ equal(meet(xx,xx),xx)
    | equal(meet(zz,yy),meet(zz,n1)) ),
    inference(spr,[status(thm),theory(equality)],[6197,9321]),
    [iquote('0:SpR:6197.1,9321.0')] ).

cnf(9600,plain,
    ( ~ equal(xx,xx)
    | equal(meet(yy,zz),zz) ),
    inference(rew,[status(thm),theory(equality)],[17,9573,62,13]),
    [iquote('0:Rew:17.0,9573.1,62.0,9573.1,17.0,9573.1,13.0,9573.0')] ).

cnf(9601,plain,
    equal(meet(yy,zz),zz),
    inference(obv,[status(thm),theory(equality)],[9600]),
    [iquote('0:Obv:9600.0')] ).

cnf(9602,plain,
    $false,
    inference(mrr,[status(thm)],[9601,8369]),
    [iquote('0:MRR:9601.0,8369.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LAT037-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n019.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 : Thu Jun 30 13:11:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.18/1.36  
% 1.18/1.36  SPASS V 3.9 
% 1.18/1.36  SPASS beiseite: Proof found.
% 1.18/1.36  % SZS status Theorem
% 1.18/1.36  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.18/1.36  SPASS derived 6368 clauses, backtracked 0 clauses, performed 0 splits and kept 827 clauses.
% 1.18/1.36  SPASS allocated 69253 KBytes.
% 1.18/1.36  SPASS spent	0:00:00.98 on the problem.
% 1.18/1.36  		0:00:00.03 for the input.
% 1.18/1.36  		0:00:00.00 for the FLOTTER CNF translation.
% 1.18/1.36  		0:00:00.04 for inferences.
% 1.18/1.36  		0:00:00.00 for the backtracking.
% 1.18/1.36  		0:00:00.88 for the reduction.
% 1.18/1.36  
% 1.18/1.36  
% 1.18/1.36  Here is a proof with depth 3, length 46 :
% 1.18/1.36  % SZS output start Refutation
% See solution above
% 1.18/1.36  Formulae used in the proof : dist_meet x_join_0 x_meet_1 x_join_1 modular lhs1 lhs2 lhs3 lhs4 rhs idempotence_of_meet absorption1 commutativity_of_meet commutativity_of_join associativity_of_join
% 1.18/1.36  
%------------------------------------------------------------------------------