TSTP Solution File: LAT254-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LAT254-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 06:49:48 EDT 2022

% Result   : Unsatisfiable 210.85s 211.22s
% Output   : Refutation 210.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   38 (  34 unt;   0 nHn;  38 RR)
%            Number of literals    :   44 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(meet(u,join(meet(u,join(v,meet(u,w))),meet(w,x))),meet(u,join(v,meet(w,join(u,x))))),
    file('LAT254-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(meet(b,a),a),
    file('LAT254-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(join(complement(b),complement(a)),complement(a)),
    file('LAT254-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(meet(u,join(u,v)),u),
    file('LAT254-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(join(u,meet(u,v)),u),
    file('LAT254-1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(meet(u,v),meet(v,u)),
    file('LAT254-1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(join(u,v),join(v,u)),
    file('LAT254-1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(meet(meet(u,v),w),meet(u,meet(v,w))),
    file('LAT254-1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(join(join(u,v),w),join(u,join(v,w))),
    file('LAT254-1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(join(u,complement(u)),one),
    file('LAT254-1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(meet(u,complement(u)),zero),
    file('LAT254-1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ equal(join(u,v),one)
    | ~ equal(meet(u,v),zero)
    | equal(complement(u),v) ),
    file('LAT254-1.p',unknown),
    [] ).

cnf(24,plain,
    equal(join(u,zero),u),
    inference(spr,[status(thm),theory(equality)],[13,7]),
    [iquote('0:SpR:13.0,7.0')] ).

cnf(31,plain,
    equal(meet(u,one),u),
    inference(spr,[status(thm),theory(equality)],[12,6]),
    [iquote('0:SpR:12.0,6.0')] ).

cnf(36,plain,
    equal(join(zero,u),u),
    inference(spr,[status(thm),theory(equality)],[9,24]),
    [iquote('0:SpR:9.0,24.0')] ).

cnf(50,plain,
    equal(meet(zero,u),zero),
    inference(spr,[status(thm),theory(equality)],[36,7]),
    [iquote('0:SpR:36.0,7.0')] ).

cnf(68,plain,
    equal(meet(one,u),u),
    inference(spr,[status(thm),theory(equality)],[8,31]),
    [iquote('0:SpR:8.0,31.0')] ).

cnf(85,plain,
    equal(join(one,u),one),
    inference(spr,[status(thm),theory(equality)],[68,7]),
    [iquote('0:SpR:68.0,7.0')] ).

cnf(100,plain,
    equal(join(u,one),one),
    inference(spr,[status(thm),theory(equality)],[85,9]),
    [iquote('0:SpR:85.0,9.0')] ).

cnf(177,plain,
    equal(join(u,join(complement(u),v)),join(one,v)),
    inference(spr,[status(thm),theory(equality)],[12,11]),
    [iquote('0:SpR:12.0,11.0')] ).

cnf(192,plain,
    equal(join(u,join(complement(u),v)),one),
    inference(rew,[status(thm),theory(equality)],[85,177]),
    [iquote('0:Rew:85.0,177.0')] ).

cnf(212,plain,
    equal(join(u,join(v,complement(u))),one),
    inference(spr,[status(thm),theory(equality)],[9,192]),
    [iquote('0:SpR:9.0,192.0')] ).

cnf(282,plain,
    equal(meet(b,meet(a,u)),meet(a,u)),
    inference(spr,[status(thm),theory(equality)],[2,10]),
    [iquote('0:SpR:2.0,10.0')] ).

cnf(284,plain,
    equal(meet(u,meet(complement(u),v)),meet(zero,v)),
    inference(spr,[status(thm),theory(equality)],[13,10]),
    [iquote('0:SpR:13.0,10.0')] ).

cnf(299,plain,
    equal(meet(u,meet(complement(u),v)),zero),
    inference(rew,[status(thm),theory(equality)],[50,284]),
    [iquote('0:Rew:50.0,284.0')] ).

cnf(448,plain,
    equal(meet(u,join(meet(u,join(v,zero)),meet(complement(u),w))),meet(u,join(v,meet(complement(u),join(u,w))))),
    inference(spr,[status(thm),theory(equality)],[13,1]),
    [iquote('0:SpR:13.0,1.0')] ).

cnf(505,plain,
    equal(meet(u,join(meet(u,v),meet(complement(u),w))),meet(u,join(v,meet(complement(u),join(u,w))))),
    inference(rew,[status(thm),theory(equality)],[24,448]),
    [iquote('0:Rew:24.0,448.0')] ).

cnf(568,plain,
    equal(meet(u,meet(v,complement(u))),zero),
    inference(spr,[status(thm),theory(equality)],[8,299]),
    [iquote('0:SpR:8.0,299.0')] ).

cnf(608,plain,
    equal(meet(a,complement(b)),zero),
    inference(spr,[status(thm),theory(equality)],[568,282]),
    [iquote('0:SpR:568.0,282.0')] ).

cnf(7870,plain,
    equal(meet(u,join(v,meet(complement(u),join(u,one)))),meet(u,join(meet(u,v),complement(u)))),
    inference(spr,[status(thm),theory(equality)],[31,505]),
    [iquote('0:SpR:31.0,505.0')] ).

cnf(7957,plain,
    equal(meet(u,join(complement(u),meet(u,v))),meet(u,join(v,complement(u)))),
    inference(rew,[status(thm),theory(equality)],[68,7870,8,100,9]),
    [iquote('0:Rew:68.0,7870.0,8.0,7870.0,100.0,7870.0,9.0,7870.0')] ).

cnf(108650,plain,
    equal(meet(a,join(complement(b),complement(a))),meet(a,join(complement(a),zero))),
    inference(spr,[status(thm),theory(equality)],[608,7957]),
    [iquote('0:SpR:608.0,7957.0')] ).

cnf(108836,plain,
    equal(meet(a,join(complement(b),complement(a))),zero),
    inference(rew,[status(thm),theory(equality)],[13,108650,36,9]),
    [iquote('0:Rew:13.0,108650.0,36.0,108650.0,9.0,108650.0')] ).

cnf(109235,plain,
    ( ~ equal(join(a,join(complement(b),complement(a))),one)
    | ~ equal(zero,zero)
    | equal(join(complement(b),complement(a)),complement(a)) ),
    inference(spl,[status(thm),theory(equality)],[108836,14]),
    [iquote('0:SpL:108836.0,14.1')] ).

cnf(109358,plain,
    ( ~ equal(join(a,join(complement(b),complement(a))),one)
    | equal(join(complement(b),complement(a)),complement(a)) ),
    inference(obv,[status(thm),theory(equality)],[109235]),
    [iquote('0:Obv:109235.1')] ).

cnf(109359,plain,
    ( ~ equal(one,one)
    | equal(join(complement(b),complement(a)),complement(a)) ),
    inference(rew,[status(thm),theory(equality)],[212,109358]),
    [iquote('0:Rew:212.0,109358.0')] ).

cnf(109360,plain,
    equal(join(complement(b),complement(a)),complement(a)),
    inference(obv,[status(thm),theory(equality)],[109359]),
    [iquote('0:Obv:109359.0')] ).

cnf(109361,plain,
    $false,
    inference(mrr,[status(thm)],[109360,3]),
    [iquote('0:MRR:109360.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LAT254-1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n007.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Thu Jun 30 15:03:53 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 210.85/211.22  
% 210.85/211.22  SPASS V 3.9 
% 210.85/211.22  SPASS beiseite: Proof found.
% 210.85/211.22  % SZS status Theorem
% 210.85/211.22  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 210.85/211.22  SPASS derived 68539 clauses, backtracked 0 clauses, performed 0 splits and kept 7592 clauses.
% 210.85/211.22  SPASS allocated 177796 KBytes.
% 210.85/211.22  SPASS spent	0:3:28.40 on the problem.
% 210.85/211.22  		0:00:00.03 for the input.
% 210.85/211.22  		0:00:00.00 for the FLOTTER CNF translation.
% 210.85/211.22  		0:00:00.60 for inferences.
% 210.85/211.22  		0:00:00.00 for the backtracking.
% 210.85/211.22  		0:3:27.62 for the reduction.
% 210.85/211.22  
% 210.85/211.22  
% 210.85/211.22  Here is a proof with depth 5, length 38 :
% 210.85/211.22  % SZS output start Refutation
% See solution above
% 210.85/211.22  Formulae used in the proof : equation_H79 prove_distributivity_hypothesis prove_distributivity absorption1 absorption2 commutativity_of_meet commutativity_of_join associativity_of_meet associativity_of_join complement_join complement_meet meet_join_complement
% 210.85/211.22  
%------------------------------------------------------------------------------