TSTP Solution File: LAT250-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LAT250-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 06:49:46 EDT 2022

% Result   : Unsatisfiable 0.70s 0.88s
% Output   : Refutation 0.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   35 (  31 unt;   0 nHn;  35 RR)
%            Number of literals    :   41 (   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    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(meet(u,join(v,meet(u,join(w,meet(u,v))))),meet(u,join(v,w))),
    file('LAT250-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(meet(b,a),a),
    file('LAT250-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(join(complement(b),complement(a)),complement(a)),
    file('LAT250-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(meet(u,join(u,v)),u),
    file('LAT250-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(join(u,meet(u,v)),u),
    file('LAT250-1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(meet(u,v),meet(v,u)),
    file('LAT250-1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(join(u,v),join(v,u)),
    file('LAT250-1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(meet(meet(u,v),w),meet(u,meet(v,w))),
    file('LAT250-1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(join(join(u,v),w),join(u,join(v,w))),
    file('LAT250-1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(join(u,complement(u)),one),
    file('LAT250-1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(meet(u,complement(u)),zero),
    file('LAT250-1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ equal(join(u,v),one)
    | ~ equal(meet(u,v),zero)
    | equal(complement(u),v) ),
    file('LAT250-1.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(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(434,plain,
    equal(meet(u,join(complement(u),meet(u,join(v,zero)))),meet(u,join(complement(u),v))),
    inference(spr,[status(thm),theory(equality)],[13,1]),
    [iquote('0:SpR:13.0,1.0')] ).

cnf(486,plain,
    equal(meet(u,join(complement(u),meet(u,v))),meet(u,join(complement(u),v))),
    inference(rew,[status(thm),theory(equality)],[24,434]),
    [iquote('0:Rew:24.0,434.0')] ).

cnf(597,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(669,plain,
    equal(meet(a,complement(b)),zero),
    inference(spr,[status(thm),theory(equality)],[282,597]),
    [iquote('0:SpR:282.0,597.0')] ).

cnf(6187,plain,
    equal(meet(a,join(complement(a),complement(b))),meet(a,join(complement(a),zero))),
    inference(spr,[status(thm),theory(equality)],[669,486]),
    [iquote('0:SpR:669.0,486.0')] ).

cnf(6221,plain,
    equal(meet(a,join(complement(b),complement(a))),zero),
    inference(rew,[status(thm),theory(equality)],[9,6187,13,36]),
    [iquote('0:Rew:9.0,6187.0,13.0,6187.0,36.0,6187.0,9.0,6187.0')] ).

cnf(6308,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)],[6221,14]),
    [iquote('0:SpL:6221.0,14.1')] ).

cnf(6334,plain,
    ( ~ equal(join(a,join(complement(b),complement(a))),one)
    | equal(join(complement(b),complement(a)),complement(a)) ),
    inference(obv,[status(thm),theory(equality)],[6308]),
    [iquote('0:Obv:6308.1')] ).

cnf(6335,plain,
    ( ~ equal(one,one)
    | equal(join(complement(b),complement(a)),complement(a)) ),
    inference(rew,[status(thm),theory(equality)],[212,6334]),
    [iquote('0:Rew:212.0,6334.0')] ).

cnf(6336,plain,
    equal(join(complement(b),complement(a)),complement(a)),
    inference(obv,[status(thm),theory(equality)],[6335]),
    [iquote('0:Obv:6335.0')] ).

cnf(6337,plain,
    $false,
    inference(mrr,[status(thm)],[6336,3]),
    [iquote('0:MRR:6336.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LAT250-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n027.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 28 18:26:19 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.70/0.88  
% 0.70/0.88  SPASS V 3.9 
% 0.70/0.88  SPASS beiseite: Proof found.
% 0.70/0.88  % SZS status Theorem
% 0.70/0.88  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.70/0.88  SPASS derived 4510 clauses, backtracked 0 clauses, performed 0 splits and kept 505 clauses.
% 0.70/0.88  SPASS allocated 67554 KBytes.
% 0.70/0.88  SPASS spent	0:00:00.51 on the problem.
% 0.70/0.88  		0:00:00.04 for the input.
% 0.70/0.88  		0:00:00.00 for the FLOTTER CNF translation.
% 0.70/0.88  		0:00:00.03 for inferences.
% 0.70/0.88  		0:00:00.00 for the backtracking.
% 0.70/0.88  		0:00:00.41 for the reduction.
% 0.70/0.88  
% 0.70/0.88  
% 0.70/0.88  Here is a proof with depth 5, length 35 :
% 0.70/0.88  % SZS output start Refutation
% See solution above
% 0.70/0.88  Formulae used in the proof : equation_H68 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
% 0.70/0.88  
%------------------------------------------------------------------------------