TSTP Solution File: SEU304+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU304+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 : Tue Jul 19 14:36:04 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   14
% Syntax   : Number of clauses     :   33 (  14 unt;  13 nHn;  33 RR)
%            Number of literals    :   96 (   0 equ;  52 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    meet_commutative(skc8),
    file('SEU304+1.p',unknown),
    [] ).

cnf(2,axiom,
    meet_absorbing(skc8),
    file('SEU304+1.p',unknown),
    [] ).

cnf(3,axiom,
    latt_str(skc8),
    file('SEU304+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ empty_carrier(skc8),
    file('SEU304+1.p',unknown),
    [] ).

cnf(15,axiom,
    element(skc10,the_carrier(skc8)),
    file('SEU304+1.p',unknown),
    [] ).

cnf(16,axiom,
    element(skc9,the_carrier(skc8)),
    file('SEU304+1.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ latt_str(u)
    | meet_semilatt_str(u) ),
    file('SEU304+1.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ latt_str(u)
    | join_semilatt_str(u) ),
    file('SEU304+1.p',unknown),
    [] ).

cnf(35,axiom,
    ~ below(skc8,meet_commut(skc8,skc9,skc10),skc9),
    file('SEU304+1.p',unknown),
    [] ).

cnf(56,axiom,
    ( ~ meet_semilatt_str(u)
    | ~ meet_commutative(u)
    | ~ element(v,the_carrier(u))
    | ~ element(w,the_carrier(u))
    | empty_carrier(u)
    | element(meet_commut(u,w,v),the_carrier(u)) ),
    file('SEU304+1.p',unknown),
    [] ).

cnf(57,axiom,
    ( ~ join_semilatt_str(u)
    | ~ element(v,the_carrier(u))
    | ~ element(w,the_carrier(u))
    | ~ equal(join(u,w,v),v)
    | empty_carrier(u)
    | below(u,w,v) ),
    file('SEU304+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ meet_semilatt_str(u)
    | ~ meet_commutative(u)
    | ~ element(v,the_carrier(u))
    | ~ element(w,the_carrier(u))
    | empty_carrier(u)
    | equal(meet(u,w,v),meet_commut(u,w,v)) ),
    file('SEU304+1.p',unknown),
    [] ).

cnf(60,axiom,
    ( ~ latt_str(u)
    | ~ meet_absorbing(u)
    | ~ element(v,the_carrier(u))
    | ~ element(w,the_carrier(u))
    | empty_carrier(u)
    | equal(join(u,meet(u,v,w),w),w) ),
    file('SEU304+1.p',unknown),
    [] ).

cnf(61,axiom,
    ( ~ meet_semilatt_str(u)
    | ~ meet_commutative(u)
    | ~ element(v,the_carrier(u))
    | ~ element(w,the_carrier(u))
    | empty_carrier(u)
    | equal(meet_commut(u,w,v),meet_commut(u,v,w)) ),
    file('SEU304+1.p',unknown),
    [] ).

cnf(69,plain,
    meet_semilatt_str(skc8),
    inference(res,[status(thm),theory(equality)],[3,25]),
    [iquote('0:Res:3.0,25.0')] ).

cnf(70,plain,
    join_semilatt_str(skc8),
    inference(res,[status(thm),theory(equality)],[3,26]),
    [iquote('0:Res:3.0,26.0')] ).

cnf(91,plain,
    ( ~ meet_absorbing(skc8)
    | ~ latt_str(skc8)
    | ~ element(u,the_carrier(skc8))
    | equal(join(skc8,meet(skc8,u,skc9),skc9),skc9)
    | empty_carrier(skc8) ),
    inference(res,[status(thm),theory(equality)],[16,60]),
    [iquote('0:Res:16.0,60.2')] ).

cnf(95,plain,
    ( ~ meet_commutative(skc8)
    | ~ meet_semilatt_str(skc8)
    | ~ element(u,the_carrier(skc8))
    | element(meet_commut(skc8,skc9,u),the_carrier(skc8))
    | empty_carrier(skc8) ),
    inference(res,[status(thm),theory(equality)],[16,56]),
    [iquote('0:Res:16.0,56.2')] ).

cnf(100,plain,
    ( ~ meet_commutative(skc8)
    | ~ meet_semilatt_str(skc8)
    | ~ element(u,the_carrier(skc8))
    | equal(meet_commut(skc8,u,skc9),meet_commut(skc8,skc9,u))
    | empty_carrier(skc8) ),
    inference(res,[status(thm),theory(equality)],[16,61]),
    [iquote('0:Res:16.0,61.3')] ).

cnf(102,plain,
    ( ~ meet_commutative(skc8)
    | ~ meet_semilatt_str(skc8)
    | ~ element(u,the_carrier(skc8))
    | equal(meet(skc8,u,skc9),meet_commut(skc8,u,skc9))
    | empty_carrier(skc8) ),
    inference(res,[status(thm),theory(equality)],[16,59]),
    [iquote('0:Res:16.0,59.3')] ).

cnf(150,plain,
    ( ~ element(u,the_carrier(skc8))
    | element(meet_commut(skc8,skc9,u),the_carrier(skc8)) ),
    inference(mrr,[status(thm)],[95,1,69,9]),
    [iquote('0:MRR:95.0,95.1,95.4,1.0,69.0,9.0')] ).

cnf(170,plain,
    ( ~ element(u,the_carrier(skc8))
    | equal(meet(skc8,u,skc9),meet_commut(skc8,u,skc9)) ),
    inference(mrr,[status(thm)],[102,1,69,9]),
    [iquote('0:MRR:102.0,102.1,102.4,1.0,69.0,9.0')] ).

cnf(173,plain,
    ( ~ element(u,the_carrier(skc8))
    | equal(meet_commut(skc8,u,skc9),meet_commut(skc8,skc9,u)) ),
    inference(mrr,[status(thm)],[100,1,69,9]),
    [iquote('0:MRR:100.0,100.1,100.4,1.0,69.0,9.0')] ).

cnf(177,plain,
    ( ~ meet_absorbing(skc8)
    | ~ latt_str(skc8)
    | ~ element(u,the_carrier(skc8))
    | equal(join(skc8,meet_commut(skc8,u,skc9),skc9),skc9)
    | empty_carrier(skc8) ),
    inference(rew,[status(thm),theory(equality)],[170,91]),
    [iquote('0:Rew:170.1,91.3')] ).

cnf(178,plain,
    ( ~ element(u,the_carrier(skc8))
    | equal(join(skc8,meet_commut(skc8,u,skc9),skc9),skc9) ),
    inference(mrr,[status(thm)],[177,2,3,9]),
    [iquote('0:MRR:177.0,177.1,177.4,2.0,3.0,9.0')] ).

cnf(229,plain,
    equal(join(skc8,meet_commut(skc8,skc10,skc9),skc9),skc9),
    inference(res,[status(thm),theory(equality)],[15,178]),
    [iquote('0:Res:15.0,178.0')] ).

cnf(232,plain,
    equal(meet_commut(skc8,skc10,skc9),meet_commut(skc8,skc9,skc10)),
    inference(res,[status(thm),theory(equality)],[15,173]),
    [iquote('0:Res:15.0,173.0')] ).

cnf(248,plain,
    element(meet_commut(skc8,skc9,skc10),the_carrier(skc8)),
    inference(res,[status(thm),theory(equality)],[15,150]),
    [iquote('0:Res:15.0,150.0')] ).

cnf(257,plain,
    equal(join(skc8,meet_commut(skc8,skc9,skc10),skc9),skc9),
    inference(rew,[status(thm),theory(equality)],[232,229]),
    [iquote('0:Rew:232.0,229.0')] ).

cnf(431,plain,
    ( ~ join_semilatt_str(skc8)
    | ~ element(skc9,the_carrier(skc8))
    | ~ element(meet_commut(skc8,skc9,skc10),the_carrier(skc8))
    | ~ equal(skc9,skc9)
    | empty_carrier(skc8)
    | below(skc8,meet_commut(skc8,skc9,skc10),skc9) ),
    inference(spl,[status(thm),theory(equality)],[257,57]),
    [iquote('0:SpL:257.0,57.3')] ).

cnf(432,plain,
    ( ~ join_semilatt_str(skc8)
    | ~ element(skc9,the_carrier(skc8))
    | ~ element(meet_commut(skc8,skc9,skc10),the_carrier(skc8))
    | empty_carrier(skc8)
    | below(skc8,meet_commut(skc8,skc9,skc10),skc9) ),
    inference(obv,[status(thm),theory(equality)],[431]),
    [iquote('0:Obv:431.3')] ).

cnf(433,plain,
    ( ~ element(skc9,the_carrier(skc8))
    | ~ element(meet_commut(skc8,skc9,skc10),the_carrier(skc8))
    | empty_carrier(skc8)
    | below(skc8,meet_commut(skc8,skc9,skc10),skc9) ),
    inference(ssi,[status(thm)],[432,2,1,3,70,69]),
    [iquote('0:SSi:432.0,2.0,1.0,3.0,70.0,69.0')] ).

cnf(434,plain,
    $false,
    inference(mrr,[status(thm)],[433,16,248,9,35]),
    [iquote('0:MRR:433.0,433.1,433.2,433.3,16.0,248.0,9.0,35.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU304+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sun Jun 19 18:26:04 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.20/0.49  
% 0.20/0.49  SPASS V 3.9 
% 0.20/0.49  SPASS beiseite: Proof found.
% 0.20/0.49  % SZS status Theorem
% 0.20/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.49  SPASS derived 273 clauses, backtracked 4 clauses, performed 1 splits and kept 227 clauses.
% 0.20/0.49  SPASS allocated 98011 KBytes.
% 0.20/0.49  SPASS spent	0:00:00.13 on the problem.
% 0.20/0.49  		0:00:00.04 for the input.
% 0.20/0.49  		0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.49  		0:00:00.00 for inferences.
% 0.20/0.49  		0:00:00.00 for the backtracking.
% 0.20/0.49  		0:00:00.01 for the reduction.
% 0.20/0.49  
% 0.20/0.49  
% 0.20/0.49  Here is a proof with depth 3, length 33 :
% 0.20/0.49  % SZS output start Refutation
% See solution above
% 0.20/0.49  Formulae used in the proof : t23_lattices dt_l3_lattices dt_k4_lattices d3_lattices redefinition_k4_lattices d8_lattices existence_m1_subset_1 commutativity_k4_lattices
% 0.20/0.49  
%------------------------------------------------------------------------------