TSTP Solution File: LAT040-1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT040-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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  : 300s
% DateTime : Fri May 19 11:26:44 EDT 2023

% Result   : Unsatisfiable 2.57s 1.72s
% Output   : Refutation 2.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   32 (  27 unt;   5 typ;   0 def)
%            Number of atoms       :   27 (  26 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  130 (   2   ~;   0   |;   0   &; 128   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   44 (   0   ^;  44   !;   0   ?;  44   :)

% Comments : 
%------------------------------------------------------------------------------
thf(yy_type,type,
    yy: $i ).

thf(zz_type,type,
    zz: $i ).

thf(meet_type,type,
    meet: $i > $i > $i ).

thf(join_type,type,
    join: $i > $i > $i ).

thf(xx_type,type,
    xx: $i ).

thf(1,negated_conjecture,
    yy != zz,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rhs) ).

thf(14,plain,
    yy != zz,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( meet @ ( meet @ A @ B ) @ C )
      = ( meet @ A @ ( meet @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).

thf(29,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( meet @ ( meet @ A @ B ) @ C )
      = ( meet @ A @ ( meet @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( meet @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).

thf(17,plain,
    ! [A: $i] :
      ( ( meet @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( join @ A @ B )
      = ( join @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ( join @ A @ B )
      = ( join @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(13,axiom,
    ( ( meet @ xx @ yy )
    = ( meet @ xx @ zz ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs2) ).

thf(39,plain,
    ( ( meet @ xx @ yy )
    = ( meet @ xx @ zz ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( meet @ A @ ( join @ B @ C ) )
      = ( join @ ( meet @ A @ B ) @ ( meet @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_meet) ).

thf(35,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( meet @ A @ ( join @ B @ C ) )
      = ( join @ ( meet @ A @ B ) @ ( meet @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( join @ ( join @ A @ B ) @ C )
      = ( join @ A @ ( join @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).

thf(31,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( join @ ( join @ A @ B ) @ C )
      = ( join @ A @ ( join @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( join @ A @ ( meet @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ( join @ A @ ( meet @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( join @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).

thf(19,plain,
    ! [A: $i] :
      ( ( join @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(12,axiom,
    ( ( join @ xx @ yy )
    = ( join @ xx @ zz ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs1) ).

thf(37,plain,
    ( ( join @ xx @ yy )
    = ( join @ xx @ zz ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(6,axiom,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ B )
      = ( meet @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ B )
      = ( meet @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ ( join @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ ( join @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( join @ A @ ( meet @ B @ C ) )
      = ( meet @ ( join @ A @ B ) @ ( join @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_join) ).

thf(33,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( join @ A @ ( meet @ B @ C ) )
      = ( meet @ ( join @ A @ B ) @ ( join @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(41,plain,
    $false,
    inference(e,[status(thm)],[14,29,17,27,39,35,31,23,19,37,25,21,33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem  : LAT040-1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n017.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu May 18 13:46:31 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.88/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.24/1.06  % [INFO] 	 Parsing done (123ms). 
% 1.30/1.07  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.30  % [INFO] 	 eprover registered as external prover. 
% 1.65/1.31  % [INFO] 	 cvc4 registered as external prover. 
% 1.65/1.31  % [INFO] 	 Scanning for conjecture ... 
% 1.85/1.36  % [INFO] 	 Found a conjecture and 12 axioms. Running axiom selection ... 
% 1.85/1.38  % [INFO] 	 Axiom selection finished. Selected 12 axioms (removed 0 axioms). 
% 1.85/1.39  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.85/1.40  % [INFO] 	 Type checking passed. 
% 1.85/1.40  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 2.57/1.72  % External prover 'e' found a proof!
% 2.57/1.72  % [INFO] 	 Killing All external provers ... 
% 2.57/1.72  % Time passed: 1155ms (effective reasoning time: 646ms)
% 2.57/1.72  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 2.57/1.72  % Axioms used in derivation (12): commutativity_of_join, absorption1, associativity_of_meet, lhs1, commutativity_of_meet, lhs2, associativity_of_join, idempotence_of_meet, dist_meet, dist_join, idempotence_of_join, absorption2
% 2.57/1.72  % No. of inferences in proof: 27
% 2.57/1.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1155 ms resp. 646 ms w/o parsing
% 2.77/1.75  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.77/1.75  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------