TSTP Solution File: LAT038-1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LAT038-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 11:26:43 EDT 2023

% Result   : Unsatisfiable 3.18s 1.76s
% Output   : Refutation 3.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   43 (  35 unt;   8 typ;   0 def)
%            Number of atoms       :   35 (  34 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  210 (   2   ~;   0   |;   0   &; 208   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   60 (   0   ^;  60   !;   0   ?;  60   :)

% Comments : 
%------------------------------------------------------------------------------
thf(f_type,type,
    f: $i > $i > $i ).

thf(aa_type,type,
    aa: $i ).

thf(dd_type,type,
    dd: $i ).

thf(cc_type,type,
    cc: $i ).

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

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

thf(bb_type,type,
    bb: $i ).

thf(n0_type,type,
    n0: $i ).

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

thf(29,plain,
    ! [B: $i,A: $i] :
      ( ( join @ A @ B )
      = ( join @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(12,axiom,
    ( ( f @ ( join @ aa @ bb ) @ dd )
    = ( f @ ( join @ cc @ bb ) @ dd ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs1) ).

thf(41,plain,
    ( ( f @ ( join @ aa @ bb ) @ dd )
    = ( f @ ( join @ cc @ bb ) @ dd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( f @ n0 @ A )
      = n0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_left_bottom) ).

thf(45,plain,
    ! [A: $i] :
      ( ( f @ n0 @ A )
      = n0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

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

thf(27,plain,
    ! [A: $i] :
      ( ( join @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( f @ ( join @ A @ B ) @ C )
      = ( join @ ( f @ A @ C ) @ ( f @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_left_join) ).

thf(49,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f @ ( join @ A @ B ) @ C )
      = ( join @ ( f @ A @ C ) @ ( f @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(11,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(39,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)],[11]) ).

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

thf(35,plain,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ B )
      = ( meet @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1,negated_conjecture,
    ( ( f @ aa @ dd )
   != ( f @ cc @ dd ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rhs) ).

thf(18,plain,
    ( ( f @ aa @ dd )
   != ( f @ cc @ dd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ ( join @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).

thf(31,plain,
    ! [B: $i,A: $i] :
      ( ( meet @ A @ ( join @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( f @ A @ ( join @ B @ C ) )
      = ( join @ ( f @ A @ B ) @ ( f @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_right_join) ).

thf(43,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( f @ A @ ( join @ B @ C ) )
      = ( join @ ( f @ A @ B ) @ ( f @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(3,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)],[3]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( f @ A @ n0 )
      = n0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_right_bottom) ).

thf(51,plain,
    ! [A: $i] :
      ( ( f @ A @ n0 )
      = n0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(15,axiom,
    ( ( meet @ ( f @ aa @ dd ) @ ( f @ bb @ dd ) )
    = ( meet @ ( f @ cc @ dd ) @ ( f @ bb @ dd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs2) ).

thf(47,plain,
    ( ( meet @ ( f @ aa @ dd ) @ ( f @ bb @ dd ) )
    = ( meet @ ( f @ cc @ dd ) @ ( f @ bb @ dd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(10,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(37,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)],[10]) ).

thf(4,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(25,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)],[4]) ).

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

thf(21,plain,
    ! [A: $i] :
      ( ( meet @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,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(33,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)],[8]) ).

thf(65,plain,
    $false,
    inference(cvc4,[status(thm)],[29,41,45,27,49,39,35,18,31,43,23,51,47,37,25,21,33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LAT038-1 : TPTP v8.1.2. Released v2.4.0.
% 0.15/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n020.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Thu May 18 14:16:48 EDT 2023
% 0.17/0.37  % CPUTime  : 
% 1.00/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.26/0.99  % [INFO] 	 Parsing done (122ms). 
% 1.26/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.71/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.71/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.25  % [INFO] 	 Found a conjecture and 16 axioms. Running axiom selection ... 
% 1.88/1.29  % [INFO] 	 Axiom selection finished. Selected 16 axioms (removed 0 axioms). 
% 1.88/1.31  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.88/1.31  % [INFO] 	 Type checking passed. 
% 2.10/1.31  % [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 ... 
% 3.18/1.75  % External prover 'cvc4' found a proof!
% 3.18/1.75  % [INFO] 	 Killing All external provers ... 
% 3.18/1.75  % Time passed: 1217ms (effective reasoning time: 749ms)
% 3.18/1.75  % 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)>
% 3.18/1.76  % Axioms used in derivation (16): f_on_right_bottom, commutativity_of_join, absorption1, lhs1, f_on_right_join, commutativity_of_meet, lhs2, associativity_of_join, idempotence_of_meet, dist_meet, dist_join, f_on_left_join, associativity_of_meet, f_on_left_bottom, idempotence_of_join, absorption2
% 3.18/1.76  % No. of inferences in proof: 35
% 3.18/1.76  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1217 ms resp. 749 ms w/o parsing
% 3.39/1.79  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.39/1.79  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------