TSTP Solution File: LCL109-4 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : LCL109-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 11:29:24 EDT 2023

% Result   : Unsatisfiable 7.41s 2.62s
% Output   : Refutation 7.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   27 (  15 unt;   8 typ;   0 def)
%            Number of atoms       :   23 (  18 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  120 (   6   ~;   4   |;   0   &; 110   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   32 (   0   ^;  32   !;   0   ?;  32   :)

% Comments : 
%------------------------------------------------------------------------------
thf(big_V_type,type,
    big_V: $i > $i > $i ).

thf(implies_type,type,
    implies: $i > $i > $i ).

thf(x_type,type,
    x: $i ).

thf(y_type,type,
    y: $i ).

thf(truth_type,type,
    truth: $i ).

thf(not_type,type,
    not: $i > $i ).

thf(big_hat_type,type,
    big_hat: $i > $i > $i ).

thf(ordered_type,type,
    ordered: $i > $i > $o ).

thf(1,negated_conjecture,
    ( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
   != truth ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mv_4) ).

thf(10,plain,
    ( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
   != truth ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( ordered @ A @ B )
      | ( ( implies @ A @ B )
        = truth ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order_definition1) ).

thf(25,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ordered @ A @ B )
      | ( ( implies @ A @ B )
        = truth ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( implies @ truth @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).

thf(13,plain,
    ! [A: $i] :
      ( ( implies @ truth @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( implies @ ( implies @ A @ B ) @ B )
      = ( implies @ ( implies @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ( implies @ ( implies @ A @ B ) @ B )
      = ( implies @ ( implies @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( big_hat @ A @ B )
      = ( not @ ( big_V @ ( not @ A ) @ ( not @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big_hat_definition) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ( big_hat @ A @ B )
      = ( not @ ( big_V @ ( not @ A ) @ ( not @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) )
      = truth ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).

thf(19,plain,
    ! [B: $i,A: $i] :
      ( ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) )
      = truth ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) )
      = truth ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_2) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) )
      = truth ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( ( implies @ A @ B )
       != truth )
      | ( ordered @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order_definition2) ).

thf(28,plain,
    ! [B: $i,A: $i] :
      ( ( ( implies @ A @ B )
       != truth )
      | ( ordered @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

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

thf(21,plain,
    ! [B: $i,A: $i] :
      ( ( big_V @ A @ B )
      = ( implies @ ( implies @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(640,plain,
    $false,
    inference(e,[status(thm)],[10,25,13,17,23,19,15,28,21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : LCL109-4 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n025.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 16:40:34 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.91/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.09/1.03  % [INFO] 	 Parsing done (121ms). 
% 1.09/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.26  % [INFO] 	 eprover registered as external prover. 
% 1.71/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 1.71/1.26  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.32  % [INFO] 	 Found a conjecture and 8 axioms. Running axiom selection ... 
% 1.87/1.34  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 1.87/1.35  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.87/1.36  % [INFO] 	 Type checking passed. 
% 1.87/1.36  % [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 ... 
% 7.41/2.62  % External prover 'e' found a proof!
% 7.41/2.62  % [INFO] 	 Killing All external provers ... 
% 7.41/2.62  % Time passed: 2083ms (effective reasoning time: 1576ms)
% 7.41/2.62  % 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)>
% 7.41/2.62  % Axioms used in derivation (8): partial_order_definition1, wajsberg_3, big_V_definition, wajsberg_1, big_hat_definition, wajsberg_2, partial_order_definition2, wajsberg_4
% 7.41/2.62  % No. of inferences in proof: 19
% 7.41/2.62  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2083 ms resp. 1576 ms w/o parsing
% 7.41/2.64  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.41/2.64  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------