%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SYN319+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.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 12:28:21 EDT 2023

% Result   : Theorem 2.64s 1.67s
% Output   : Refutation 2.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of formulae    :    7 (   1 unt;   3 typ;   0 def)
%            Number of atoms       :   37 (   0 equ;   0 cnn)
%            Maximal formula atoms :   12 (   9 avg)
%            Number of connectives :   74 (   5   ~;   6   |;   6   &;  36   @)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   12 (   0   ^;   6   !;   6   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
thf(big_f_type,type,
    big_f: $i > $o ).

thf(big_g_type,type,
    big_g: $i > $o ).

thf(big_h_type,type,
    big_h: $i > $o ).

thf(1,conjecture,
    ? [A: $i,B: $i] :
    ! [C: $i,D: $i] :
      ( ( ( ( big_f @ B )
         => ( big_g @ C ) )
       => ( ( big_g @ A )
          & ~ ( big_f @ C ) ) )
     => ( ( ( ( big_f @ A )
            | ( big_g @ A ) )
         => ( big_h @ A ) )
       => ( ( big_h @ D )
          & ( ( big_h @ B )
           => ( ( ( big_f @ D )
                | ( big_g @ D ) )
             => ( big_h @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_2_5) ).

thf(2,negated_conjecture,
    ~ ? [A: $i,B: $i] :
      ! [C: $i,D: $i] :
        ( ( ( ( big_f @ B )
           => ( big_g @ C ) )
         => ( ( big_g @ A )
            & ~ ( big_f @ C ) ) )
       => ( ( ( ( big_f @ A )
              | ( big_g @ A ) )
           => ( big_h @ A ) )
         => ( ( big_h @ D )
            & ( ( big_h @ B )
             => ( ( ( big_f @ D )
                  | ( big_g @ D ) )
               => ( big_h @ D ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ? [A: $i,B: $i] :
      ! [C: $i,D: $i] :
        ( ( ( ( big_f @ B )
           => ( big_g @ C ) )
         => ( ( big_g @ A )
            & ~ ( big_f @ C ) ) )
       => ( ( ( ( big_f @ A )
              | ( big_g @ A ) )
           => ( big_h @ A ) )
         => ( ( big_h @ D )
            & ( ( big_h @ B )
             => ( ( ( big_f @ D )
                  | ( big_g @ D ) )
               => ( big_h @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(21,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYN319+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.38  % Computer : n013.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Thu May 18 19:32:51 EDT 2023
% 0.17/0.38  % CPUTime  : 
% 1.06/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.29/1.05  % [INFO] 	 Parsing done (115ms). 
% 1.29/1.06  % [INFO] 	 Running in sequential loop mode. 
% 1.56/1.27  % [INFO] 	 eprover registered as external prover. 
% 1.56/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 1.56/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.33  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.97/1.36  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.97/1.36  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.97/1.36  % [INFO] 	 Type checking passed. 
% 1.97/1.36  % [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 ... 
% 2.64/1.67  % External prover 'e' found a proof!
% 2.64/1.67  % [INFO] 	 Killing All external provers ... 
% 2.64/1.67  % Time passed: 1100ms (effective reasoning time: 604ms)
% 2.64/1.67  % 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)>
% 2.64/1.67  % Axioms used in derivation (0): 
% 2.64/1.67  % No. of inferences in proof: 4
% 2.64/1.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1100 ms resp. 604 ms w/o parsing
% 2.64/1.69  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.64/1.69  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------