%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYN318+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 : Tue May 21 08:11:30 EDT 2024

% Result   : Theorem 2.72s 1.55s
% Output   : Refutation 2.72s
% 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       :   19 (   0 equ;   0 cnn)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :   32 (   2   ~;   0   |;   0   &;  15   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :    9 (   0   ^   6   !;   3   ?;   9   :)

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

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

thf(p_type,type,
    p: $o ).

thf(1,conjecture,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( big_f @ B )
         => ( ( big_f @ A )
           => ( big_g @ B ) ) )
     => ( p
       => ! [B: $i] :
            ( ( big_f @ B )
           => ( big_g @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_2_4) ).

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

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

thf(19,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SYN318+1 : TPTP v8.2.0. Released v2.0.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon May 20 14:39:38 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.85/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/0.94  % [INFO] 	 Parsing done (86ms). 
% 1.20/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.49/1.15  % [INFO] 	 eprover registered as external prover. 
% 1.49/1.15  % [INFO] 	 cvc4 registered as external prover. 
% 1.49/1.15  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.20  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.76/1.22  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.76/1.22  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.84/1.23  % [INFO] 	 Type checking passed. 
% 1.84/1.23  % [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 ... 
% 2.72/1.55  % External prover 'e' found a proof!
% 2.72/1.55  % [INFO] 	 Killing All external provers ... 
% 2.72/1.55  % Time passed: 1021ms (effective reasoning time: 591ms)
% 2.72/1.55  % 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)>
% 2.72/1.55  % Axioms used in derivation (0): 
% 2.72/1.55  % No. of inferences in proof: 4
% 2.72/1.55  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1021 ms resp. 591 ms w/o parsing
% 2.72/1.56  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.72/1.56  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------