%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV427^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n032.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 : Mon Jun 24 16:00:14 EDT 2024

% Result   : Theorem 1.96s 1.37s
% Output   : Refutation 1.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   17 (   3 unt;   0 typ;   0 def)
%            Number of atoms       :   37 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   57 (  10   ~;  11   |;   0   &;  35   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 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   ^  10   !;   2   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
thf(eps_type,type,
    eps: ( $i > $o ) > $i ).

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

thf(q_type,type,
    q: $i > $o ).

thf(4,axiom,
    ! [A: $i] :
      ( ( p @ A )
      | ( q @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pq) ).

thf(10,plain,
    ! [A: $i] :
      ( ( p @ A )
      | ( q @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(11,plain,
    ! [A: $i] :
      ( ( p @ A )
      | ( q @ A ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(13,axiom,
    ? [A: ( $i > $o ) > $i] :
    ! [B: $i > $o] :
      ( ? [C: $i] : ( B @ C )
     => ( B @ ( A @ B ) ) ),
    introduced(axiom_of_choice) ).

thf(14,plain,
    ! [A: $i] :
      ( ~ ( q @ A )
      | ( q @ ( eps @ q ) ) ),
    inference(choice,[status(esa)],[13]) ).

thf(1,conjecture,
    ( ( p @ ( eps @ p ) )
    | ( q @ ( eps @ q ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ( ( p @ ( eps @ p ) )
      | ( q @ ( eps @ q ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ( ( p @ ( eps @ p ) )
      | ( q @ ( eps @ q ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ~ ( q @ ( eps @ q ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(16,plain,
    ! [A: $i] :
      ( ~ ( q @ A )
      | $false ),
    inference(rewrite,[status(thm)],[14,6]) ).

thf(17,plain,
    ! [A: $i] :
      ~ ( q @ A ),
    inference(simp,[status(thm)],[16]) ).

thf(15,plain,
    ! [A: $i] :
      ( ~ ( p @ A )
      | ( p @ ( eps @ p ) ) ),
    inference(choice,[status(esa)],[13]) ).

thf(7,plain,
    ~ ( p @ ( eps @ p ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(19,plain,
    ! [A: $i] :
      ( ~ ( p @ A )
      | $false ),
    inference(rewrite,[status(thm)],[15,7]) ).

thf(20,plain,
    ! [A: $i] :
      ~ ( p @ A ),
    inference(simp,[status(thm)],[19]) ).

thf(22,plain,
    ( $false
    | $false ),
    inference(rewrite,[status(thm)],[11,17,20]) ).

thf(23,plain,
    $false,
    inference(simp,[status(thm)],[22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08  % Problem  : SEV427^1 : TPTP v8.2.0. Released v5.2.0.
% 0.02/0.08  % Command  : run_Leo-III %s %d SAT
% 0.08/0.27  % Computer : n032.cluster.edu
% 0.08/0.27  % Model    : x86_64 x86_64
% 0.08/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27  % Memory   : 8042.1875MB
% 0.08/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27  % CPULimit : 300
% 0.08/0.27  % WCLimit  : 300
% 0.08/0.27  % DateTime : Fri Jun 21 19:23:40 EDT 2024
% 0.08/0.27  % CPUTime  : 
% 0.74/0.73  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 0.99/0.84  % [INFO] 	 Parsing done (108ms). 
% 0.99/0.85  % [INFO] 	 Running in sequential loop mode. 
% 1.26/1.06  % [INFO] 	 nitpick registered as external prover. 
% 1.26/1.06  % [INFO] 	 Scanning for conjecture ... 
% 1.41/1.10  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 1.41/1.12  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.41/1.13  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.41/1.13  % [INFO] 	 Type checking passed. 
% 1.41/1.13  % [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 ... 
% 1.96/1.37  % [INFO] 	 Killing All external provers ... 
% 1.96/1.37  % Time passed: 961ms (effective reasoning time: 516ms)
% 1.96/1.37  % 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)>
% 1.96/1.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 961 ms resp. 516 ms w/o parsing
% 1.96/1.39  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.96/1.39  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------