%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : NUM654^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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  7 08:00:22 EDT 2024

% Result   : Theorem 2.67s 1.70s
% Output   : Refutation 2.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   15 (   4 unt;   5 typ;   0 def)
%            Number of atoms       :   16 (   5 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   39 (  13   ~;   0   |;   0   &;  18   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :    5 (   0   ^   5   !;   0   ?;   5   :)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $tType ).

thf(x_type,type,
    x: nat ).

thf(y_type,type,
    y: nat ).

thf(more_type,type,
    more: nat > nat > $o ).

thf(less_type,type,
    less: nat > nat > $o ).

thf(1,conjecture,
    ( ~ ( less @ x @ y )
   => ( x = y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10e) ).

thf(2,negated_conjecture,
    ~ ( ~ ( less @ x @ y )
     => ( x = y ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ( ~ ( less @ x @ y )
     => ( x = y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(3,axiom,
    ~ ( more @ x @ y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).

thf(10,plain,
    ~ ( more @ x @ y ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $o] :
      ( ~ ~ A
     => A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',et) ).

thf(12,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( more @ A @ B )
       => ( less @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a) ).

thf(13,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( more @ A @ B )
       => ( less @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(16,plain,
    $false,
    inference(cvc4,[status(thm)],[6,10,12,13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUM654^1 : TPTP v8.1.2. Released v3.7.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n007.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  6 12:35:39 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.91/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.21/1.03  % [INFO] 	 Parsing done (141ms). 
% 1.21/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.29  % [INFO] 	 eprover registered as external prover. 
% 1.67/1.29  % [INFO] 	 cvc4 registered as external prover. 
% 1.67/1.29  % [INFO] 	 Scanning for conjecture ... 
% 1.67/1.34  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.85/1.37  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.92/1.38  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.92/1.38  % [INFO] 	 Type checking passed. 
% 1.92/1.39  % [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 ... 
% 2.67/1.70  % External prover 'cvc4' found a proof!
% 2.67/1.70  % [INFO] 	 Killing All external provers ... 
% 2.67/1.70  % Time passed: 1174ms (effective reasoning time: 657ms)
% 2.67/1.70  % 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)>
% 2.67/1.70  % Axioms used in derivation (3): n, et, satz10a
% 2.67/1.70  % No. of inferences in proof: 10
% 2.67/1.70  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1174 ms resp. 657 ms w/o parsing
% 2.67/1.73  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.67/1.73  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------