%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : NUM659_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 11:41:42 EDT 2023

% Result   : Theorem 2.48s 1.61s
% Output   : Refutation 2.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   15 (   5 unt;   5 typ;   0 def)
%            Number of atoms       :   15 (   4 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   37 (  12   ~;   0   |;   0   &;  18   @)
%                                         (   0 <=>;   7  =>;   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(less_type,type,
    less: nat > nat > $o ).

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

thf(1,conjecture,
    more @ x @ y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10k) ).

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

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

thf(3,axiom,
    ~ ( ~ ( less @ x @ y )
     => ( x = y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).

thf(7,plain,
    ~ ( ~ ( less @ x @ y )
     => ( x = y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(4,axiom,
    ! [A: $o] :
      ( ~ ~ A
     => A ),
    file('/export/starexec/sandbox/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/sandbox/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)],[6,7,12,13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM659_8 : TPTP v8.1.2. Released v8.0.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n019.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Thu May 18 16:41:13 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/0.98  % [INFO] 	 Parsing done (107ms). 
% 1.20/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.23  % [INFO] 	 eprover registered as external prover. 
% 1.70/1.23  % [INFO] 	 cvc4 registered as external prover. 
% 1.70/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.29  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.77/1.31  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.97/1.32  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 1.97/1.33  % [INFO] 	 Type checking passed. 
% 1.97/1.33  % [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 ... 
% 2.48/1.60  % External prover 'cvc4' found a proof!
% 2.48/1.60  % [INFO] 	 Killing All external provers ... 
% 2.48/1.60  % Time passed: 1077ms (effective reasoning time: 611ms)
% 2.48/1.61  % 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)>
% 2.48/1.61  % Axioms used in derivation (3): n, et, satz10a
% 2.48/1.61  % No. of inferences in proof: 10
% 2.48/1.61  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1077 ms resp. 611 ms w/o parsing
% 2.48/1.63  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.48/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------