%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NUM660^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 01:35:41 EDT 2024

% Result   : Theorem 2.34s 1.48s
% Output   : Refutation 2.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   23 (   7 unt;   5 typ;   0 def)
%            Number of atoms       :   31 (  10 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   64 (  15   ~;   4   |;   0   &;  38   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 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   :    8 (   0   ^   8   !;   0   ?;   8   :)

% 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(4,axiom,
    ! [A: nat,B: nat] :
      ( ( more @ A @ B )
     => ( less @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz11) ).

thf(12,plain,
    ! [A: nat,B: nat] :
      ( ( more @ A @ B )
     => ( less @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13,plain,
    ! [B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ( less @ B @ A ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(1,conjecture,
    ( ~ ( less @ y @ x )
   => ( y = x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).

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

thf(5,plain,
    ~ ( ~ ( less @ y @ x )
     => ( y = x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ~ ( less @ y @ x ),
    inference(cnf,[status(esa)],[5]) ).

thf(15,plain,
    ! [B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ( ( less @ B @ A )
       != ( less @ y @ x ) ) ),
    inference(paramod_ordered,[status(thm)],[13,7]) ).

thf(16,plain,
    ~ ( more @ x @ y ),
    inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).

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

thf(9,plain,
    ( ~ ( more @ x @ y )
   => ( x = y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,plain,
    ( ( more @ x @ y )
    | ( x = y ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(11,plain,
    ( ( y = x )
    | ( more @ x @ y ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(6,plain,
    y != x,
    inference(cnf,[status(esa)],[5]) ).

thf(8,plain,
    y != x,
    inference(lifteq,[status(thm)],[6]) ).

thf(14,plain,
    more @ x @ y,
    inference(simplifyReflect,[status(thm)],[11,8]) ).

thf(19,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[16,14]) ).

thf(20,plain,
    $false,
    inference(simp,[status(thm)],[19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : NUM660^1 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n003.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Mon May 20 05:54:54 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.96/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/0.96  % [INFO] 	 Parsing done (93ms). 
% 1.19/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.43/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.62/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.21  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 1.73/1.23  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 1.82/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.82/1.24  % [INFO] 	 Type checking passed. 
% 1.82/1.24  % [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 ... 
% 2.34/1.48  % [INFO] 	 Killing All external provers ... 
% 2.34/1.48  % Time passed: 942ms (effective reasoning time: 507ms)
% 2.34/1.48  % 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)>
% 2.34/1.48  % Axioms used in derivation (2): satz11, m
% 2.34/1.48  % No. of inferences in proof: 18
% 2.34/1.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 942 ms resp. 507 ms w/o parsing
% 2.53/1.54  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.53/1.55  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------