%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : NUM670_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 01:31:23 EDT 2024

% Result   : Theorem 2.84s 1.57s
% Output   : Refutation 2.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   17 (  11 unt;   5 typ;   0 def)
%            Number of atoms       :   11 (   9 equ;   0 cnn)
%            Maximal formula atoms :    1 (   0 avg)
%            Number of connectives :   61 (  14   ~;   0   |;   0   &;  46   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   5 con; 0-2 aty)
%            Number of variables   :   16 (   0   ^  16   !;   0   ?;  16   :)

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

thf(x_type,type,
    x: nat ).

thf(y_type,type,
    y: nat ).

thf(z_type,type,
    z: nat ).

thf(pl_type,type,
    pl: nat > nat > nat ).

thf(6,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( pl @ ( pl @ A @ B ) @ C )
      = ( pl @ A @ ( pl @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz5) ).

thf(21,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( pl @ ( pl @ A @ B ) @ C )
      = ( pl @ A @ ( pl @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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

thf(17,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(3,axiom,
    ~ ! [A: nat] :
        ( x
       != ( pl @ y @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).

thf(12,plain,
    ~ ! [A: nat] :
        ( x
       != ( pl @ y @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,conjecture,
    ~ ! [A: nat] :
        ( ( pl @ x @ z )
       != ( pl @ ( pl @ y @ z ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).

thf(2,negated_conjecture,
    ~ ~ ! [A: nat] :
          ( ( pl @ x @ z )
         != ( pl @ ( pl @ y @ z ) @ A ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ~ ! [A: nat] :
          ( ( pl @ x @ z )
         != ( pl @ ( pl @ y @ z ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
    ! [A: nat,B: nat] :
      ( ( pl @ A @ B )
      = ( pl @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).

thf(18,plain,
    ! [A: nat,B: nat] :
      ( ( pl @ A @ B )
      = ( pl @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(36,plain,
    $false,
    inference(cvc4,[status(thm)],[21,17,12,7,18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM670_8 : TPTP v8.2.0. Released v8.0.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n017.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May 20 06:09:09 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.94/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.96  % [INFO] 	 Parsing done (94ms). 
% 1.18/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.64/1.16  % [INFO] 	 cvc4 registered as external prover. 
% 1.64/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.64/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 1.86/1.24  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.86/1.25  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 1.86/1.25  % [INFO] 	 Type checking passed. 
% 1.86/1.25  % [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 ... 
% 2.71/1.57  % External prover 'cvc4' found a proof!
% 2.71/1.57  % [INFO] 	 Killing All external provers ... 
% 2.71/1.57  % Time passed: 1043ms (effective reasoning time: 602ms)
% 2.84/1.57  % 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)>
% 2.84/1.57  % Axioms used in derivation (4): satz5, et, m, satz6
% 2.84/1.57  % No. of inferences in proof: 12
% 2.84/1.57  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1043 ms resp. 602 ms w/o parsing
% 2.84/1.59  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.84/1.59  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------