%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : NUM713_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 11:41:56 EDT 2023

% Result   : Theorem 2.64s 1.53s
% Output   : Refutation 2.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   18 (  11 unt;   6 typ;   0 def)
%            Number of atoms       :   11 (   9 equ;   0 cnn)
%            Maximal formula atoms :    1 (   0 avg)
%            Number of connectives :   65 (  14   ~;   0   |;   0   &;  50   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 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(ts_type,type,
    ts: nat > nat > nat ).

thf(6,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ts @ A @ ( pl @ B @ C ) )
      = ( pl @ ( ts @ A @ B ) @ ( ts @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz30) ).

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

thf(4,axiom,
    ! [A: $o] :
      ( ~ ~ A
     => A ),
    file('/export/starexec/sandbox2/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/sandbox2/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] :
        ( ( ts @ x @ z )
       != ( pl @ ( ts @ y @ z ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz32a) ).

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

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

thf(5,axiom,
    ! [A: nat,B: nat] :
      ( ( ts @ A @ B )
      = ( ts @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).

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

thf(27,plain,
    $false,
    inference(cvc4,[status(thm)],[21,17,12,7,18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : NUM713_8 : TPTP v8.1.2. Released v8.0.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n018.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 17:08:13 EDT 2023
% 0.22/0.36  % CPUTime  : 
% 0.84/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/0.94  % [INFO] 	 Parsing done (107ms). 
% 1.23/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.49/1.14  % [INFO] 	 eprover registered as external prover. 
% 1.49/1.14  % [INFO] 	 cvc4 registered as external prover. 
% 1.49/1.15  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.21  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 1.85/1.23  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.85/1.24  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 1.91/1.24  % [INFO] 	 Type checking passed. 
% 1.91/1.25  % [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 ... 
% 2.49/1.53  % External prover 'cvc4' found a proof!
% 2.64/1.53  % [INFO] 	 Killing All external provers ... 
% 2.64/1.53  % Time passed: 1019ms (effective reasoning time: 580ms)
% 2.64/1.53  % 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)>
% 2.64/1.53  % Axioms used in derivation (4): satz30, et, m, satz29
% 2.64/1.53  % No. of inferences in proof: 12
% 2.64/1.53  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1019 ms resp. 580 ms w/o parsing
% 2.67/1.55  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.67/1.55  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------