%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM640^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 10:44:59 EDT 2024

% Result   : Theorem 2.39s 1.72s
% Output   : Refutation 2.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   15 (  10 unt;   5 typ;   0 def)
%            Number of atoms       :   10 (   9 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   58 (   4   ~;   0   |;   0   &;  54   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 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(suc_type,type,
    suc: nat > nat ).

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

thf(1,conjecture,
    ( ( suc @ ( pl @ x @ y ) )
    = ( pl @ x @ ( suc @ y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4f) ).

thf(2,negated_conjecture,
    ( ( suc @ ( pl @ x @ y ) )
   != ( pl @ x @ ( suc @ y ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(4,plain,
    ( ( suc @ ( pl @ x @ y ) )
   != ( pl @ x @ ( suc @ y ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ( ( pl @ x @ ( suc @ y ) )
   != ( suc @ ( pl @ x @ y ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(3,axiom,
    ! [A: nat,B: nat] :
      ( ( pl @ A @ ( suc @ B ) )
      = ( suc @ ( pl @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4b) ).

thf(6,plain,
    ! [A: nat,B: nat] :
      ( ( pl @ A @ ( suc @ B ) )
      = ( suc @ ( pl @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,plain,
    ! [B: nat,A: nat] :
      ( ( pl @ A @ ( suc @ B ) )
      = ( suc @ ( pl @ A @ B ) ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(8,plain,
    ! [B: nat,A: nat] :
      ( ( pl @ A @ ( suc @ B ) )
      = ( suc @ ( pl @ A @ B ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(9,plain,
    ( ( suc @ ( pl @ x @ y ) )
   != ( suc @ ( pl @ x @ y ) ) ),
    inference(rewrite,[status(thm)],[5,8]) ).

thf(10,plain,
    $false,
    inference(simp,[status(thm)],[9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : NUM640^1 : TPTP v8.1.2. Released v3.7.0.
% 0.02/0.12  % Command  : run_Leo-III %s %d
% 0.13/0.32  % Computer : n025.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 300
% 0.13/0.32  % DateTime : Mon May  6 20:01:54 EDT 2024
% 0.13/0.32  % CPUTime  : 
% 0.98/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.17/1.07  % [INFO] 	 Parsing done (131ms). 
% 1.17/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.63/1.34  % [INFO] 	 nitpick registered as external prover. 
% 1.63/1.35  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.40  % [INFO] 	 Found a conjecture and 1 axioms. Running axiom selection ... 
% 1.77/1.43  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.77/1.45  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.77/1.45  % [INFO] 	 Type checking passed. 
% 1.77/1.46  % [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 ... 
% 2.39/1.71  % [INFO] 	 Killing All external provers ... 
% 2.39/1.71  % Time passed: 1251ms (effective reasoning time: 622ms)
% 2.39/1.71  % 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)>
% 2.39/1.72  % Axioms used in derivation (1): satz4b
% 2.39/1.72  % No. of inferences in proof: 10
% 2.39/1.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1251 ms resp. 622 ms w/o parsing
% 2.39/1.74  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.39/1.74  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------