%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM674^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 10:45:09 EDT 2024

% Result   : Theorem 2.20s 1.47s
% Output   : Refutation 2.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   14 (   9 unt;   5 typ;   0 def)
%            Number of atoms       :    9 (   8 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   24 (   4   ~;   0   |;   0   &;  20   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0   ^   0   !;   0   ?;   0   :)

% 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(1,conjecture,
    ( ( pl @ z @ x )
    = ( pl @ z @ y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19e) ).

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

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

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

thf(3,axiom,
    x = y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',i) ).

thf(6,plain,
    x = y,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,plain,
    y = x,
    inference(lifteq,[status(thm)],[6]) ).

thf(8,plain,
    ( ( pl @ z @ x )
   != ( pl @ z @ x ) ),
    inference(rewrite,[status(thm)],[5,7]) ).

thf(9,plain,
    $false,
    inference(simp,[status(thm)],[8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM674^1 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n023.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon May  6 19:35:54 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.98/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.07/1.00  % [INFO] 	 Parsing done (122ms). 
% 1.33/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.78/1.23  % [INFO] 	 nitpick registered as external prover. 
% 1.78/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.27  % [INFO] 	 Found a conjecture and 1 axioms. Running axiom selection ... 
% 1.78/1.29  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.78/1.29  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.78/1.30  % [INFO] 	 Type checking passed. 
% 1.78/1.30  % [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 ... 
% 2.20/1.46  % [INFO] 	 Killing All external provers ... 
% 2.20/1.46  % Time passed: 942ms (effective reasoning time: 446ms)
% 2.20/1.46  % 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)>
% 2.20/1.47  % Axioms used in derivation (1): i
% 2.20/1.47  % No. of inferences in proof: 9
% 2.20/1.47  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 942 ms resp. 446 ms w/o parsing
% 2.36/1.48  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.36/1.48  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------