TSTP Solution File: NUM647^1 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM647^1 : TPTP v8.1.2. 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  7 10:45:00 EDT 2024

% Result   : Theorem 2.43s 1.59s
% Output   : Refutation 2.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   22 (  11 unt;   6 typ;   0 def)
%            Number of atoms       :   21 (  20 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   59 (  10   ~;   3   |;   0   &;  44   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   4 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(sk1_type,type,
    sk1: nat > nat > nat ).

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

thf(8,plain,
    ( ( pl @ x @ y )
    = ( pl @ x @ z ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,plain,
    ( ( pl @ x @ z )
    = ( pl @ x @ y ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(5,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B != C )
     => ( ( pl @ A @ B )
       != ( pl @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8) ).

thf(11,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B != C )
     => ( ( pl @ A @ B )
       != ( pl @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(12,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( B = C )
      | ( ( pl @ A @ B )
       != ( pl @ A @ C ) ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(13,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( B = C )
      | ( ( pl @ A @ B )
       != ( pl @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[12]) ).

thf(14,plain,
    ! [B: nat,A: nat] :
      ( ( sk1 @ A @ ( pl @ A @ B ) )
      = B ),
    introduced(tautology,[new_symbols(inverse(pl),[sk1])]) ).

thf(15,plain,
    ! [B: nat,A: nat] :
      ( ( ( sk1 @ A @ ( pl @ x @ y ) )
        = B )
      | ( ( pl @ x @ z )
       != ( pl @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9,14]) ).

thf(16,plain,
    ( ( sk1 @ x @ ( pl @ x @ y ) )
    = z ),
    inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).

thf(17,plain,
    z = y,
    inference(rewrite,[status(thm)],[16,14]) ).

thf(1,conjecture,
    y = z,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8a) ).

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

thf(6,plain,
    y != z,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(18,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[17,7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM647^1 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n003.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  6 19:34:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.96/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.17/1.00  % [INFO] 	 Parsing done (134ms). 
% 1.17/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.25  % [INFO] 	 nitpick registered as external prover. 
% 1.68/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.68/1.30  % [INFO] 	 Found a conjecture and 3 axioms. Running axiom selection ... 
% 1.68/1.32  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.95/1.33  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.95/1.33  % [INFO] 	 Type checking passed. 
% 1.95/1.34  % [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 ... 
% 2.43/1.59  % [INFO] 	 Killing All external provers ... 
% 2.43/1.59  % Time passed: 1056ms (effective reasoning time: 580ms)
% 2.43/1.59  % 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)>
% 2.43/1.59  % Axioms used in derivation (2): i, satz8
% 2.43/1.59  % No. of inferences in proof: 16
% 2.43/1.59  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1056 ms resp. 580 ms w/o parsing
% 2.43/1.62  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.43/1.62  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------