TSTP Solution File: NUM664^1 by Leo-III-SAT---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM664^1 : 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 10:45:06 EDT 2024

% Result   : Theorem 3.27s 1.76s
% Output   : Refutation 3.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   29 (  11 unt;   5 typ;   0 def)
%            Number of atoms       :   48 (  10 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  111 (  21   ~;  10   |;   0   &;  72   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 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   :   18 (   0   ^  18   !;   0   ?;  18   :)

% 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(less_type,type,
    less: nat > nat > $o ).

thf(3,axiom,
    less @ x @ y,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).

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

thf(6,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( less @ A @ B )
     => ( ( less @ B @ C )
       => ( less @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).

thf(13,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( less @ A @ B )
     => ( ( less @ B @ C )
       => ( less @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(14,plain,
    ! [A: nat,B: nat] :
      ( ( less @ A @ B )
     => ! [C: nat] :
          ( ( less @ B @ C )
         => ( less @ A @ C ) ) ),
    inference(miniscope,[status(thm)],[13]) ).

thf(15,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ~ ( less @ A @ B )
      | ~ ( less @ B @ C )
      | ( less @ A @ C ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(1,conjecture,
    less @ x @ z,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16b) ).

thf(2,negated_conjecture,
    ~ ( less @ x @ z ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ( less @ x @ z ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(23,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ~ ( less @ A @ B )
      | ~ ( less @ B @ C )
      | ( ( less @ A @ C )
       != ( less @ x @ z ) ) ),
    inference(paramod_ordered,[status(thm)],[15,7]) ).

thf(24,plain,
    ! [A: nat] :
      ( ~ ( less @ x @ A )
      | ~ ( less @ A @ z ) ),
    inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( x )),bind(B,$thf( B )),bind(C,$thf( z ))]]) ).

thf(41,plain,
    ! [A: nat] :
      ( ~ ( less @ x @ A )
      | ~ ( less @ A @ z ) ),
    inference(simp,[status(thm)],[24]) ).

thf(66,plain,
    ! [A: nat] :
      ( ~ ( less @ A @ z )
      | ( ( less @ x @ y )
       != ( less @ x @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[8,41]) ).

thf(67,plain,
    ~ ( less @ y @ z ),
    inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( y ))]]) ).

thf(4,axiom,
    ( ~ ( less @ y @ z )
   => ( y = z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).

thf(9,plain,
    ( ~ ( less @ y @ z )
   => ( y = z ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,plain,
    ( ( less @ y @ z )
    | ( y = z ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(11,plain,
    ( ( z = y )
    | ( less @ y @ z ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(16,plain,
    ( ( less @ x @ z )
   != ( less @ x @ y ) ),
    inference(paramod_ordered,[status(thm)],[8,7]) ).

thf(17,plain,
    ( ( x != x )
    | ( z != y ) ),
    inference(simp,[status(thm)],[16]) ).

thf(18,plain,
    z != y,
    inference(simp,[status(thm)],[17]) ).

thf(19,plain,
    less @ y @ z,
    inference(simplifyReflect,[status(thm)],[11,18]) ).

thf(113,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[67,19]) ).

thf(114,plain,
    $false,
    inference(simp,[status(thm)],[113]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM664^1 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n025.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May  6 19:39:24 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.82/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.96  % [INFO] 	 Parsing done (110ms). 
% 1.18/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.44/1.17  % [INFO] 	 nitpick registered as external prover. 
% 1.44/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.21  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 1.71/1.23  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.77/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.77/1.25  % [INFO] 	 Type checking passed. 
% 1.77/1.25  % [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 ... 
% 3.27/1.76  % [INFO] 	 Killing All external provers ... 
% 3.27/1.76  % Time passed: 1231ms (effective reasoning time: 785ms)
% 3.27/1.76  % 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)>
% 3.27/1.76  % Axioms used in derivation (3): l, satz15, k
% 3.27/1.76  % No. of inferences in proof: 24
% 3.27/1.76  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1231 ms resp. 785 ms w/o parsing
% 3.27/1.79  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.27/1.79  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------