TSTP Solution File: NUM682^1 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 10:45:11 EDT 2024

% Result   : Theorem 4.71s 2.07s
% Output   : Refutation 4.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   44 (  14 unt;   7 typ;   0 def)
%            Number of atoms       :   85 (  24 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  260 (  50   ~;  20   |;   0   &; 168   @)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   49 (   0   ^  49   !;   0   ?;  49   :)

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

thf(more_type,type,
    more: nat > nat > $o ).

thf(6,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( more @ A @ B )
     => ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).

thf(22,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( more @ A @ B )
     => ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(23,plain,
    ! [A: nat,B: nat] :
      ( ( more @ A @ B )
     => ! [C: nat] : ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
    inference(miniscope,[status(thm)],[22]) ).

thf(24,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
    inference(cnf,[status(esa)],[23]) ).

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

thf(10,plain,
    less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ! [A: nat,B: nat] :
      ~ ( ( ( A = B )
         => ~ ( more @ A @ B ) )
       => ~ ~ ( ( ( more @ A @ B )
               => ~ ( less @ A @ B ) )
             => ~ ( ( less @ A @ B )
                 => ( A != B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10b) ).

thf(12,plain,
    ! [A: nat,B: nat] :
      ~ ( ( ( A = B )
         => ~ ( more @ A @ B ) )
       => ( ( ( more @ A @ B )
           => ~ ( less @ A @ B ) )
         => ~ ( ( less @ A @ B )
             => ( A != B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(13,plain,
    ~ ( ! [A: nat,B: nat] :
          ( ( A = B )
         => ~ ( more @ A @ B ) )
     => ( ! [A: nat,B: nat] :
            ( ( more @ A @ B )
           => ~ ( less @ A @ B ) )
       => ~ ! [A: nat,B: nat] :
              ( ( less @ A @ B )
             => ( A != B ) ) ) ),
    inference(miniscope,[status(thm)],[12]) ).

thf(15,plain,
    ! [B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ~ ( less @ A @ B ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(19,plain,
    ! [B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ~ ( less @ A @ B ) ),
    inference(simp,[status(thm)],[15]) ).

thf(164,plain,
    ! [B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
       != ( less @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[10,19]) ).

thf(165,plain,
    ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ),
    inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( pl @ x @ z )),bind(B,$thf( pl @ y @ z ))]]) ).

thf(338,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ( ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) )
       != ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24,165]) ).

thf(339,plain,
    ~ ( more @ x @ y ),
    inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).

thf(8,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( more @ A @ B )
       => ( less @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10a) ).

thf(30,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( more @ A @ B )
       => ( less @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(31,plain,
    ! [B: nat,A: nat] :
      ( ( A = B )
      | ( more @ A @ B )
      | ( less @ A @ B ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(32,plain,
    ! [B: nat,A: nat] :
      ( ( A = B )
      | ( more @ A @ B )
      | ( less @ A @ B ) ),
    inference(lifteq,[status(thm)],[31]) ).

thf(14,plain,
    ! [B: nat,A: nat] :
      ( ~ ( less @ A @ B )
      | ( A != B ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(17,plain,
    ! [B: nat,A: nat] :
      ( ( A != B )
      | ~ ( less @ A @ B ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(18,plain,
    ! [A: nat] :
      ~ ( less @ A @ A ),
    inference(simp,[status(thm)],[17]) ).

thf(35,plain,
    ! [A: nat] :
      ( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
     != ( less @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[10,18]) ).

thf(36,plain,
    ! [A: nat] :
      ( ( ( pl @ x @ z )
       != A )
      | ( ( pl @ y @ z )
       != A ) ),
    inference(simp,[status(thm)],[35]) ).

thf(37,plain,
    ( ( pl @ y @ z )
   != ( pl @ x @ z ) ),
    inference(simp,[status(thm)],[36]) ).

thf(38,plain,
    ( ( y != x )
    | ( z != z ) ),
    inference(simp,[status(thm)],[37]) ).

thf(39,plain,
    y != x,
    inference(simp,[status(thm)],[38]) ).

thf(86,plain,
    ! [B: nat,A: nat] :
      ( ( more @ A @ B )
      | ( less @ A @ B )
      | ( A != x )
      | ( B != y ) ),
    inference(paramod_ordered,[status(thm)],[32,39]) ).

thf(87,plain,
    ! [A: nat] :
      ( ( more @ A @ y )
      | ( less @ A @ y )
      | ( A != x ) ),
    inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( A )),bind(B,$thf( y ))]]) ).

thf(119,plain,
    ( ( more @ x @ y )
    | ( less @ x @ y ) ),
    inference(simp,[status(thm)],[87]) ).

thf(1,conjecture,
    less @ x @ y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz20c) ).

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

thf(9,plain,
    ~ ( less @ x @ y ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(303,plain,
    ( ( more @ x @ y )
    | $false ),
    inference(rewrite,[status(thm)],[119,9]) ).

thf(304,plain,
    more @ x @ y,
    inference(simp,[status(thm)],[303]) ).

thf(364,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[339,304]) ).

thf(365,plain,
    $false,
    inference(simp,[status(thm)],[364]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n022.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 19:58:54 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.85/0.80  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.06/0.92  % [INFO] 	 Parsing done (114ms). 
% 1.06/0.92  % [INFO] 	 Running in sequential loop mode. 
% 1.48/1.12  % [INFO] 	 nitpick registered as external prover. 
% 1.48/1.13  % [INFO] 	 Scanning for conjecture ... 
% 1.66/1.18  % [INFO] 	 Found a conjecture and 6 axioms. Running axiom selection ... 
% 1.75/1.20  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 1.75/1.22  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.75/1.22  % [INFO] 	 Type checking passed. 
% 1.75/1.22  % [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 ... 
% 4.71/2.07  % [INFO] 	 Killing All external provers ... 
% 4.71/2.07  % Time passed: 1542ms (effective reasoning time: 1142ms)
% 4.71/2.07  % 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)>
% 4.71/2.07  % Axioms used in derivation (4): satz19a, l, satz10b, satz10a
% 4.71/2.07  % No. of inferences in proof: 37
% 4.71/2.07  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1542 ms resp. 1142 ms w/o parsing
% 4.77/2.10  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.77/2.10  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------