TSTP Solution File: NUM741^1 by Leo-III---1.7.10

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : NUM741^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 08:00:41 EDT 2024

% Result   : Theorem 5.38s 2.22s
% Output   : Refutation 5.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   25 (  12 unt;   9 typ;   0 def)
%            Number of atoms       :   22 (   4 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  138 (   2   ~;   0   |;   0   &; 130   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   24 (   0   ^  24   !;   0   ?;  24   :)

% Comments : 
%------------------------------------------------------------------------------
thf(frac_type,type,
    frac: $tType ).

thf(x_type,type,
    x: frac ).

thf(y_type,type,
    y: frac ).

thf(z_type,type,
    z: frac ).

thf(nat_type,type,
    nat: $tType ).

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

thf(ts_type,type,
    ts: nat > nat > nat ).

thf(num_type,type,
    num: frac > nat ).

thf(den_type,type,
    den: frac > nat ).

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

thf(10,plain,
    less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ts @ ( ts @ A @ B ) @ C )
      = ( ts @ A @ ( ts @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz31) ).

thf(21,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ts @ ( ts @ A @ B ) @ C )
      = ( ts @ A @ ( ts @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1,conjecture,
    less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz50) ).

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

thf(9,plain,
    ~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( less @ ( ts @ A @ C ) @ ( ts @ B @ C ) )
     => ( less @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz33c) ).

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

thf(7,axiom,
    ! [A: nat,B: nat] :
      ( ( ts @ A @ B )
      = ( ts @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).

thf(18,plain,
    ! [A: nat,B: nat] :
      ( ( ts @ A @ B )
      = ( ts @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(4,axiom,
    less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).

thf(11,plain,
    less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( less @ A @ B )
     => ( ( less @ C @ D )
       => ( less @ ( ts @ A @ C ) @ ( ts @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz34a) ).

thf(15,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( less @ A @ B )
     => ( ( less @ C @ D )
       => ( less @ ( ts @ A @ C ) @ ( ts @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(345,plain,
    $false,
    inference(e,[status(thm)],[10,21,9,12,18,11,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM741^1 : TPTP v8.1.2. Released v3.7.0.
% 0.14/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n010.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon May  6 12:31:54 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.94/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.31/0.98  % [INFO] 	 Parsing done (121ms). 
% 1.31/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.26  % [INFO] 	 Found a conjecture and 6 axioms. Running axiom selection ... 
% 1.91/1.28  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 1.91/1.31  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.91/1.31  % [INFO] 	 Type checking passed. 
% 1.91/1.31  % [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 ... 
% 5.38/2.22  % External prover 'e' found a proof!
% 5.38/2.22  % [INFO] 	 Killing All external provers ... 
% 5.38/2.22  % Time passed: 1689ms (effective reasoning time: 1225ms)
% 5.38/2.22  % 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)>
% 5.38/2.22  % Axioms used in derivation (6): satz29, satz33c, satz31, l, satz34a, k
% 5.38/2.22  % No. of inferences in proof: 16
% 5.38/2.22  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1689 ms resp. 1225 ms w/o parsing
% 5.38/2.25  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.38/2.25  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------