TSTP Solution File: NUM672^1 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM672^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.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 10:45:08 EDT 2024

% Result   : Theorem 3.15s 1.80s
% Output   : Refutation 3.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   32 (  12 unt;   7 typ;   0 def)
%            Number of atoms       :   44 (   3 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :  152 (   9   ~;   6   |;   0   &; 130   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   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   :   36 (   0   ^  36   !;   0   ?;  36   :)

% 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(1,conjecture,
    less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19c) ).

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

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

thf(3,axiom,
    less @ x @ y,
    file('/export/starexec/sandbox/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] :
      ( ( less @ A @ B )
     => ( more @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz12) ).

thf(14,plain,
    ! [A: nat,B: nat] :
      ( ( less @ A @ B )
     => ( more @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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

thf(20,plain,
    ! [B: nat,A: nat] :
      ( ( more @ B @ A )
      | ( ( less @ x @ y )
       != ( less @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8,15]) ).

thf(21,plain,
    more @ y @ x,
    inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).

thf(5,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(11,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)],[5]) ).

thf(12,plain,
    ! [A: nat,B: nat] :
      ( ( more @ A @ B )
     => ! [C: nat] : ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
    inference(miniscope,[status(thm)],[11]) ).

thf(13,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(33,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) )
      | ( ( more @ y @ x )
       != ( more @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[21,13]) ).

thf(34,plain,
    ! [A: nat] : ( more @ ( pl @ y @ A ) @ ( pl @ x @ A ) ),
    inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( y )),bind(B,$thf( x ))]]) ).

thf(35,plain,
    ! [A: nat] : ( more @ ( pl @ y @ A ) @ ( pl @ x @ A ) ),
    inference(simp,[status(thm)],[34]) ).

thf(4,axiom,
    ! [A: nat,B: nat] :
      ( ( more @ A @ B )
     => ( less @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz11) ).

thf(9,plain,
    ! [A: nat,B: nat] :
      ( ( more @ A @ B )
     => ( less @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,plain,
    ! [B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ( less @ B @ A ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(36,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( less @ C @ B )
      | ( ( more @ ( pl @ y @ A ) @ ( pl @ x @ A ) )
       != ( more @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[35,10]) ).

thf(37,plain,
    ! [A: nat] : ( less @ ( pl @ x @ A ) @ ( pl @ y @ A ) ),
    inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( G )),bind(B,$thf( pl @ y @ G )),bind(C,$thf( pl @ x @ G ))]]) ).

thf(40,plain,
    ! [A: nat] : ( less @ ( pl @ x @ A ) @ ( pl @ y @ A ) ),
    inference(simp,[status(thm)],[37]) ).

thf(42,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[7,40]) ).

thf(43,plain,
    $false,
    inference(simp,[status(thm)],[42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM672^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n015.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Mon May  6 19:25:39 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.98/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/1.04  % [INFO] 	 Parsing done (128ms). 
% 1.22/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.27  % [INFO] 	 nitpick registered as external prover. 
% 1.71/1.28  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.33  % [INFO] 	 Found a conjecture and 4 axioms. Running axiom selection ... 
% 1.95/1.35  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 1.95/1.36  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.95/1.37  % [INFO] 	 Type checking passed. 
% 1.95/1.37  % [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 ... 
% 3.15/1.79  % [INFO] 	 Killing All external provers ... 
% 3.15/1.80  % Time passed: 1254ms (effective reasoning time: 737ms)
% 3.15/1.80  % 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)>
% 3.15/1.80  % Axioms used in derivation (4): l, satz12, satz19a, satz11
% 3.15/1.80  % No. of inferences in proof: 25
% 3.15/1.80  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1254 ms resp. 737 ms w/o parsing
% 3.25/1.87  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.25/1.87  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------