TSTP Solution File: NUM692^1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NUM692^1 : TPTP v8.2.0. 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 21 01:35:53 EDT 2024

% Result   : Theorem 39.88s 8.79s
% Output   : Refutation 39.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   37 (  13 unt;   8 typ;   0 def)
%            Number of atoms       :   60 (   5 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  192 (  13   ~;  11   |;   0   &; 158   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   42 (   0   ^  42   !;   0   ?;  42   :)

% 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(u_type,type,
    u: nat ).

thf(lessis_type,type,
    lessis: nat > nat > $o ).

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

thf(moreis_type,type,
    moreis: nat > nat > $o ).

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

thf(9,plain,
    lessis @ x @ y,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [A: nat,B: nat] :
      ( ( lessis @ A @ B )
     => ( moreis @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz14) ).

thf(16,plain,
    ! [A: nat,B: nat] :
      ( ( lessis @ A @ B )
     => ( moreis @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(17,plain,
    ! [B: nat,A: nat] :
      ( ~ ( lessis @ A @ B )
      | ( moreis @ B @ A ) ),
    inference(cnf,[status(esa)],[16]) ).

thf(33,plain,
    ! [B: nat,A: nat] :
      ( ( moreis @ B @ A )
      | ( ( lessis @ x @ y )
       != ( lessis @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9,17]) ).

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

thf(4,axiom,
    lessis @ z @ u,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).

thf(10,plain,
    lessis @ z @ u,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(31,plain,
    ! [B: nat,A: nat] :
      ( ( moreis @ B @ A )
      | ( ( lessis @ z @ u )
       != ( lessis @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[10,17]) ).

thf(32,plain,
    moreis @ u @ z,
    inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( z )),bind(B,$thf( u ))]]) ).

thf(6,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( moreis @ A @ B )
     => ( ( moreis @ C @ D )
       => ( moreis @ ( ts @ A @ C ) @ ( ts @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23) ).

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

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

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

thf(46,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ~ ( moreis @ A @ B )
      | ( moreis @ ( ts @ A @ C ) @ ( ts @ B @ D ) )
      | ( ( moreis @ u @ z )
       != ( moreis @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[32,15]) ).

thf(47,plain,
    ! [B: nat,A: nat] :
      ( ~ ( moreis @ A @ B )
      | ( moreis @ ( ts @ A @ u ) @ ( ts @ B @ z ) ) ),
    inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( u )),bind(D,$thf( z ))]]) ).

thf(124,plain,
    ! [B: nat,A: nat] :
      ( ( moreis @ ( ts @ A @ u ) @ ( ts @ B @ z ) )
      | ( ( moreis @ y @ x )
       != ( moreis @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[34,47]) ).

thf(125,plain,
    moreis @ ( ts @ y @ u ) @ ( ts @ x @ z ),
    inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( y )),bind(B,$thf( x ))]]) ).

thf(5,axiom,
    ! [A: nat,B: nat] :
      ( ( moreis @ A @ B )
     => ( lessis @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).

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

thf(12,plain,
    ! [B: nat,A: nat] :
      ( ~ ( moreis @ A @ B )
      | ( lessis @ B @ A ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(161,plain,
    ! [B: nat,A: nat] :
      ( ( lessis @ B @ A )
      | ( ( moreis @ ( ts @ y @ u ) @ ( ts @ x @ z ) )
       != ( moreis @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[125,12]) ).

thf(162,plain,
    lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ),
    inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( ts @ y @ u )),bind(B,$thf( ts @ x @ z ))]]) ).

thf(1,conjecture,
    lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23a) ).

thf(2,negated_conjecture,
    ~ ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(8,plain,
    ~ ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(840,plain,
    $false,
    inference(rewrite,[status(thm)],[162,8]) ).

thf(841,plain,
    $false,
    inference(simp,[status(thm)],[840]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : NUM692^1 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n015.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon May 20 07:37:54 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.84/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.98  % [INFO] 	 Parsing done (128ms). 
% 1.20/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.25  % [INFO] 	 nitpick registered as external prover. 
% 1.68/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.68/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ... 
% 1.90/1.33  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.90/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.90/1.35  % [INFO] 	 Type checking passed. 
% 1.90/1.35  % [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 ... 
% 39.88/8.78  % [INFO] 	 Killing All external provers ... 
% 39.88/8.79  % Time passed: 8274ms (effective reasoning time: 7785ms)
% 39.88/8.79  % 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)>
% 39.88/8.79  % Axioms used in derivation (5): satz14, l, satz23, k, satz13
% 39.88/8.79  % No. of inferences in proof: 29
% 39.88/8.79  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8274 ms resp. 7785 ms w/o parsing
% 39.88/8.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.88/8.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------