TSTP Solution File: NUM687_8 by Leo-III-SAT---1.7.10

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : NUM687_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 10:45:12 EDT 2024

% Result   : Theorem 4.74s 2.04s
% Output   : Refutation 4.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   36 (   8 unt;   7 typ;   0 def)
%            Number of atoms       :   65 (  12 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  229 (  23   ~;  18   |;   0   &; 174   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   6 con; 0-2 aty)
%            Number of variables   :   47 (   0   ^  47   !;   0   ?;  47   :)

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

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

thf(7,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( more @ A @ B )
     => ( ( more @ C @ D )
       => ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz21) ).

thf(19,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( more @ A @ B )
     => ( ( more @ C @ D )
       => ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(20,plain,
    ! [A: nat,B: nat] :
      ( ( more @ A @ B )
     => ! [C: nat,D: nat] :
          ( ( more @ C @ D )
         => ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
    inference(miniscope,[status(thm)],[19]) ).

thf(21,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ~ ( more @ C @ D )
      | ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ),
    inference(cnf,[status(esa)],[20]) ).

thf(1,conjecture,
    more @ ( pl @ x @ z ) @ ( pl @ y @ u ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz22a) ).

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

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

thf(128,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ~ ( more @ A @ B )
      | ~ ( more @ C @ D )
      | ( ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) )
       != ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ) ),
    inference(paramod_ordered,[status(thm)],[21,8]) ).

thf(129,plain,
    ( ~ ( more @ x @ y )
    | ~ ( more @ z @ u ) ),
    inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).

thf(3,axiom,
    ( ~ ( more @ x @ y )
   => ( x = y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).

thf(9,plain,
    ( ~ ( more @ x @ y )
   => ( x = y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

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

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

thf(24,plain,
    ( ( more @ x @ y )
    | ~ ( more @ ( pl @ x @ z ) @ ( pl @ x @ u ) )
    | ( y != y ) ),
    inference(paramod_ordered,[status(thm)],[11,8]) ).

thf(25,plain,
    ( ( more @ x @ y )
    | ~ ( more @ ( pl @ x @ z ) @ ( pl @ x @ u ) ) ),
    inference(pattern_uni,[status(thm)],[24:[]]) ).

thf(4,axiom,
    more @ z @ u,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).

thf(12,plain,
    more @ z @ u,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( A = B )
     => ( ( more @ C @ D )
       => ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19g) ).

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

thf(15,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ! [C: nat,D: nat] :
          ( ( more @ C @ D )
         => ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
    inference(miniscope,[status(thm)],[14]) ).

thf(16,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( A != B )
      | ~ ( more @ C @ D )
      | ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(17,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( A != B )
      | ~ ( more @ C @ D )
      | ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ),
    inference(lifteq,[status(thm)],[16]) ).

thf(18,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ~ ( more @ B @ C )
      | ( more @ ( pl @ A @ B ) @ ( pl @ A @ C ) ) ),
    inference(simp,[status(thm)],[17]) ).

thf(40,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( more @ ( pl @ A @ B ) @ ( pl @ A @ C ) )
      | ( ( more @ z @ u )
       != ( more @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[12,18]) ).

thf(41,plain,
    ! [A: nat] : ( more @ ( pl @ A @ z ) @ ( pl @ A @ u ) ),
    inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( A )),bind(B,$thf( z )),bind(C,$thf( u ))]]) ).

thf(49,plain,
    ( ( more @ x @ y )
    | ~ $true ),
    inference(rewrite,[status(thm)],[25,41]) ).

thf(50,plain,
    more @ x @ y,
    inference(simp,[status(thm)],[49]) ).

thf(177,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[129,50,12]) ).

thf(178,plain,
    $false,
    inference(simp,[status(thm)],[177]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM687_8 : TPTP v8.1.2. Released v8.0.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n016.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 19:52:38 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.83/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/0.94  % [INFO] 	 Parsing done (107ms). 
% 1.22/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.46/1.14  % [INFO] 	 nitpick registered as external prover. 
% 1.46/1.15  % [INFO] 	 Scanning for conjecture ... 
% 1.69/1.20  % [INFO] 	 Found a conjecture and 5 axioms. Running axiom selection ... 
% 1.77/1.22  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.88/1.24  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 1.88/1.24  % [INFO] 	 Type checking passed. 
% 1.88/1.24  % [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 ... 
% 4.74/2.03  % [INFO] 	 Killing All external provers ... 
% 4.74/2.03  % Time passed: 1517ms (effective reasoning time: 1082ms)
% 4.74/2.03  % 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)>
% 4.74/2.03  % Axioms used in derivation (4): satz21, m, n, satz19g
% 4.74/2.03  % No. of inferences in proof: 29
% 4.74/2.04  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1517 ms resp. 1082 ms w/o parsing
% 4.74/2.06  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.74/2.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------