TSTP Solution File: LCL962^16 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : LCL962^16 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 00:11:42 EDT 2024

% Result   : Theorem 8.81s 2.76s
% Output   : Refutation 8.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   51 (  14 unt;  13 typ;   4 def)
%            Number of atoms       :  116 (   9 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  281 (  37   ~;  34   |;   0   &; 200   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :   37 (   9   ^  28   !;   0   ?;  37   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mworld_type,type,
    mworld: $tType ).

thf(mindex_type,type,
    mindex: $tType ).

thf(mrel_type,type,
    mrel: mindex > mworld > mworld > $o ).

thf('\'#b\'_type',type,
    '\'#b\'': mindex ).

thf('\'#a\'_type',type,
    '\'#a\'': mindex ).

thf(mactual_type,type,
    mactual: mworld ).

thf(mlocal_type,type,
    mlocal: ( mworld > $o ) > $o ).

thf(mlocal_def,definition,
    ( mlocal
    = ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).

thf(mnot_type,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: mworld > $o,B: mworld] :
          ~ ( A @ B ) ) ) ).

thf(mimplies_type,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
         => ( B @ C ) ) ) ) ).

thf(mbox_type,type,
    mbox: mindex > ( mworld > $o ) > mworld > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: mindex,B: mworld > $o,C: mworld] :
        ! [D: mworld] :
          ( ( mrel @ A @ C @ D )
         => ( B @ D ) ) ) ) ).

thf(p_type,type,
    p: mworld > $o ).

thf(sk1_type,type,
    sk1: mworld ).

thf(sk2_type,type,
    sk2: mworld > mworld ).

thf(3,axiom,
    ! [A: mworld] : ( mrel @ '\'#b\'' @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#b_reflexive') ).

thf(13,plain,
    ! [A: mworld] : ( mrel @ '\'#b\'' @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,plain,
    ! [A: mworld] : ( mrel @ '\'#b\'' @ A @ A ),
    inference(cnf,[status(esa)],[13]) ).

thf(1,conjecture,
    mlocal @ ( mbox @ '\'#a\'' @ ( mnot @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ( mlocal @ ( mbox @ '\'#a\'' @ ( mnot @ p ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(10,plain,
    ~ ! [A: mworld] :
        ( ( mrel @ '\'#a\'' @ mactual @ A )
       => ~ ( p @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(12,plain,
    mrel @ '\'#a\'' @ mactual @ sk1,
    inference(cnf,[status(esa)],[10]) ).

thf(8,axiom,
    mlocal @ ( mimplies @ ( mnot @ ( mbox @ '\'#b\'' @ p ) ) @ ( mbox @ '\'#a\'' @ ( mnot @ ( mbox @ '\'#b\'' @ p ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_axiom_2) ).

thf(23,plain,
    ( ~ ! [A: mworld] :
          ( ( mrel @ '\'#b\'' @ mactual @ A )
         => ( p @ A ) )
   => ! [A: mworld] :
        ( ( mrel @ '\'#a\'' @ mactual @ A )
       => ~ ! [B: mworld] :
              ( ( mrel @ '\'#b\'' @ A @ B )
             => ( p @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(25,plain,
    ! [B: mworld,A: mworld] :
      ( ~ ( mrel @ '\'#b\'' @ mactual @ A )
      | ( p @ A )
      | ~ ( mrel @ '\'#a\'' @ mactual @ B )
      | ( mrel @ '\'#b\'' @ B @ ( sk2 @ B ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(116,plain,
    ! [B: mworld,A: mworld] :
      ( ~ ( mrel @ '\'#b\'' @ mactual @ A )
      | ( p @ A )
      | ( mrel @ '\'#b\'' @ B @ ( sk2 @ B ) )
      | ( ( mrel @ '\'#a\'' @ mactual @ sk1 )
       != ( mrel @ '\'#a\'' @ mactual @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12,25]) ).

thf(117,plain,
    ! [A: mworld] :
      ( ~ ( mrel @ '\'#b\'' @ mactual @ A )
      | ( p @ A )
      | ( mrel @ '\'#b\'' @ sk1 @ ( sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(242,plain,
    ! [B: mworld,A: mworld] :
      ( ( p @ B )
      | ( mrel @ '\'#b\'' @ sk1 @ ( sk2 @ sk1 ) )
      | ( ( mrel @ '\'#b\'' @ A @ A )
       != ( mrel @ '\'#b\'' @ mactual @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[14,117]) ).

thf(243,plain,
    ( ( p @ mactual )
    | ( mrel @ '\'#b\'' @ sk1 @ ( sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).

thf(9,axiom,
    mlocal @ ( mnot @ p ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_a_axiom_1) ).

thf(26,plain,
    ~ ( p @ mactual ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(27,plain,
    ~ ( p @ mactual ),
    inference(polarity_switch,[status(thm)],[26]) ).

thf(286,plain,
    ( $false
    | ( mrel @ '\'#b\'' @ sk1 @ ( sk2 @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[243,27]) ).

thf(287,plain,
    mrel @ '\'#b\'' @ sk1 @ ( sk2 @ sk1 ),
    inference(simp,[status(thm)],[286]) ).

thf(7,axiom,
    mlocal @ ( mbox @ '\'#a\'' @ ( mimplies @ p @ ( mbox @ '\'#b\'' @ p ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_axiom_1) ).

thf(21,plain,
    ! [A: mworld] :
      ( ( mrel @ '\'#a\'' @ mactual @ A )
     => ( ( p @ A )
       => ! [B: mworld] :
            ( ( mrel @ '\'#b\'' @ A @ B )
           => ( p @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(22,plain,
    ! [B: mworld,A: mworld] :
      ( ~ ( mrel @ '\'#a\'' @ mactual @ A )
      | ~ ( p @ A )
      | ~ ( mrel @ '\'#b\'' @ A @ B )
      | ( p @ B ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(335,plain,
    ! [B: mworld,A: mworld] :
      ( ~ ( mrel @ '\'#a\'' @ mactual @ A )
      | ~ ( p @ A )
      | ( p @ B )
      | ( ( mrel @ '\'#b\'' @ sk1 @ ( sk2 @ sk1 ) )
       != ( mrel @ '\'#b\'' @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[287,22]) ).

thf(336,plain,
    ( ~ ( mrel @ '\'#a\'' @ mactual @ sk1 )
    | ~ ( p @ sk1 )
    | ( p @ ( sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[335:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ sk1 ))]]) ).

thf(24,plain,
    ! [B: mworld,A: mworld] :
      ( ~ ( mrel @ '\'#b\'' @ mactual @ A )
      | ( p @ A )
      | ~ ( mrel @ '\'#a\'' @ mactual @ B )
      | ~ ( p @ ( sk2 @ B ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(31,plain,
    ! [B: mworld,A: mworld] :
      ( ~ ( mrel @ '\'#b\'' @ mactual @ A )
      | ( p @ A )
      | ~ ( p @ ( sk2 @ B ) )
      | ( ( mrel @ '\'#a\'' @ mactual @ sk1 )
       != ( mrel @ '\'#a\'' @ mactual @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12,24]) ).

thf(32,plain,
    ! [A: mworld] :
      ( ~ ( mrel @ '\'#b\'' @ mactual @ A )
      | ( p @ A )
      | ~ ( p @ ( sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(48,plain,
    ! [B: mworld,A: mworld] :
      ( ( p @ B )
      | ~ ( p @ ( sk2 @ sk1 ) )
      | ( ( mrel @ '\'#b\'' @ A @ A )
       != ( mrel @ '\'#b\'' @ mactual @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[14,32]) ).

thf(49,plain,
    ( ( p @ mactual )
    | ~ ( p @ ( sk2 @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( mactual )),bind(B,$thf( mactual ))]]) ).

thf(55,plain,
    ( $false
    | ~ ( p @ ( sk2 @ sk1 ) ) ),
    inference(rewrite,[status(thm)],[49,27]) ).

thf(56,plain,
    ~ ( p @ ( sk2 @ sk1 ) ),
    inference(simp,[status(thm)],[55]) ).

thf(11,plain,
    p @ sk1,
    inference(cnf,[status(esa)],[10]) ).

thf(1157,plain,
    ( ~ $true
    | ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[336,56,11,12]) ).

thf(1158,plain,
    $false,
    inference(simp,[status(thm)],[1157]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL962^16 : TPTP v8.2.0. Released v8.1.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n019.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 20 02:25:39 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.92/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.21/1.05  % [INFO] 	 Parsing done (149ms). 
% 1.21/1.06  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.27  % [INFO] 	 nitpick registered as external prover. 
% 1.72/1.27  % [INFO] 	 Scanning for conjecture ... 
% 1.82/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 2.01/1.36  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 2.08/1.37  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.08/1.37  % [INFO] 	 Type checking passed. 
% 2.08/1.37  % [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 ... 
% 8.81/2.74  % [INFO] 	 Killing All external provers ... 
% 8.81/2.76  % Time passed: 2210ms (effective reasoning time: 1682ms)
% 8.81/2.76  % 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)>
% 8.81/2.76  % Axioms used in derivation (4): mrel_#b_reflexive, ab_axiom_2, not_a_axiom_1, ab_axiom_1
% 8.81/2.76  % No. of inferences in proof: 34
% 8.81/2.76  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2210 ms resp. 1682 ms w/o parsing
% 8.81/2.82  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.81/2.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------