TSTP Solution File: LCL943^24 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : LCL943^24 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 00:11:38 EDT 2024

% Result   : Theorem 4.90s 2.33s
% Output   : Refutation 4.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   41 (  14 unt;  15 typ;   4 def)
%            Number of atoms       :  114 (   5 equ;   0 cnn)
%            Maximal formula atoms :   24 (   4 avg)
%            Number of connectives :  181 (  19   ~;  23   |;   0   &; 124   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   7 con; 0-3 aty)
%            Number of variables   :   47 (   9   ^  38   !;   0   ?;  47   :)

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

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

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(mor_type,type,
    mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mor_def,definition,
    ( mor
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
          | ( B @ C ) ) ) ) ).

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: ( mworld > $o ) > mworld > $o ).

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

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

thf(q_type,type,
    q: mworld > $o ).

thf(r_type,type,
    r: mworld > $o ).

thf(sk1_type,type,
    sk1: mworld ).

thf(sk3_type,type,
    sk3: mworld > mworld ).

thf(sk4_type,type,
    sk4: mworld ).

thf(sk5_type,type,
    sk5: mworld ).

thf(sk6_type,type,
    sk6: mworld ).

thf(1,conjecture,
    mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel5) ).

thf(2,negated_conjecture,
    ~ ( mlocal @ ( mbox @ ( mimplies @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ r ) ) ) ) @ ( mor @ ( mbox @ p ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ r ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(4,plain,
    ~ ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( ( ! [C: mworld] :
                      ( ( mrel @ B @ C )
                     => ( p @ C ) )
                  | ! [C: mworld] :
                      ( ( mrel @ B @ C )
                     => ( q @ C ) ) )
               => ( ! [C: mworld] :
                      ( ( mrel @ B @ C )
                     => ( p @ C ) )
                  | ! [C: mworld] :
                      ( ( mrel @ B @ C )
                     => ( r @ C ) ) ) ) )
         => ( ! [B: mworld] :
                ( ( mrel @ A @ B )
               => ( p @ B ) )
            | ! [B: mworld] :
                ( ( mrel @ A @ B )
               => ( ! [C: mworld] :
                      ( ( mrel @ B @ C )
                     => ( q @ C ) )
                 => ! [C: mworld] :
                      ( ( mrel @ B @ C )
                     => ( r @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,plain,
    ~ ( p @ sk4 ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ! [C: mworld,B: mworld,A: mworld] :
      ( ~ ( mrel @ sk1 @ A )
      | ~ ( q @ ( sk3 @ A ) )
      | ~ ( mrel @ A @ B )
      | ( p @ B )
      | ~ ( mrel @ A @ C )
      | ( r @ C ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(3,axiom,
    ! [A: mworld,B: mworld] : ( mrel @ A @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).

thf(17,plain,
    ! [A: mworld,B: mworld] : ( mrel @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(18,plain,
    ! [B: mworld,A: mworld] : ( mrel @ A @ B ),
    inference(cnf,[status(esa)],[17]) ).

thf(158,plain,
    ! [C: mworld,B: mworld,A: mworld] :
      ( ~ $true
      | ~ ( q @ ( sk3 @ A ) )
      | ~ $true
      | ( p @ B )
      | ~ $true
      | ( r @ C ) ),
    inference(rewrite,[status(thm)],[11,18]) ).

thf(159,plain,
    ! [C: mworld,B: mworld,A: mworld] :
      ( ~ ( q @ ( sk3 @ A ) )
      | ( p @ B )
      | ( r @ C ) ),
    inference(simp,[status(thm)],[158]) ).

thf(7,plain,
    ! [A: mworld] :
      ( ~ ( mrel @ sk5 @ A )
      | ( q @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(16,plain,
    ! [A: mworld] :
      ( ~ ( mrel @ sk5 @ A )
      | ( q @ A ) ),
    inference(simp,[status(thm)],[7]) ).

thf(156,plain,
    ! [A: mworld] :
      ( ~ $true
      | ( q @ A ) ),
    inference(rewrite,[status(thm)],[16,18]) ).

thf(157,plain,
    ! [A: mworld] : ( q @ A ),
    inference(simp,[status(thm)],[156]) ).

thf(184,plain,
    ! [B: mworld,A: mworld] :
      ( ~ $true
      | ( p @ A )
      | ( r @ B ) ),
    inference(rewrite,[status(thm)],[159,157]) ).

thf(185,plain,
    ! [B: mworld,A: mworld] :
      ( ( p @ A )
      | ( r @ B ) ),
    inference(simp,[status(thm)],[184]) ).

thf(9,plain,
    ~ ( r @ sk6 ),
    inference(cnf,[status(esa)],[4]) ).

thf(187,plain,
    ! [B: mworld,A: mworld] :
      ( ( p @ A )
      | ( ( r @ B )
       != ( r @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[185,9]) ).

thf(188,plain,
    ! [A: mworld] : ( p @ A ),
    inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( A )),bind(B,$thf( sk6 ))]]) ).

thf(191,plain,
    ! [A: mworld] : ( p @ A ),
    inference(simp,[status(thm)],[188]) ).

thf(193,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[10,191]) ).

thf(194,plain,
    $false,
    inference(simp,[status(thm)],[193]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL943^24 : TPTP v8.2.0. Released v8.1.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.35  % Computer : n002.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Mon May 20 01:50:24 EDT 2024
% 0.16/0.35  % CPUTime  : 
% 0.91/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/0.95  % [INFO] 	 Parsing done (110ms). 
% 1.22/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.59/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.26  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ... 
% 1.93/1.29  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.93/1.30  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.93/1.30  % [INFO] 	 Type checking passed. 
% 1.93/1.30  % [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 ... 
% 4.90/2.32  % [INFO] 	 Killing All external provers ... 
% 4.90/2.32  % Time passed: 1820ms (effective reasoning time: 1363ms)
% 4.90/2.32  % 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)>
% 4.90/2.33  % Axioms used in derivation (1): mrel_universal
% 4.90/2.33  % No. of inferences in proof: 22
% 4.90/2.33  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1820 ms resp. 1363 ms w/o parsing
% 4.92/2.36  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.92/2.36  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------