TSTP Solution File: SYO891^16 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO891^16 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n029.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 09:01:58 EDT 2024

% Result   : Theorem 5.54s 2.18s
% Output   : Refutation 5.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   41 (  13 unt;  14 typ;   6 def)
%            Number of atoms       :   94 (   9 equ;   0 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  197 (  27   ~;  14   |;   9   &; 138   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   39 (  39   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   5 con; 0-3 aty)
%            Number of variables   :   47 (  16   ^  24   !;   7   ?;  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(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(mdia_type,type,
    mdia: ( mworld > $o ) > mworld > $o ).

thf(mdia_def,definition,
    ( mdia
    = ( ^ [A: mworld > $o,B: mworld] :
        ? [C: mworld] :
          ( ( mrel @ B @ C )
          & ( A @ C ) ) ) ) ).

thf(eiw_di_type,type,
    eiw_di: $i > mworld > $o ).

thf(mforall_di_type,type,
    mforall_di: ( $i > mworld > $o ) > mworld > $o ).

thf(mforall_di_def,definition,
    ( mforall_di
    = ( ^ [A: $i > mworld > $o,B: mworld] :
        ! [C: $i] :
          ( ( eiw_di @ C @ B )
         => ( A @ C @ B ) ) ) ) ).

thf(mexists_di_type,type,
    mexists_di: ( $i > mworld > $o ) > mworld > $o ).

thf(mexists_di_def,definition,
    ( mexists_di
    = ( ^ [A: $i > mworld > $o,B: mworld] :
        ? [C: $i] :
          ( ( eiw_di @ C @ B )
          & ( A @ C @ B ) ) ) ) ).

thf(qmltpeq_type,type,
    qmltpeq: $i > $i > mworld > $o ).

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

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: mworld ).

thf(1,conjecture,
    ( mlocal
    @ ( mimplies
      @ ( mforall_di
        @ ^ [A: $i] : ( mbox @ ( mexists_di @ ( qmltpeq @ A ) ) ) )
      @ ( mimplies
        @ ( mexists_di
          @ ^ [A: $i] : ( mdia @ ( p @ A ) ) )
        @ ( mdia @ ( mexists_di @ p ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( mlocal
      @ ( mimplies
        @ ( mforall_di
          @ ^ [A: $i] : ( mbox @ ( mexists_di @ ( qmltpeq @ A ) ) ) )
        @ ( mimplies
          @ ( mexists_di
            @ ^ [A: $i] : ( mdia @ ( p @ A ) ) )
          @ ( mdia @ ( mexists_di @ p ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(11,plain,
    ~ ( ! [A: $i] :
          ( ( eiw_di @ A @ mactual )
         => ! [B: mworld] :
              ( ( mrel @ mactual @ B )
             => ? [C: $i] :
                  ( ( eiw_di @ C @ B )
                  & ( qmltpeq @ A @ C @ B ) ) ) )
     => ( ? [A: $i] :
            ( ( eiw_di @ A @ mactual )
            & ? [B: mworld] :
                ( ( mrel @ mactual @ B )
                & ( p @ A @ B ) ) )
       => ? [A: mworld] :
            ( ( mrel @ mactual @ A )
            & ? [B: $i] :
                ( ( eiw_di @ B @ A )
                & ( p @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(14,plain,
    mrel @ mactual @ sk3,
    inference(cnf,[status(esa)],[11]) ).

thf(6,axiom,
    ! [A: mworld,B: mworld,C: $i] :
      ( ( ( eiw_di @ C @ A )
        & ( mrel @ A @ B ) )
     => ( eiw_di @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_cumul) ).

thf(25,plain,
    ! [A: mworld,B: mworld,C: $i] :
      ( ( ( eiw_di @ C @ A )
        & ( mrel @ A @ B ) )
     => ( eiw_di @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(26,plain,
    ! [C: $i,B: mworld,A: mworld] :
      ( ~ ( eiw_di @ C @ A )
      | ~ ( mrel @ A @ B )
      | ( eiw_di @ C @ B ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(17,plain,
    p @ sk2 @ sk3,
    inference(cnf,[status(esa)],[11]) ).

thf(13,plain,
    ! [B: $i,A: mworld] :
      ( ~ ( mrel @ mactual @ A )
      | ~ ( eiw_di @ B @ A )
      | ~ ( p @ B @ A ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(18,plain,
    ! [B: $i,A: mworld] :
      ( ~ ( mrel @ mactual @ A )
      | ~ ( eiw_di @ B @ A )
      | ~ ( p @ B @ A ) ),
    inference(simp,[status(thm)],[13]) ).

thf(39,plain,
    ! [B: $i,A: mworld] :
      ( ~ ( mrel @ mactual @ A )
      | ~ ( eiw_di @ B @ A )
      | ( ( p @ sk2 @ sk3 )
       != ( p @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[17,18]) ).

thf(40,plain,
    ( ~ ( mrel @ mactual @ sk3 )
    | ~ ( eiw_di @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).

thf(45,plain,
    ( ~ $true
    | ~ ( eiw_di @ sk2 @ sk3 ) ),
    inference(rewrite,[status(thm)],[40,14]) ).

thf(46,plain,
    ~ ( eiw_di @ sk2 @ sk3 ),
    inference(simp,[status(thm)],[45]) ).

thf(296,plain,
    ! [C: $i,B: mworld,A: mworld] :
      ( ~ ( eiw_di @ C @ A )
      | ~ ( mrel @ A @ B )
      | ( ( eiw_di @ C @ B )
       != ( eiw_di @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[26,46]) ).

thf(297,plain,
    ! [A: mworld] :
      ( ~ ( eiw_di @ sk2 @ A )
      | ~ ( mrel @ A @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[296:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk2 ))]]) ).

thf(334,plain,
    ! [A: mworld] :
      ( ~ ( eiw_di @ sk2 @ A )
      | ( ( mrel @ mactual @ sk3 )
       != ( mrel @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[14,297]) ).

thf(335,plain,
    ~ ( eiw_di @ sk2 @ mactual ),
    inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( mactual ))]]) ).

thf(12,plain,
    eiw_di @ sk2 @ mactual,
    inference(cnf,[status(esa)],[11]) ).

thf(360,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[335,12]) ).

thf(361,plain,
    $false,
    inference(simp,[status(thm)],[360]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYO891^16 : TPTP v8.2.0. Released v8.1.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n029.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 10:31:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.94/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.30/0.97  % [INFO] 	 Parsing done (121ms). 
% 1.30/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.18  % [INFO] 	 nitpick registered as external prover. 
% 1.75/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.95/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 1.95/1.27  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 1.95/1.28  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.95/1.29  % [INFO] 	 Type checking passed. 
% 1.95/1.29  % [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 ... 
% 5.54/2.18  % [INFO] 	 Killing All external provers ... 
% 5.54/2.18  % Time passed: 1654ms (effective reasoning time: 1194ms)
% 5.54/2.18  % 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)>
% 5.54/2.18  % Axioms used in derivation (1): eiw_di_cumul
% 5.54/2.18  % No. of inferences in proof: 21
% 5.54/2.18  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1654 ms resp. 1194 ms w/o parsing
% 5.54/2.21  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.54/2.21  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------