TSTP Solution File: GEG011^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : GEG011^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 : Mon May 20 19:57:00 EDT 2024

% Result   : Theorem 5.20s 2.88s
% Output   : Refutation 5.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   45 (  12 unt;  17 typ;   8 def)
%            Number of atoms       :  162 (   8 equ;   0 cnn)
%            Maximal formula atoms :   37 (   5 avg)
%            Number of connectives :  395 (  37   ~;  14   |;  44   &; 265   @)
%                                         (   0 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   7 avg)
%            Number of types       :    4 (   2 usr)
%            Number of type conns  :   46 (  46   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;  10 con; 0-3 aty)
%            Number of variables   :   98 (  22   ^  61   !;  15   ?;  98   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

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

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).

thf(mforall_prop_type,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(mforall_prop_def,definition,
    ( mforall_prop
    = ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
        ! [C: $i > $o] : ( A @ C @ B ) ) ) ).

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

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
        ! [D: $i] :
          ( ~ ( A @ C @ D )
          | ( B @ D ) ) ) ) ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid_def,definition,
    ( mvalid
    = ( '!' @ $i ) ) ).

thf(reg_type,type,
    reg: $tType ).

thf(c_type,type,
    c: reg > reg > $o ).

thf(ec_type,type,
    ec: reg > reg > $o ).

thf(ec_def,definition,
    ( ec
    = ( ^ [A: reg,B: reg] :
          ( ( c @ A @ B )
          & ~ ( o @ A @ B ) ) ) ) ).

thf(pp_type,type,
    pp: reg > reg > $o ).

thf(pp_def,definition,
    ( pp
    = ( ^ [A: reg,B: reg] :
          ( ( p @ A @ B )
          & ~ ( p @ B @ A ) ) ) ) ).

thf(tpp_type,type,
    tpp: reg > reg > $o ).

thf(tpp_def,definition,
    ( tpp
    = ( ^ [A: reg,B: reg] :
          ( ( pp @ A @ B )
          & ? [C: reg] :
              ( ( ec @ C @ A )
              & ( ec @ C @ B ) ) ) ) ) ).

thf(ntpp_type,type,
    ntpp: reg > reg > $o ).

thf(ntpp_def,definition,
    ( ntpp
    = ( ^ [A: reg,B: reg] :
          ( ( pp @ A @ B )
          & ~ ? [C: reg] :
                ( ( ec @ C @ A )
                & ( ec @ C @ B ) ) ) ) ) ).

thf(catalunya_type,type,
    catalunya: reg ).

thf(france_type,type,
    france: reg ).

thf(spain_type,type,
    spain: reg ).

thf(paris_type,type,
    paris: reg ).

thf(a_type,type,
    a: $i > $i > $o ).

thf(fool_type,type,
    fool: $i > $i > $o ).

thf(10,axiom,
    ( mvalid
    @ ( mbox @ a
      @ ^ [A: $i] : ( ntpp @ paris @ france ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

thf(88,plain,
    ! [A: $i,B: $i] :
      ( ~ ( a @ A @ B )
      | ( ! [C: reg] :
            ( ( c @ C @ paris )
           => ( c @ C @ france ) )
        & ~ ! [C: reg] :
              ( ( c @ C @ france )
             => ( c @ C @ paris ) )
        & ~ ? [C: reg] :
              ( ( c @ C @ paris )
              & ~ ? [D: reg] :
                    ( ! [E: reg] :
                        ( ( c @ E @ D )
                       => ( c @ E @ C ) )
                    & ! [E: reg] :
                        ( ( c @ E @ D )
                       => ( c @ E @ paris ) ) )
              & ( c @ C @ france )
              & ~ ? [D: reg] :
                    ( ! [E: reg] :
                        ( ( c @ E @ D )
                       => ( c @ E @ C ) )
                    & ! [E: reg] :
                        ( ( c @ E @ D )
                       => ( c @ E @ france ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(6,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ fool @ ( mbox @ fool @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_axiom_for_fool) ).

thf(52,plain,
    ! [A: $i,B: $i > $o] :
      ( ~ ! [C: $i] :
            ( ~ ( fool @ A @ C )
            | ( B @ C ) )
      | ! [C: $i] :
          ( ~ ( fool @ A @ C )
          | ! [D: $i] :
              ( ~ ( fool @ C @ D )
              | ( B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(3,axiom,
    ! [A: reg] : ( c @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_reflexive) ).

thf(45,plain,
    ! [A: reg] : ( c @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(5,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_axiom_for_fool) ).

thf(49,plain,
    ! [A: $i,B: $i > $o] :
      ( ~ ! [C: $i] :
            ( ~ ( fool @ A @ C )
            | ( B @ C ) )
      | ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(9,axiom,
    ( mvalid
    @ ( mbox @ fool
      @ ^ [A: $i] : ( ec @ spain @ france ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

thf(81,plain,
    ! [A: $i,B: $i] :
      ( ~ ( fool @ A @ B )
      | ( ( c @ spain @ france )
        & ~ ? [C: reg] :
              ( ! [D: reg] :
                  ( ( c @ D @ C )
                 => ( c @ D @ spain ) )
              & ! [D: reg] :
                  ( ( c @ D @ C )
                 => ( c @ D @ france ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1,conjecture,
    ( mvalid
    @ ( mbox @ a
      @ ^ [A: $i] :
        ! [B: reg] :
          ( ( ( ntpp @ france @ B )
            & ( ntpp @ spain @ B ) )
         => ( ( pp @ paris @ B )
            & ( pp @ catalunya @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( mvalid
      @ ( mbox @ a
        @ ^ [A: $i] :
          ! [B: reg] :
            ( ( ( ntpp @ france @ B )
              & ( ntpp @ spain @ B ) )
           => ( ( pp @ paris @ B )
              & ( pp @ catalunya @ B ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(11,plain,
    ~ ! [A: $i,B: $i] :
        ( ~ ( a @ A @ B )
        | ! [C: reg] :
            ( ( ! [D: reg] :
                  ( ( c @ D @ france )
                 => ( c @ D @ C ) )
              & ~ ! [D: reg] :
                    ( ( c @ D @ C )
                   => ( c @ D @ france ) )
              & ~ ? [D: reg] :
                    ( ( c @ D @ france )
                    & ~ ? [E: reg] :
                          ( ! [F: reg] :
                              ( ( c @ F @ E )
                             => ( c @ F @ D ) )
                          & ! [F: reg] :
                              ( ( c @ F @ E )
                             => ( c @ F @ france ) ) )
                    & ( c @ D @ C )
                    & ~ ? [E: reg] :
                          ( ! [F: reg] :
                              ( ( c @ F @ E )
                             => ( c @ F @ D ) )
                          & ! [F: reg] :
                              ( ( c @ F @ E )
                             => ( c @ F @ C ) ) ) )
              & ! [D: reg] :
                  ( ( c @ D @ spain )
                 => ( c @ D @ C ) )
              & ~ ! [D: reg] :
                    ( ( c @ D @ C )
                   => ( c @ D @ spain ) )
              & ~ ? [D: reg] :
                    ( ( c @ D @ spain )
                    & ~ ? [E: reg] :
                          ( ! [F: reg] :
                              ( ( c @ F @ E )
                             => ( c @ F @ D ) )
                          & ! [F: reg] :
                              ( ( c @ F @ E )
                             => ( c @ F @ spain ) ) )
                    & ( c @ D @ C )
                    & ~ ? [E: reg] :
                          ( ! [F: reg] :
                              ( ( c @ F @ E )
                             => ( c @ F @ D ) )
                          & ! [F: reg] :
                              ( ( c @ F @ E )
                             => ( c @ F @ C ) ) ) ) )
           => ( ! [D: reg] :
                  ( ( c @ D @ paris )
                 => ( c @ D @ C ) )
              & ~ ! [D: reg] :
                    ( ( c @ D @ C )
                   => ( c @ D @ paris ) )
              & ! [D: reg] :
                  ( ( c @ D @ catalunya )
                 => ( c @ D @ C ) )
              & ~ ! [D: reg] :
                    ( ( c @ D @ C )
                   => ( c @ D @ catalunya ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ fool @ A ) @ ( mbox @ a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_axiom_for_fool_a) ).

thf(55,plain,
    ! [A: $i,B: $i > $o] :
      ( ~ ! [C: $i] :
            ( ~ ( fool @ A @ C )
            | ( B @ C ) )
      | ! [C: $i] :
          ( ~ ( a @ A @ C )
          | ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(8,axiom,
    ( mvalid
    @ ( mbox @ a
      @ ^ [A: $i] : ( tpp @ catalunya @ spain ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

thf(58,plain,
    ! [A: $i,B: $i] :
      ( ~ ( a @ A @ B )
      | ( ! [C: reg] :
            ( ( c @ C @ catalunya )
           => ( c @ C @ spain ) )
        & ~ ! [C: reg] :
              ( ( c @ C @ spain )
             => ( c @ C @ catalunya ) )
        & ? [C: reg] :
            ( ( c @ C @ catalunya )
            & ~ ? [D: reg] :
                  ( ! [E: reg] :
                      ( ( c @ E @ D )
                     => ( c @ E @ C ) )
                  & ! [E: reg] :
                      ( ( c @ E @ D )
                     => ( c @ E @ catalunya ) ) )
            & ( c @ C @ spain )
            & ~ ? [D: reg] :
                  ( ! [E: reg] :
                      ( ( c @ E @ D )
                     => ( c @ E @ C ) )
                  & ! [E: reg] :
                      ( ( c @ E @ D )
                     => ( c @ E @ spain ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(4,axiom,
    ! [A: reg,B: reg] :
      ( ( c @ A @ B )
     => ( c @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_symmetric) ).

thf(47,plain,
    ! [A: reg,B: reg] :
      ( ( c @ A @ B )
     => ( c @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(101,plain,
    $false,
    inference(e,[status(thm)],[88,52,45,49,81,11,55,58,47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GEG011^1 : TPTP v8.2.0. Released v4.1.0.
% 0.03/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat May 18 21:55:24 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 1.03/1.01  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.64/1.28  % [INFO] 	 Parsing done (263ms). 
% 1.64/1.29  % [INFO] 	 Running in sequential loop mode. 
% 2.27/1.67  % [INFO] 	 eprover registered as external prover. 
% 2.27/1.67  % [INFO] 	 cvc4 registered as external prover. 
% 2.40/1.68  % [INFO] 	 Scanning for conjecture ... 
% 2.75/1.88  % [INFO] 	 Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ... 
% 2.96/1.92  % [INFO] 	 Axiom selection finished. Selected 8 axioms (removed 0 axioms). 
% 2.96/1.93  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.96/1.93  % [INFO] 	 Type checking passed. 
% 2.96/1.93  % [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 ... 
% 5.20/2.88  % External prover 'e' found a proof!
% 5.20/2.88  % [INFO] 	 Killing All external provers ... 
% 5.20/2.88  % Time passed: 2380ms (effective reasoning time: 1581ms)
% 5.20/2.88  % 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)>
% 5.20/2.88  % Axioms used in derivation (8): k_axiom_for_fool, ax2, c_symmetric, i_axiom_for_fool_a, ax1, t_axiom_for_fool, ax3, c_reflexive
% 5.20/2.88  % No. of inferences in proof: 20
% 5.20/2.88  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2380 ms resp. 1581 ms w/o parsing
% 5.62/2.96  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.62/2.96  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------