TSTP Solution File: PUZ086^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : PUZ086^1 : TPTP v8.2.0. Released v4.0.0.
% 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 21 02:26:52 EDT 2024

% Result   : Theorem 3.42s 1.88s
% Output   : Refutation 3.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   49 (  10 unt;  14 typ;   7 def)
%            Number of atoms       :  155 (   7 equ;   0 cnn)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  240 (  29   ~;  25   |;   4   &; 178   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   59 (  59   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   4 con; 0-3 aty)
%            Number of variables   :   57 (  12   ^  45   !;   0   ?;  57   :)

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

thf(mand_type,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mand_def,definition,
    ( mand
    = ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).

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(mreflexive_type,type,
    mreflexive: ( $i > $i > $o ) > $o ).

thf(mreflexive_def,definition,
    ( mreflexive
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i] : ( A @ B @ B ) ) ) ).

thf(mtransitive_type,type,
    mtransitive: ( $i > $i > $o ) > $o ).

thf(mtransitive_def,definition,
    ( mtransitive
    = ( ^ [A: $i > $i > $o] :
        ! [B: $i,C: $i,D: $i] :
          ( ( ( A @ B @ C )
            & ( A @ C @ D ) )
         => ( A @ B @ D ) ) ) ) ).

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

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

thf(peter_type,type,
    peter: $i > $i > $o ).

thf(john_type,type,
    john: $i > $i > $o ).

thf(wife_type,type,
    wife: ( $i > $i > $o ) > $i > $i > $o ).

thf(time_type,type,
    time: $i > $o ).

thf(place_type,type,
    place: $i > $o ).

thf(appointment_type,type,
    appointment: $i > $o ).

thf(8,axiom,
    mtransitive @ ( wife @ peter ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_wife_peter) ).

thf(33,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( wife @ peter @ A @ B )
        & ( wife @ peter @ B @ C ) )
     => ( wife @ peter @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(14,axiom,
    mvalid @ ( mbox @ peter @ ( mbox @ john @ ( mimplies @ ( mand @ place @ time ) @ appointment ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_d) ).

thf(49,plain,
    ! [A: $i,B: $i] :
      ( ~ ( peter @ A @ B )
      | ! [C: $i] :
          ( ~ ( john @ B @ C )
          | ~ ( place @ C )
          | ~ ( time @ C )
          | ( appointment @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(10,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ ( wife @ peter ) @ A ) @ ( mbox @ peter @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_ii) ).

thf(39,plain,
    ! [A: $i,B: $i > $o] :
      ( ~ ! [C: $i] :
            ( ~ ( wife @ peter @ A @ C )
            | ( B @ C ) )
      | ! [C: $i] :
          ( ~ ( peter @ A @ C )
          | ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(9,axiom,
    ( mvalid
    @ ( mforall_prop
      @ ^ [A: $i > $o] : ( mimplies @ ( mbox @ peter @ ( mbox @ john @ A ) ) @ ( mbox @ john @ ( mbox @ peter @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_i) ).

thf(35,plain,
    ! [A: $i,B: $i > $o] :
      ( ~ ! [C: $i] :
            ( ~ ( peter @ A @ C )
            | ! [D: $i] :
                ( ~ ( john @ C @ D )
                | ( B @ D ) ) )
      | ! [C: $i] :
          ( ~ ( john @ A @ C )
          | ! [D: $i] :
              ( ~ ( peter @ C @ D )
              | ( B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(7,axiom,
    mtransitive @ john,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_john) ).

thf(31,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( john @ A @ B )
        & ( john @ B @ C ) )
     => ( john @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(3,axiom,
    mreflexive @ peter,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_peter) ).

thf(23,plain,
    ! [A: $i] : ( peter @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,conjecture,
    mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mand @ ( mbox @ peter @ ( mbox @ john @ appointment ) ) @ ( mbox @ john @ ( mbox @ peter @ appointment ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(15,plain,
    ~ ! [A: $i] :
        ~ ( ~ ! [B: $i] :
                ( ~ ( peter @ A @ B )
                | ! [C: $i] :
                    ( ~ ( john @ B @ C )
                    | ( appointment @ C ) ) )
          | ~ ! [B: $i] :
                ( ~ ( john @ A @ B )
                | ! [C: $i] :
                    ( ~ ( peter @ B @ C )
                    | ( appointment @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,axiom,
    mvalid @ ( mbox @ peter @ time ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_a) ).

thf(42,plain,
    ! [A: $i,B: $i] :
      ( ~ ( peter @ A @ B )
      | ( time @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(4,axiom,
    mreflexive @ john,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_john) ).

thf(25,plain,
    ! [A: $i] : ( john @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13,axiom,
    mvalid @ ( mbox @ ( wife @ peter ) @ ( mimplies @ ( mbox @ peter @ time ) @ ( mbox @ john @ time ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_c) ).

thf(46,plain,
    ! [A: $i,B: $i] :
      ( ~ ( wife @ peter @ A @ B )
      | ~ ! [C: $i] :
            ( ~ ( peter @ B @ C )
            | ( time @ C ) )
      | ! [C: $i] :
          ( ~ ( john @ B @ C )
          | ( time @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(6,axiom,
    mtransitive @ peter,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_peter) ).

thf(29,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( peter @ A @ B )
        & ( peter @ B @ C ) )
     => ( peter @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(12,axiom,
    mvalid @ ( mbox @ peter @ ( mbox @ john @ place ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_b) ).

thf(44,plain,
    ! [A: $i,B: $i] :
      ( ~ ( peter @ A @ B )
      | ! [C: $i] :
          ( ~ ( john @ B @ C )
          | ( place @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(5,axiom,
    mreflexive @ ( wife @ peter ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_wife_peter) ).

thf(27,plain,
    ! [A: $i] : ( wife @ peter @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(51,plain,
    $false,
    inference(e,[status(thm)],[33,49,39,35,31,23,15,42,25,46,29,44,27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : PUZ086^1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n016.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sat May 18 10:37:39 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.86/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.32/0.99  % [INFO] 	 Parsing done (155ms). 
% 1.32/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.81/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.81/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.81/1.25  % [INFO] 	 Scanning for conjecture ... 
% 2.16/1.37  % [INFO] 	 Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ... 
% 2.16/1.39  % [INFO] 	 Axiom selection finished. Selected 12 axioms (removed 0 axioms). 
% 2.16/1.39  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.16/1.40  % [INFO] 	 Type checking passed. 
% 2.16/1.40  % [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 ... 
% 3.42/1.88  % External prover 'e' found a proof!
% 3.42/1.88  % [INFO] 	 Killing All external provers ... 
% 3.42/1.88  % Time passed: 1370ms (effective reasoning time: 872ms)
% 3.42/1.88  % 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)>
% 3.42/1.88  % Axioms used in derivation (12): ax_i, trans_peter, ax_c, ax_b, trans_john, ax_ii, ax_a, refl_john, ax_d, refl_wife_peter, trans_wife_peter, refl_peter
% 3.42/1.88  % No. of inferences in proof: 28
% 3.42/1.88  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1370 ms resp. 872 ms w/o parsing
% 3.67/1.93  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.67/1.93  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------