TSTP Solution File: AGT038^1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : AGT038^1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 17:58:30 EDT 2024

% Result   : Theorem 111.99s 18.26s
% Output   : Refutation 112.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   57 (  19 unt;  17 typ;   7 def)
%            Number of atoms       :   95 (  11 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  211 (  30   ~;  17   |;   0   &; 162   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   52 (  52   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  19 usr;   9 con; 0-3 aty)
%            Number of variables   :   63 (  12   ^  48   !;   3   ?;  63   :)

% 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_ind_type,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

thf(mforall_ind_def,definition,
    ( mforall_ind
    = ( ^ [A: mu > $i > $o,B: $i] :
        ! [C: mu] : ( 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(mdia_type,type,
    mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mdia_def,definition,
    ( mdia
    = ( ^ [A: $i > $i > $o,B: $i > $o] : ( mnot @ ( mbox @ A @ ( mnot @ B ) ) ) ) ) ).

thf(msymmetric_type,type,
    msymmetric: ( $i > $i > $o ) > $o ).

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

thf(mserial_type,type,
    mserial: ( $i > $i > $o ) > $o ).

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

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

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

thf(a1_type,type,
    a1: $i > $i > $o ).

thf(piotr_type,type,
    piotr: mu ).

thf(pepsi_type,type,
    pepsi: mu ).

thf(beer_type,type,
    beer: mu ).

thf(likes_type,type,
    likes: mu > mu > $i > $o ).

thf(possibly_likes_type,type,
    possibly_likes: mu > mu > $i > $o ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk3_type,type,
    sk3: $i > $i ).

thf(sk7_type,type,
    sk7: $i > $i ).

thf(29,axiom,
    mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_3) ).

thf(99,plain,
    ! [A: $i] :
      ~ ! [B: $i] :
          ( ~ ( a1 @ A @ B )
          | ~ ( likes @ piotr @ beer @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(100,plain,
    ~ ? [A: $i] :
      ! [B: $i] :
        ( ~ ( a1 @ A @ B )
        | ~ ( likes @ piotr @ beer @ B ) ),
    inference(miniscope,[status(thm)],[99]) ).

thf(102,plain,
    ! [A: $i] : ( a1 @ A @ ( sk7 @ A ) ),
    inference(cnf,[status(esa)],[100]) ).

thf(30,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [A: mu] :
          ( mforall_ind
          @ ^ [B: mu] : ( mimplies @ ( mdia @ a1 @ ( likes @ A @ B ) ) @ ( possibly_likes @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_user_communication_3) ).

thf(103,plain,
    ! [A: $i,B: mu,C: mu] :
      ( ! [D: $i] :
          ( ~ ( a1 @ A @ D )
          | ~ ( likes @ B @ C @ D ) )
      | ( possibly_likes @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(104,plain,
    ! [D: $i,C: mu,B: mu,A: $i] :
      ( ~ ( a1 @ A @ D )
      | ~ ( likes @ B @ C @ D )
      | ( possibly_likes @ B @ C @ A ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(1,conjecture,
    mvalid @ ( possibly_likes @ piotr @ pepsi ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( possibly_likes @ piotr @ pepsi ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(42,plain,
    ~ ! [A: $i] : ( possibly_likes @ piotr @ pepsi @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(43,plain,
    ~ ( possibly_likes @ piotr @ pepsi @ sk1 ),
    inference(cnf,[status(esa)],[42]) ).

thf(14714,plain,
    ! [D: $i,C: mu,B: mu,A: $i] :
      ( ~ ( a1 @ A @ D )
      | ~ ( likes @ B @ C @ D )
      | ( ( possibly_likes @ B @ C @ A )
       != ( possibly_likes @ piotr @ pepsi @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[104,43]) ).

thf(14715,plain,
    ! [A: $i] :
      ( ~ ( a1 @ sk1 @ A )
      | ~ ( likes @ piotr @ pepsi @ A ) ),
    inference(pattern_uni,[status(thm)],[14714:[bind(A,$thf( sk1 )),bind(B,$thf( piotr )),bind(C,$thf( pepsi ))]]) ).

thf(14735,plain,
    ! [A: $i] :
      ( ~ ( a1 @ sk1 @ A )
      | ~ ( likes @ piotr @ pepsi @ A ) ),
    inference(simp,[status(thm)],[14715]) ).

thf(10,axiom,
    mserial @ a1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_D_a1) ).

thf(58,plain,
    ! [A: $i] :
    ? [B: $i] : ( a1 @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(59,plain,
    ! [A: $i] : ( a1 @ A @ ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[58]) ).

thf(9,axiom,
    msymmetric @ a1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_B_a1) ).

thf(56,plain,
    ! [A: $i,B: $i] :
      ( ( a1 @ A @ B )
     => ( a1 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(57,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a1 @ A @ B )
      | ( a1 @ B @ A ) ),
    inference(cnf,[status(esa)],[56]) ).

thf(460,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( a1 @ C @ B )
      | ( ( a1 @ A @ ( sk3 @ A ) )
       != ( a1 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[59,57]) ).

thf(461,plain,
    ! [A: $i] : ( a1 @ ( sk3 @ A ) @ A ),
    inference(pattern_uni,[status(thm)],[460:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk3 @ D ))]]) ).

thf(471,plain,
    ! [A: $i] : ( a1 @ ( sk3 @ A ) @ A ),
    inference(simp,[status(thm)],[461]) ).

thf(37,axiom,
    mvalid @ ( mbox @ a1 @ ( likes @ piotr @ pepsi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_2) ).

thf(117,plain,
    ! [A: $i,B: $i] :
      ( ~ ( a1 @ A @ B )
      | ( likes @ piotr @ pepsi @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(118,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a1 @ A @ B )
      | ( likes @ piotr @ pepsi @ B ) ),
    inference(cnf,[status(esa)],[117]) ).

thf(704,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( likes @ piotr @ pepsi @ C )
      | ( ( a1 @ ( sk3 @ A ) @ A )
       != ( a1 @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[471,118]) ).

thf(705,plain,
    ! [A: $i] : ( likes @ piotr @ pepsi @ A ),
    inference(pattern_uni,[status(thm)],[704:[bind(A,$thf( D )),bind(B,$thf( sk3 @ D )),bind(C,$thf( D ))]]) ).

thf(722,plain,
    ! [A: $i] : ( likes @ piotr @ pepsi @ A ),
    inference(simp,[status(thm)],[705]) ).

thf(14737,plain,
    ! [A: $i] :
      ( ~ ( a1 @ sk1 @ A )
      | ~ $true ),
    inference(rewrite,[status(thm)],[14735,722]) ).

thf(14738,plain,
    ! [A: $i] :
      ~ ( a1 @ sk1 @ A ),
    inference(simp,[status(thm)],[14737]) ).

thf(14744,plain,
    ! [B: $i,A: $i] :
      ( ( a1 @ A @ ( sk7 @ A ) )
     != ( a1 @ sk1 @ B ) ),
    inference(paramod_ordered,[status(thm)],[102,14738]) ).

thf(14745,plain,
    $false,
    inference(pattern_uni,[status(thm)],[14744:[bind(A,$thf( sk1 )),bind(B,$thf( sk7 @ sk1 ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : AGT038^1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.06/0.13  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n025.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sat May 18 18:53:39 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 1.07/1.01  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.73/1.29  % [INFO] 	 Parsing done (285ms). 
% 1.73/1.31  % [INFO] 	 Running in sequential loop mode. 
% 2.47/1.69  % [INFO] 	 nitpick registered as external prover. 
% 2.47/1.70  % [INFO] 	 Scanning for conjecture ... 
% 2.86/1.91  % [INFO] 	 Found a conjecture (or negated_conjecture) and 39 axioms. Running axiom selection ... 
% 3.17/1.98  % [INFO] 	 Axiom selection finished. Selected 39 axioms (removed 0 axioms). 
% 3.17/2.00  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.17/2.01  % [INFO] 	 Type checking passed. 
% 3.17/2.02  % [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 ... 
% 111.99/18.25  % [INFO] 	 Killing All external provers ... 
% 111.99/18.26  % Time passed: 17759ms (effective reasoning time: 16943ms)
% 111.99/18.26  % 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)>
% 111.99/18.26  % Axioms used in derivation (5): axioms_B_a1, axiom_a3_3, axiom_user_communication_3, axioms_D_a1, axiom_a1_2
% 111.99/18.26  % No. of inferences in proof: 33
% 111.99/18.26  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17759 ms resp. 16943 ms w/o parsing
% 112.12/18.36  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 112.12/18.36  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------