TSTP Solution File: SYO566^7 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO566^7 : TPTP v8.2.0. Released v5.5.0.
% 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 09:00:57 EDT 2024

% Result   : Theorem 3.48s 1.89s
% Output   : Refutation 3.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   36 (  13 unt;  12 typ;   5 def)
%            Number of atoms       :   81 (   7 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  151 (  22   ~;  18   |;   0   &; 107   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   7 con; 0-3 aty)
%            Number of variables   :   25 (   8   ^  17   !;   0   ?;  25   :)

% 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(exists_in_world_type,type,
    exists_in_world: mu > $i > $o ).

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] :
          ( ( exists_in_world @ C @ B )
         => ( A @ C @ B ) ) ) ) ).

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

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

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

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

thf(rel_s4_type,type,
    rel_s4: $i > $i > $o ).

thf(mbox_s4_type,type,
    mbox_s4: ( $i > $o ) > $i > $o ).

thf(mbox_s4_def,definition,
    ( mbox_s4
    = ( ^ [A: $i > $o,B: $i] :
        ! [C: $i] :
          ( ~ ( rel_s4 @ B @ C )
          | ( A @ C ) ) ) ) ).

thf(g_type,type,
    g: mu > $i > $o ).

thf(f_type,type,
    f: mu > $i > $o ).

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

thf(sk2_type,type,
    sk2: mu ).

thf(1,conjecture,
    ( mvalid
    @ ( mimplies
      @ ( mbox_s4
        @ ( mforall_ind
          @ ^ [A: mu] : ( mimplies @ ( f @ A ) @ ( g @ A ) ) ) )
      @ ( mimplies @ ( mforall_ind @ f ) @ ( mforall_ind @ g ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( mvalid
      @ ( mimplies
        @ ( mbox_s4
          @ ( mforall_ind
            @ ^ [A: mu] : ( mimplies @ ( f @ A ) @ ( g @ A ) ) ) )
        @ ( mimplies @ ( mforall_ind @ f ) @ ( mforall_ind @ g ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(7,plain,
    ~ ! [A: $i] :
        ( ~ ! [B: $i] :
              ( ~ ( rel_s4 @ A @ B )
              | ! [C: mu] :
                  ( ( exists_in_world @ C @ B )
                 => ( ~ ( f @ C @ B )
                    | ( g @ C @ B ) ) ) )
        | ~ ! [B: mu] :
              ( ( exists_in_world @ B @ A )
             => ( f @ B @ A ) )
        | ! [B: mu] :
            ( ( exists_in_world @ B @ A )
           => ( g @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    exists_in_world @ sk2 @ sk1,
    inference(cnf,[status(esa)],[7]) ).

thf(10,plain,
    ! [A: mu] :
      ( ~ ( exists_in_world @ A @ sk1 )
      | ( f @ A @ sk1 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(12,plain,
    ! [A: mu] :
      ( ~ ( exists_in_world @ A @ sk1 )
      | ( f @ A @ sk1 ) ),
    inference(simp,[status(thm)],[10]) ).

thf(33,plain,
    ! [A: mu] :
      ( ( f @ A @ sk1 )
      | ( ( exists_in_world @ sk2 @ sk1 )
       != ( exists_in_world @ A @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[9,12]) ).

thf(34,plain,
    f @ sk2 @ sk1,
    inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( sk2 ))]]) ).

thf(11,plain,
    ! [B: mu,A: $i] :
      ( ~ ( rel_s4 @ sk1 @ A )
      | ~ ( exists_in_world @ B @ A )
      | ~ ( f @ B @ A )
      | ( g @ B @ A ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(23,plain,
    ! [B: mu,A: $i] :
      ( ~ ( rel_s4 @ sk1 @ A )
      | ~ ( f @ B @ A )
      | ( g @ B @ A )
      | ( ( exists_in_world @ sk2 @ sk1 )
       != ( exists_in_world @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9,11]) ).

thf(24,plain,
    ( ~ ( rel_s4 @ sk1 @ sk1 )
    | ~ ( f @ sk2 @ sk1 )
    | ( g @ sk2 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(4,axiom,
    mreflexive @ rel_s4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).

thf(15,plain,
    ! [A: $i] : ( rel_s4 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(16,plain,
    ! [A: $i] : ( rel_s4 @ A @ A ),
    inference(cnf,[status(esa)],[15]) ).

thf(8,plain,
    ~ ( g @ sk2 @ sk1 ),
    inference(cnf,[status(esa)],[7]) ).

thf(29,plain,
    ( ~ $true
    | ~ ( f @ sk2 @ sk1 )
    | $false ),
    inference(rewrite,[status(thm)],[24,16,8]) ).

thf(30,plain,
    ~ ( f @ sk2 @ sk1 ),
    inference(simp,[status(thm)],[29]) ).

thf(40,plain,
    $false,
    inference(rewrite,[status(thm)],[34,30]) ).

thf(41,plain,
    $false,
    inference(simp,[status(thm)],[40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYO566^7 : TPTP v8.2.0. Released v5.5.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n002.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May 20 08:44:09 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.03/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.47/1.11  % [INFO] 	 Parsing done (172ms). 
% 1.47/1.12  % [INFO] 	 Running in sequential loop mode. 
% 2.06/1.33  % [INFO] 	 nitpick registered as external prover. 
% 2.06/1.33  % [INFO] 	 Scanning for conjecture ... 
% 2.26/1.43  % [INFO] 	 Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ... 
% 2.26/1.46  % [INFO] 	 Axiom selection finished. Selected 4 axioms (removed 0 axioms). 
% 2.26/1.46  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.26/1.46  % [INFO] 	 Type checking passed. 
% 2.52/1.47  % [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 ... 
% 3.48/1.88  % [INFO] 	 Killing All external provers ... 
% 3.48/1.88  % Time passed: 1357ms (effective reasoning time: 760ms)
% 3.48/1.88  % 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)>
% 3.48/1.88  % Axioms used in derivation (1): a1
% 3.48/1.88  % No. of inferences in proof: 19
% 3.48/1.89  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1357 ms resp. 760 ms w/o parsing
% 3.59/1.92  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.59/1.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------