TSTP Solution File: SYO480^6 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO480^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 09:00:39 EDT 2024

% Result   : Theorem 2.89s 1.68s
% Output   : Refutation 3.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   26 (   9 unt;  10 typ;   4 def)
%            Number of atoms       :   51 (   5 equ;   0 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   90 (  21   ~;   9   |;   0   &;  60   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   9 con; 0-3 aty)
%            Number of variables   :   22 (   6   ^  15   !;   1   ?;  22   :)

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

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

thf(rel_s5_type,type,
    rel_s5: $i > $i > $o ).

thf(mdia_s5_type,type,
    mdia_s5: ( $i > $o ) > $i > $o ).

thf(mdia_s5_def,definition,
    ( mdia_s5
    = ( ^ [A: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ A ) ) ) ) ) ).

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

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

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

thf(sk3_type,type,
    sk3: mu ).

thf(1,conjecture,
    ( mvalid
    @ ( mimplies @ ( mdia_s5 @ ( mforall_ind @ f ) )
      @ ( mforall_ind
        @ ^ [A: mu] : ( mdia_s5 @ ( f @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid
      @ ( mimplies @ ( mdia_s5 @ ( mforall_ind @ f ) )
        @ ( mforall_ind
          @ ^ [A: mu] : ( mdia_s5 @ ( f @ A ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [A: $i] :
        ( ! [B: $i] :
            ( ~ ( rel_s5 @ A @ B )
            | ~ ! [C: mu] : ( f @ C @ B ) )
        | ! [B: mu] :
            ~ ! [C: $i] :
                ( ~ ( rel_s5 @ A @ C )
                | ~ ( f @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ~ ! [A: $i] :
        ( ! [B: $i] :
            ( ~ ( rel_s5 @ A @ B )
            | ~ ! [C: mu] : ( f @ C @ B ) )
        | ~ ? [B: mu] :
            ! [C: $i] :
              ( ~ ( rel_s5 @ A @ C )
              | ~ ( f @ B @ C ) ) ),
    inference(miniscope,[status(thm)],[6]) ).

thf(9,plain,
    ! [A: mu] : ( f @ A @ sk2 ),
    inference(cnf,[status(esa)],[7]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk1 @ A )
      | ~ ( f @ sk3 @ A ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(11,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk1 @ A )
      | ~ ( f @ sk3 @ A ) ),
    inference(simp,[status(thm)],[8]) ).

thf(18,plain,
    ! [B: $i,A: mu] :
      ( ~ ( rel_s5 @ sk1 @ B )
      | ( ( f @ A @ sk2 )
       != ( f @ sk3 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[9,11]) ).

thf(19,plain,
    ~ ( rel_s5 @ sk1 @ sk2 ),
    inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).

thf(10,plain,
    rel_s5 @ sk1 @ sk2,
    inference(cnf,[status(esa)],[7]) ).

thf(24,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[19,10]) ).

thf(25,plain,
    $false,
    inference(simp,[status(thm)],[24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYO480^6 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n027.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 : Mon May 20 08:36:39 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.83/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.19/1.00  % [INFO] 	 Parsing done (151ms). 
% 1.47/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.81/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.81/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.92/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 2.18/1.35  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 2.18/1.36  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.18/1.36  % [INFO] 	 Type checking passed. 
% 2.18/1.36  % [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 ... 
% 2.89/1.68  % [INFO] 	 Killing All external provers ... 
% 2.89/1.68  % Time passed: 1160ms (effective reasoning time: 665ms)
% 2.89/1.68  % 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)>
% 2.89/1.68  % Axioms used in derivation (0): 
% 2.89/1.68  % No. of inferences in proof: 12
% 2.89/1.68  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1160 ms resp. 665 ms w/o parsing
% 3.05/1.71  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.05/1.71  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------