TSTP Solution File: SYO457^6 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO457^6 : TPTP v8.2.0. Released v4.0.0.
% 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 09:00:24 EDT 2024

% Result   : Theorem 3.55s 2.19s
% Output   : Refutation 3.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   32 (  12 unt;  11 typ;   5 def)
%            Number of atoms       :   64 (   7 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :   95 (  20   ~;  11   |;   0   &;  64   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   7 con; 0-3 aty)
%            Number of variables   :   19 (   5   ^  14   !;   0   ?;  19   :)

% 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(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_s5_type,type,
    rel_s5: $i > $i > $o ).

thf(mbox_s5_type,type,
    mbox_s5: ( $i > $o ) > $i > $o ).

thf(mbox_s5_def,definition,
    ( mbox_s5
    = ( ^ [A: $i > $o,B: $i] :
        ! [C: $i] :
          ( ~ ( rel_s5 @ B @ C )
          | ( A @ C ) ) ) ) ).

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(p_type,type,
    p: $i > $o ).

thf(q_type,type,
    q: $i > $o ).

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

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

thf(1,conjecture,
    mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mdia_s5 @ ( mimplies @ q @ p ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mdia_s5 @ ( mimplies @ q @ p ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(10,plain,
    rel_s5 @ sk1 @ sk2,
    inference(cnf,[status(esa)],[6]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk1 @ A )
      | ~ ( p @ A ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(12,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk1 @ A )
      | ~ ( p @ A ) ),
    inference(simp,[status(thm)],[8]) ).

thf(24,plain,
    ! [A: $i] :
      ( ~ ( p @ A )
      | ( ( rel_s5 @ sk1 @ sk2 )
       != ( rel_s5 @ sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10,12]) ).

thf(25,plain,
    ~ ( p @ sk2 ),
    inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( sk2 ))]]) ).

thf(3,axiom,
    mreflexive @ rel_s5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).

thf(13,plain,
    ! [A: $i] : ( rel_s5 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,plain,
    ! [A: $i] : ( rel_s5 @ A @ A ),
    inference(cnf,[status(esa)],[13]) ).

thf(9,plain,
    ! [A: $i] :
      ( ~ ( rel_s5 @ sk2 @ A )
      | ( p @ A ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(20,plain,
    ! [B: $i,A: $i] :
      ( ( p @ B )
      | ( ( rel_s5 @ A @ A )
       != ( rel_s5 @ sk2 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[14,9]) ).

thf(21,plain,
    p @ sk2,
    inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(30,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[25,21]) ).

thf(31,plain,
    $false,
    inference(simp,[status(thm)],[30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SYO457^6 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n002.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May 20 09:21:09 EDT 2024
% 0.15/0.31  % CPUTime  : 
% 0.85/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.43/1.14  % [INFO] 	 Parsing done (238ms). 
% 1.51/1.16  % [INFO] 	 Running in sequential loop mode. 
% 1.91/1.49  % [INFO] 	 nitpick registered as external prover. 
% 1.91/1.50  % [INFO] 	 Scanning for conjecture ... 
% 2.40/1.66  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 2.46/1.69  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 2.46/1.70  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.46/1.70  % [INFO] 	 Type checking passed. 
% 2.46/1.70  % [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 ... 
% 3.55/2.18  % [INFO] 	 Killing All external provers ... 
% 3.55/2.18  % Time passed: 1731ms (effective reasoning time: 1021ms)
% 3.55/2.18  % 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)>
% 3.55/2.19  % Axioms used in derivation (1): a1
% 3.55/2.19  % No. of inferences in proof: 16
% 3.55/2.19  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1731 ms resp. 1021 ms w/o parsing
% 3.55/2.23  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.55/2.23  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------