TSTP Solution File: SYO431^1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO431^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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 09:00:14 EDT 2024

% Result   : Theorem 4.55s 2.06s
% Output   : Refutation 4.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   39 (  13 unt;  12 typ;   6 def)
%            Number of atoms       :   87 (  10 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  155 (  28   ~;  16   |;   0   &; 109   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   6 con; 0-3 aty)
%            Number of variables   :   30 (   8   ^  22   !;   0   ?;  30   :)

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

thf(mnot_type,type,
    mnot: ( $i > $o ) > $i > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: $i > $o,B: $i] :
          ~ ( A @ B ) ) ) ).

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

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

thf(rel_b_type,type,
    rel_b: $i > $i > $o ).

thf(mbox_b_type,type,
    mbox_b: ( $i > $o ) > $i > $o ).

thf(mbox_b_def,definition,
    ( mbox_b
    = ( ^ [A: $i > $o,B: $i] :
        ! [C: $i] :
          ( ~ ( rel_b @ B @ C )
          | ( A @ C ) ) ) ) ).

thf(mdia_b_type,type,
    mdia_b: ( $i > $o ) > $i > $o ).

thf(mdia_b_def,definition,
    ( mdia_b
    = ( ^ [A: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ A ) ) ) ) ) ).

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

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

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

thf(sk4_type,type,
    sk4: $i > $i ).

thf(1,conjecture,
    mvalid @ ( mnot @ ( mdia_b @ ( mand @ ( mdia_b @ ( mbox_b @ ( mdia_b @ p ) ) ) @ ( mbox_b @ ( mnot @ p ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mnot @ ( mdia_b @ ( mand @ ( mdia_b @ ( mbox_b @ ( mdia_b @ p ) ) ) @ ( mbox_b @ ( mnot @ p ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(5,plain,
    ~ ! [A: $i,B: $i] :
        ( ~ ( rel_b @ A @ B )
        | ! [C: $i] :
            ( ~ ( rel_b @ B @ C )
            | ~ ! [D: $i] :
                  ( ~ ( rel_b @ C @ D )
                  | ~ ! [E: $i] :
                        ( ~ ( rel_b @ D @ E )
                        | ~ ( p @ E ) ) ) )
        | ~ ! [C: $i] :
              ( ~ ( rel_b @ B @ C )
              | ~ ( p @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    rel_b @ sk2 @ sk3,
    inference(cnf,[status(esa)],[5]) ).

thf(4,axiom,
    msymmetric @ rel_b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).

thf(14,plain,
    ! [A: $i,B: $i] :
      ( ( rel_b @ A @ B )
     => ( rel_b @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rel_b @ A @ B )
      | ( rel_b @ B @ A ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(87,plain,
    ! [B: $i,A: $i] :
      ( ( rel_b @ B @ A )
      | ( ( rel_b @ sk2 @ sk3 )
       != ( rel_b @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8,15]) ).

thf(88,plain,
    rel_b @ sk3 @ sk2,
    inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(9,plain,
    ! [A: $i] :
      ( ~ ( rel_b @ sk3 @ A )
      | ( rel_b @ A @ ( sk4 @ A ) ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(115,plain,
    ! [A: $i] :
      ( ( rel_b @ A @ ( sk4 @ A ) )
      | ( ( rel_b @ sk3 @ sk2 )
       != ( rel_b @ sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[88,9]) ).

thf(116,plain,
    rel_b @ sk2 @ ( sk4 @ sk2 ),
    inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( sk2 ))]]) ).

thf(10,plain,
    ! [A: $i] :
      ( ~ ( rel_b @ sk2 @ A )
      | ~ ( p @ A ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(11,plain,
    ! [A: $i] :
      ( ~ ( rel_b @ sk2 @ A )
      | ~ ( p @ A ) ),
    inference(simp,[status(thm)],[10]) ).

thf(150,plain,
    ! [A: $i] :
      ( ~ ( p @ A )
      | ( ( rel_b @ sk2 @ ( sk4 @ sk2 ) )
       != ( rel_b @ sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[116,11]) ).

thf(151,plain,
    ~ ( p @ ( sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( sk4 @ sk2 ))]]) ).

thf(7,plain,
    ! [A: $i] :
      ( ~ ( rel_b @ sk3 @ A )
      | ( p @ ( sk4 @ A ) ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(121,plain,
    ! [A: $i] :
      ( ( p @ ( sk4 @ A ) )
      | ( ( rel_b @ sk3 @ sk2 )
       != ( rel_b @ sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[88,7]) ).

thf(122,plain,
    p @ ( sk4 @ sk2 ),
    inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( sk2 ))]]) ).

thf(161,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[151,122]) ).

thf(162,plain,
    $false,
    inference(simp,[status(thm)],[161]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SYO431^1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n004.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon May 20 09:37:09 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.89/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.99  % [INFO] 	 Parsing done (152ms). 
% 1.20/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.82/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.91/1.22  % [INFO] 	 Scanning for conjecture ... 
% 2.22/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 2.22/1.35  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.22/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.22/1.35  % [INFO] 	 Type checking passed. 
% 2.22/1.35  % [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 ... 
% 4.55/2.05  % [INFO] 	 Killing All external provers ... 
% 4.55/2.06  % Time passed: 1547ms (effective reasoning time: 1048ms)
% 4.55/2.06  % 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)>
% 4.55/2.06  % Axioms used in derivation (1): a2
% 4.55/2.06  % No. of inferences in proof: 21
% 4.55/2.06  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1547 ms resp. 1048 ms w/o parsing
% 4.56/2.10  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.56/2.10  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------