TSTP Solution File: SYO462^4 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO462^4 : 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 09:00:29 EDT 2024

% Result   : Theorem 3.59s 2.02s
% Output   : Refutation 3.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   49 (   8 unt;  12 typ;   4 def)
%            Number of atoms       :  136 (  11 equ;   0 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  236 (  57   ~;  55   |;   0   &; 124   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;  10 con; 0-3 aty)
%            Number of variables   :   24 (   5   ^  19   !;   0   ?;  24   :)

% 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(mequiv_type,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mequiv_def,definition,
    ( mequiv
    = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ A ) ) ) ) ).

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

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

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

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

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

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

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

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

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

thf(9,plain,
    ( ( rel_b @ sk1 @ sk3 )
    | sk2 ),
    inference(cnf,[status(esa)],[5]) ).

thf(7,plain,
    ! [A: $i] :
      ( ~ ( rel_b @ sk1 @ A )
      | ~ ( p @ A )
      | ( q @ A ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(30,plain,
    ! [A: $i] :
      ( sk2
      | ~ ( p @ A )
      | ( q @ A )
      | ( ( rel_b @ sk1 @ sk3 )
       != ( rel_b @ sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9,7]) ).

thf(31,plain,
    ( sk2
    | ~ ( p @ sk3 )
    | ( q @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk3 ))]]) ).

thf(10,plain,
    ( ~ ( q @ sk3 )
    | sk2 ),
    inference(cnf,[status(esa)],[5]) ).

thf(66,plain,
    ( sk2
    | ~ ( p @ sk3 )
    | ( ( q @ sk3 )
     != ( q @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[31,10]) ).

thf(67,plain,
    ( sk2
    | ~ ( p @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[66:[]]) ).

thf(6,plain,
    ( ~ sk2
    | ( rel_b @ sk1 @ sk4 ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(13,plain,
    ! [A: $i] :
      ( ~ sk2
      | ~ ( rel_b @ sk1 @ A )
      | ( q @ A ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(14,plain,
    ! [A: $i] :
      ( ~ sk2
      | ~ ( rel_b @ sk1 @ A )
      | ( q @ A ) ),
    inference(simp,[status(thm)],[13]) ).

thf(20,plain,
    ! [A: $i] :
      ( ~ sk2
      | ( q @ A )
      | ( ( rel_b @ sk1 @ sk4 )
       != ( rel_b @ sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[6,14]) ).

thf(21,plain,
    ( ~ sk2
    | ( q @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( sk4 ))]]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( rel_b @ sk1 @ A )
      | ~ ( q @ A )
      | ( p @ A ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(34,plain,
    ! [A: $i] :
      ( ~ sk2
      | ~ ( q @ A )
      | ( p @ A )
      | ( ( rel_b @ sk1 @ sk4 )
       != ( rel_b @ sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[6,8]) ).

thf(35,plain,
    ( ~ sk2
    | ~ ( q @ sk4 )
    | ( p @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( sk4 ))]]) ).

thf(60,plain,
    ( ~ sk2
    | ( p @ sk4 )
    | ( ( q @ sk4 )
     != ( q @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[21,35]) ).

thf(61,plain,
    ( ~ sk2
    | ( p @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[60:[]]) ).

thf(11,plain,
    ( ~ sk2
    | ~ ( p @ sk4 ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(77,plain,
    ( ~ sk2
    | ( ( p @ sk4 )
     != ( p @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[61,11]) ).

thf(78,plain,
    ~ sk2,
    inference(pattern_uni,[status(thm)],[77:[]]) ).

thf(83,plain,
    ( ( rel_b @ sk1 @ sk3 )
    | $false ),
    inference(rewrite,[status(thm)],[9,78]) ).

thf(84,plain,
    rel_b @ sk1 @ sk3,
    inference(simp,[status(thm)],[83]) ).

thf(12,plain,
    ! [A: $i] :
      ( ~ ( rel_b @ sk1 @ A )
      | ( p @ A )
      | sk2 ),
    inference(cnf,[status(esa)],[5]) ).

thf(15,plain,
    ! [A: $i] :
      ( ~ ( rel_b @ sk1 @ A )
      | ( p @ A )
      | sk2 ),
    inference(simp,[status(thm)],[12]) ).

thf(87,plain,
    ! [A: $i] :
      ( ~ ( rel_b @ sk1 @ A )
      | ( p @ A )
      | $false ),
    inference(rewrite,[status(thm)],[15,78]) ).

thf(88,plain,
    ! [A: $i] :
      ( ~ ( rel_b @ sk1 @ A )
      | ( p @ A ) ),
    inference(simp,[status(thm)],[87]) ).

thf(103,plain,
    ! [A: $i] :
      ( ( p @ A )
      | ( ( rel_b @ sk1 @ sk3 )
       != ( rel_b @ sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[84,88]) ).

thf(104,plain,
    p @ sk3,
    inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( sk3 ))]]) ).

thf(109,plain,
    ( $false
    | ~ $true ),
    inference(rewrite,[status(thm)],[67,104,78]) ).

thf(110,plain,
    $false,
    inference(simp,[status(thm)],[109]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SYO462^4 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12  % 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 09:05:53 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.81/0.80  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.20/0.95  % [INFO] 	 Parsing done (151ms). 
% 1.32/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.75/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.75/1.21  % [INFO] 	 Scanning for conjecture ... 
% 2.09/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ... 
% 2.09/1.35  % [INFO] 	 Axiom selection finished. Selected 2 axioms (removed 0 axioms). 
% 2.09/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.09/1.35  % [INFO] 	 Type checking passed. 
% 2.09/1.36  % [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 ... 
% 3.59/2.01  % [INFO] 	 Killing All external provers ... 
% 3.59/2.02  % Time passed: 1567ms (effective reasoning time: 1050ms)
% 3.59/2.02  % 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)>
% 3.59/2.02  % Axioms used in derivation (0): 
% 3.59/2.02  % No. of inferences in proof: 33
% 3.59/2.02  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1567 ms resp. 1050 ms w/o parsing
% 3.80/2.07  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.80/2.07  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------