TSTP Solution File: SYO061^4 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO061^4 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 08:59:08 EDT 2024

% Result   : Theorem 5.42s 2.93s
% Output   : Refutation 5.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   34 (  10 unt;   9 typ;   3 def)
%            Number of atoms       :   73 (   6 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  125 (  16   ~;  16   |;   0   &;  89   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :   19 (   3   ^  16   !;   0   ?;  19   :)

% Comments : 
%------------------------------------------------------------------------------
thf(irel_type,type,
    irel: $i > $i > $o ).

thf(iatom_type,type,
    iatom: ( $i > $o ) > $i > $o ).

thf(iatom_def,definition,
    ( iatom
    = ( ^ [A: $i > $o] : A ) ) ).

thf(iimplies_type,type,
    iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(iimplies_def,definition,
    ( iimplies
    = ( ^ [A: $i > $o,B: $i > $o] : ( mimplies @ ( mbox_s4 @ A ) @ ( mbox_s4 @ B ) ) ) ) ).

thf(ivalid_type,type,
    ivalid: ( $i > $o ) > $o ).

thf(ivalid_def,definition,
    ( ivalid
    = ( '!' @ $i ) ) ).

thf(a_type,type,
    a: $i > $o ).

thf(b_type,type,
    b: $i > $o ).

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

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

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

thf(1,conjecture,
    ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ( ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [A: $i] :
        ( ~ ! [B: $i] :
              ( ( irel @ A @ B )
             => ( a @ B ) )
        | ! [B: $i] :
            ( ( irel @ A @ B )
           => ( b @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    irel @ sk1 @ sk2,
    inference(cnf,[status(esa)],[6]) ).

thf(5,axiom,
    ivalid @ ( iimplies @ ( iatom @ a ) @ ( iatom @ b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).

thf(14,plain,
    ! [A: $i] :
      ( ~ ! [B: $i] :
            ( ( irel @ A @ B )
           => ( a @ B ) )
      | ! [B: $i] :
          ( ( irel @ A @ B )
         => ( b @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ( irel @ A @ ( sk3 @ A ) )
      | ~ ( irel @ A @ B )
      | ( b @ B ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(69,plain,
    ! [B: $i,A: $i] :
      ( ( irel @ A @ ( sk3 @ A ) )
      | ( b @ B )
      | ( ( irel @ sk1 @ sk2 )
       != ( irel @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8,15]) ).

thf(70,plain,
    ( ( irel @ sk1 @ ( sk3 @ sk1 ) )
    | ( b @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(7,plain,
    ~ ( b @ sk2 ),
    inference(cnf,[status(esa)],[6]) ).

thf(78,plain,
    ( ( irel @ sk1 @ ( sk3 @ sk1 ) )
    | $false ),
    inference(rewrite,[status(thm)],[70,7]) ).

thf(79,plain,
    irel @ sk1 @ ( sk3 @ sk1 ),
    inference(simp,[status(thm)],[78]) ).

thf(9,plain,
    ! [A: $i] :
      ( ~ ( irel @ sk1 @ A )
      | ( a @ A ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(80,plain,
    ! [A: $i] :
      ( ( a @ A )
      | ( ( irel @ sk1 @ ( sk3 @ sk1 ) )
       != ( irel @ sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[79,9]) ).

thf(81,plain,
    a @ ( sk3 @ sk1 ),
    inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( sk3 @ sk1 ))]]) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a @ ( sk3 @ A ) )
      | ~ ( irel @ A @ B )
      | ( b @ B ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a @ ( sk3 @ A ) )
      | ( b @ B )
      | ( ( irel @ sk1 @ sk2 )
       != ( irel @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8,16]) ).

thf(24,plain,
    ( ~ ( a @ ( sk3 @ sk1 ) )
    | ( b @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(51,plain,
    ( ~ ( a @ ( sk3 @ sk1 ) )
    | $false ),
    inference(rewrite,[status(thm)],[24,7]) ).

thf(52,plain,
    ~ ( a @ ( sk3 @ sk1 ) ),
    inference(simp,[status(thm)],[51]) ).

thf(91,plain,
    $false,
    inference(rewrite,[status(thm)],[81,52]) ).

thf(92,plain,
    $false,
    inference(simp,[status(thm)],[91]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SYO061^4 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n032.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon May 20 10:31:24 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.16/1.10  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.75/1.36  % [INFO] 	 Parsing done (255ms). 
% 1.75/1.38  % [INFO] 	 Running in sequential loop mode. 
% 2.47/1.82  % [INFO] 	 nitpick registered as external prover. 
% 2.47/1.82  % [INFO] 	 Scanning for conjecture ... 
% 2.79/1.98  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 2.79/2.01  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 2.79/2.02  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.79/2.02  % [INFO] 	 Type checking passed. 
% 2.79/2.03  % [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 ... 
% 5.42/2.92  % [INFO] 	 Killing All external provers ... 
% 5.42/2.93  % Time passed: 2410ms (effective reasoning time: 1542ms)
% 5.42/2.93  % 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)>
% 5.42/2.93  % Axioms used in derivation (1): axiom1
% 5.42/2.93  % No. of inferences in proof: 22
% 5.42/2.93  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2410 ms resp. 1542 ms w/o parsing
% 5.43/2.99  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.43/2.99  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------