%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEV061^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.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 04:10:52 EDT 2024

% Result   : Theorem 4.24s 2.39s
% Output   : Refutation 4.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   32 (   8 unt;   8 typ;   0 def)
%            Number of atoms       :   56 (  33 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  124 (  20   ~;  22   |;   9   &;  64   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   36 (   0   ^  36   !;   0   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
thf(b_type,type,
    b: $tType ).

thf(a_type,type,
    a: $tType ).

thf(sk1_type,type,
    sk1: b ).

thf(sk2_type,type,
    sk2: a ).

thf(sk3_type,type,
    sk3: b > a > $o ).

thf(sk4_type,type,
    sk4: b > a > $o ).

thf(sk5_type,type,
    sk5: b ).

thf(sk6_type,type,
    sk6: a ).

thf(1,conjecture,
    ! [A: b,B: a,C: b > a > $o,D: b > a > $o] :
      ( ! [E: b,F: a] :
          ( ( D @ E @ F )
         => ( ( C @ E @ F )
            | ( ( E = A )
              & ( F = B ) ) ) )
     => ! [E: b,F: a] :
          ( ( ( D @ E @ F )
            & ~ ( ( E = A )
                & ( F = B ) ) )
         => ( C @ E @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM176_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: b,B: a,C: b > a > $o,D: b > a > $o] :
        ( ! [E: b,F: a] :
            ( ( D @ E @ F )
           => ( ( C @ E @ F )
              | ( ( E = A )
                & ( F = B ) ) ) )
       => ! [E: b,F: a] :
            ( ( ( D @ E @ F )
              & ~ ( ( E = A )
                  & ( F = B ) ) )
           => ( C @ E @ F ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: b,B: a,C: b > a > $o,D: b > a > $o] :
        ( ! [E: b,F: a] :
            ( ( D @ E @ F )
           => ( ( C @ E @ F )
              | ( ( E = A )
                & ( F = B ) ) ) )
       => ! [E: b,F: a] :
            ( ( ( D @ E @ F )
              & ~ ( ( E = A )
                  & ( F = B ) ) )
           => ( C @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    sk4 @ sk5 @ sk6,
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [B: a,A: b] :
      ( ~ ( sk4 @ A @ B )
      | ( sk3 @ A @ B )
      | ( A = sk1 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ! [B: a,A: b] :
      ( ( A = sk1 )
      | ~ ( sk4 @ A @ B )
      | ( sk3 @ A @ B ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(16,plain,
    ! [B: a,A: b] :
      ( ( A = sk1 )
      | ( sk3 @ A @ B )
      | ( ( sk4 @ sk5 @ sk6 )
       != ( sk4 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[8,10]) ).

thf(17,plain,
    ( ( sk5 = sk1 )
    | ( sk3 @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(5,plain,
    ~ ( sk3 @ sk5 @ sk6 ),
    inference(cnf,[status(esa)],[3]) ).

thf(38,plain,
    ( ( sk5 = sk1 )
    | $false ),
    inference(rewrite,[status(thm)],[17,5]) ).

thf(39,plain,
    sk5 = sk1,
    inference(simp,[status(thm)],[38]) ).

thf(45,plain,
    sk4 @ sk1 @ sk6,
    inference(rewrite,[status(thm)],[8,39]) ).

thf(4,plain,
    ! [B: a,A: b] :
      ( ~ ( sk4 @ A @ B )
      | ( sk3 @ A @ B )
      | ( B = sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [B: a,A: b] :
      ( ( B = sk2 )
      | ~ ( sk4 @ A @ B )
      | ( sk3 @ A @ B ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(63,plain,
    ! [B: a,A: b] :
      ( ( B = sk2 )
      | ( sk3 @ A @ B )
      | ( ( sk4 @ sk1 @ sk6 )
       != ( sk4 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[45,11]) ).

thf(64,plain,
    ( ( sk6 = sk2 )
    | ( sk3 @ sk1 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( sk1 )),bind(B,$thf( sk6 ))]]) ).

thf(40,plain,
    ~ ( sk3 @ sk1 @ sk6 ),
    inference(rewrite,[status(thm)],[5,39]) ).

thf(69,plain,
    ( ( sk6 = sk2 )
    | $false ),
    inference(rewrite,[status(thm)],[64,40]) ).

thf(70,plain,
    sk6 = sk2,
    inference(simp,[status(thm)],[69]) ).

thf(6,plain,
    ( ( sk5 != sk1 )
    | ( sk6 != sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ( ( sk5 != sk1 )
    | ( sk6 != sk2 ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(43,plain,
    ( ( sk1 != sk1 )
    | ( sk6 != sk2 ) ),
    inference(rewrite,[status(thm)],[9,39]) ).

thf(44,plain,
    sk6 != sk2,
    inference(simp,[status(thm)],[43]) ).

thf(71,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[70,44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10  % Problem  : SEV061^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun May 19 18:26:09 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.99/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.11  % [INFO] 	 Parsing done (155ms). 
% 1.28/1.13  % [INFO] 	 Running in sequential loop mode. 
% 1.85/1.50  % [INFO] 	 nitpick registered as external prover. 
% 1.93/1.50  % [INFO] 	 Scanning for conjecture ... 
% 2.03/1.60  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.19/1.64  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.19/1.64  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.19/1.65  % [INFO] 	 Type checking passed. 
% 2.19/1.65  % [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 ... 
% 4.24/2.39  % [INFO] 	 Killing All external provers ... 
% 4.24/2.39  % Time passed: 1902ms (effective reasoning time: 1254ms)
% 4.24/2.39  % 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)>
% 4.24/2.39  % Axioms used in derivation (0): 
% 4.24/2.39  % No. of inferences in proof: 24
% 4.24/2.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1902 ms resp. 1254 ms w/o parsing
% 4.29/2.44  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.29/2.44  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------