TSTP Solution File: SYO266^5 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYO266^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 08:59:45 EDT 2024

% Result   : Theorem 16.86s 3.73s
% Output   : Refutation 17.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   54 (   6 unt;   5 typ;   0 def)
%            Number of atoms       :  206 (  17 equ;   0 cnn)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  431 (  86   ~; 100   |;   6   &; 239   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   52 (   0   ^  46   !;   6   ?;  52   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cQ_type,type,
    cQ: $i > $o ).

thf(cP_type,type,
    cP: $i > $o ).

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

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

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

thf(1,conjecture,
    ( ( ? [A: $i > $o] :
        ! [B: $i] :
          ( ( ( A @ B )
            | ( cP @ B ) )
          & ( ~ ( A @ B )
            | ( cQ @ B ) ) ) )
    = ( ! [A: $i] :
          ( ( cP @ A )
          | ( cQ @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM44) ).

thf(2,negated_conjecture,
    ( ( ? [A: $i > $o] :
        ! [B: $i] :
          ( ( ( A @ B )
            | ( cP @ B ) )
          & ( ~ ( A @ B )
            | ( cQ @ B ) ) ) )
   != ( ! [A: $i] :
          ( ( cP @ A )
          | ( cQ @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ? [A: $i > $o] :
        ! [B: $i] :
          ( ( ( A @ B )
            | ( cP @ B ) )
          & ( ~ ( A @ B )
            | ( cQ @ B ) ) ) )
   != ( ! [A: $i] :
          ( ( cP @ A )
          | ( cQ @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ? [A: $i > $o] :
        ! [B: $i] :
          ( ( ( A @ B )
            | ( cP @ B ) )
          & ( ~ ( A @ B )
            | ( cQ @ B ) ) ) )
   != ( ! [A: $i] :
          ( ( cP @ A )
          | ( cQ @ A ) ) ) ),
    inference(lifteq,[status(thm)],[3]) ).

thf(6,plain,
    ( ? [A: $i > $o] :
      ! [B: $i] :
        ( ( ( A @ B )
          | ( cP @ B ) )
        & ( ~ ( A @ B )
          | ( cQ @ B ) ) )
    | ! [A: $i] :
        ( ( cP @ A )
        | ( cQ @ A ) ) ),
    inference(bool_ext,[status(thm)],[4]) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ B )
      | ( cQ @ B )
      | ( sk3 @ A )
      | ( cP @ A ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(122,plain,
    ! [B: $i,A: $i] :
      ( ( cQ @ B )
      | ( sk3 @ A )
      | ( cP @ A )
      | ( ( cP @ B )
       != ( cP @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[15]) ).

thf(123,plain,
    ! [A: $i] :
      ( ( cQ @ A )
      | ( sk3 @ A )
      | ( cP @ A ) ),
    inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( B ))]]) ).

thf(126,plain,
    ! [A: $i] :
      ( ( cQ @ A )
      | ( sk3 @ A )
      | ( cP @ A ) ),
    inference(simp,[status(thm)],[123]) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ( cP @ B )
      | ( cQ @ B )
      | ~ ( sk3 @ A )
      | ( cQ @ A ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( cQ @ A )
      | ( cP @ A )
      | ( cP @ C )
      | ( cQ @ C )
      | ( cQ @ B )
      | ( ( sk3 @ A )
       != ( sk3 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[126,16]) ).

thf(724,plain,
    ! [B: $i,A: $i] :
      ( ( cQ @ A )
      | ( cP @ A )
      | ( cP @ B )
      | ( cQ @ B )
      | ( cQ @ A ) ),
    inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(736,plain,
    ! [B: $i,A: $i] :
      ( ( cQ @ A )
      | ( cP @ A )
      | ( cP @ B )
      | ( cQ @ B ) ),
    inference(simp,[status(thm)],[724]) ).

thf(1216,plain,
    ! [B: $i,A: $i] :
      ( ( cQ @ A )
      | ( cP @ A )
      | ( cQ @ B )
      | ( ( cP @ B )
       != ( cP @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[736]) ).

thf(1221,plain,
    ! [A: $i] :
      ( ( cQ @ A )
      | ( cP @ A )
      | ( cQ @ A ) ),
    inference(pattern_uni,[status(thm)],[1216:[bind(A,$thf( B ))]]) ).

thf(1252,plain,
    ! [A: $i] :
      ( ( cQ @ A )
      | ( cP @ A ) ),
    inference(simp,[status(thm)],[1221]) ).

thf(5,plain,
    ( ~ ? [A: $i > $o] :
        ! [B: $i] :
          ( ( ( A @ B )
            | ( cP @ B ) )
          & ( ~ ( A @ B )
            | ( cQ @ B ) ) )
    | ~ ! [A: $i] :
          ( ( cP @ A )
          | ( cQ @ A ) ) ),
    inference(bool_ext,[status(thm)],[4]) ).

thf(11,plain,
    ! [A: $i > $o] :
      ( ~ ( cP @ ( sk2 @ A ) )
      | ~ ( A @ ( sk1 @ A ) )
      | ~ ( cQ @ ( sk1 @ A ) ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(244,plain,
    ! [A: $i > $o] :
      ( ~ ( cP @ ( sk2 @ A ) )
      | ~ ( A @ ( sk1 @ A ) )
      | ( ( cQ @ ( sk1 @ A ) )
       != ( A @ ( sk1 @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[11]) ).

thf(264,plain,
    ( ~ ( cP @ ( sk2 @ cQ ) )
    | ~ ( cQ @ ( sk1 @ cQ ) ) ),
    inference(pre_uni,[status(thm)],[244:[bind(A,$thf( cQ ))]]) ).

thf(7,plain,
    ! [A: $i > $o] :
      ( ~ ( cP @ ( sk2 @ A ) )
      | ~ ( cP @ ( sk1 @ A ) )
      | ( A @ ( sk1 @ A ) ) ),
    inference(cnf,[status(esa)],[5]) ).

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

thf(29,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ~ ( cP @ ( sk2 @ A ) )
      | ~ ( cP @ ( sk1 @ A ) )
      | ~ ( cP @ ( sk2 @ B ) )
      | ~ ( cP @ ( sk1 @ B ) )
      | ( ( A @ ( sk1 @ A ) )
       != ( cQ @ ( sk1 @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,13]) ).

thf(47,plain,
    ( ~ ( cP @ ( sk2 @ cQ ) )
    | ~ ( cP @ ( sk1 @ cQ ) )
    | ~ ( cP @ ( sk2 @ cQ ) )
    | ~ ( cP @ ( sk1 @ cQ ) ) ),
    inference(pre_uni,[status(thm)],[29:[bind(A,$thf( cQ )),bind(B,$thf( cQ ))]]) ).

thf(73,plain,
    ( ~ ( cP @ ( sk2 @ cQ ) )
    | ~ ( cP @ ( sk1 @ cQ ) ) ),
    inference(simp,[status(thm)],[47]) ).

thf(1281,plain,
    ! [A: $i] :
      ( ( cQ @ A )
      | ~ ( cP @ ( sk1 @ cQ ) )
      | ( ( cP @ A )
       != ( cP @ ( sk2 @ cQ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1252,73]) ).

thf(1282,plain,
    ( ( cQ @ ( sk2 @ cQ ) )
    | ~ ( cP @ ( sk1 @ cQ ) ) ),
    inference(pattern_uni,[status(thm)],[1281:[bind(A,$thf( sk2 @ cQ ))]]) ).

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

thf(14,plain,
    ! [A: $i > $o] :
      ( ~ ( cQ @ ( sk2 @ A ) )
      | ~ ( cP @ ( sk1 @ A ) )
      | ~ ( cQ @ ( sk1 @ A ) ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(353,plain,
    ! [B: $i > $o,A: $i > $o] :
      ( ~ ( cQ @ ( sk2 @ A ) )
      | ~ ( cP @ ( sk1 @ A ) )
      | ~ ( cQ @ ( sk2 @ B ) )
      | ~ ( cP @ ( sk1 @ B ) )
      | ( ( A @ ( sk1 @ A ) )
       != ( cQ @ ( sk1 @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,14]) ).

thf(441,plain,
    ( ~ ( cQ @ ( sk2 @ cQ ) )
    | ~ ( cP @ ( sk1 @ cQ ) )
    | ~ ( cQ @ ( sk2 @ cQ ) )
    | ~ ( cP @ ( sk1 @ cQ ) ) ),
    inference(pre_uni,[status(thm)],[353:[bind(A,$thf( cQ )),bind(B,$thf( cQ ))]]) ).

thf(516,plain,
    ( ~ ( cQ @ ( sk2 @ cQ ) )
    | ~ ( cP @ ( sk1 @ cQ ) ) ),
    inference(simp,[status(thm)],[441]) ).

thf(1405,plain,
    ( ~ ( cP @ ( sk1 @ cQ ) )
    | ( ( cQ @ ( sk2 @ cQ ) )
     != ( cQ @ ( sk2 @ cQ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1282,516]) ).

thf(1406,plain,
    ~ ( cP @ ( sk1 @ cQ ) ),
    inference(pattern_uni,[status(thm)],[1405:[]]) ).

thf(1793,plain,
    ! [A: $i] :
      ( ( cQ @ A )
      | ( ( cP @ A )
       != ( cP @ ( sk1 @ cQ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1252,1406]) ).

thf(1794,plain,
    cQ @ ( sk1 @ cQ ),
    inference(pattern_uni,[status(thm)],[1793:[bind(A,$thf( sk1 @ cQ ))]]) ).

thf(1802,plain,
    ( ~ ( cP @ ( sk2 @ cQ ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[264,1794]) ).

thf(1803,plain,
    ~ ( cP @ ( sk2 @ cQ ) ),
    inference(simp,[status(thm)],[1802]) ).

thf(1888,plain,
    ! [A: $i] :
      ( ( cQ @ A )
      | ( ( cP @ A )
       != ( cP @ ( sk2 @ cQ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1252,1803]) ).

thf(1889,plain,
    cQ @ ( sk2 @ cQ ),
    inference(pattern_uni,[status(thm)],[1888:[bind(A,$thf( sk2 @ cQ ))]]) ).

thf(9,plain,
    ! [A: $i > $o] :
      ( ~ ( cQ @ ( sk2 @ A ) )
      | ~ ( A @ ( sk1 @ A ) )
      | ~ ( cQ @ ( sk1 @ A ) ) ),
    inference(cnf,[status(esa)],[5]) ).

thf(146,plain,
    ! [A: $i > $o] :
      ( ~ ( cQ @ ( sk2 @ A ) )
      | ~ ( cQ @ ( sk1 @ A ) )
      | ( ( A @ ( sk1 @ A ) )
       != ( cQ @ ( sk1 @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[9]) ).

thf(167,plain,
    ( ~ ( cQ @ ( sk2 @ cQ ) )
    | ~ ( cQ @ ( sk1 @ cQ ) ) ),
    inference(pre_uni,[status(thm)],[146:[bind(A,$thf( cQ ))]]) ).

thf(185,plain,
    ( ~ ( cQ @ ( sk1 @ cQ ) )
    | ( ( cQ @ ( sk2 @ cQ ) )
     != ( cQ @ ( sk1 @ cQ ) ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[167]) ).

thf(189,plain,
    ( ~ ( cQ @ ( sk1 @ cQ ) )
    | ( ( cQ @ ( sk2 @ cQ ) )
     != ( cQ @ ( sk1 @ cQ ) ) ) ),
    inference(simp,[status(thm)],[185]) ).

thf(1798,plain,
    ( ~ $true
    | ~ ( cQ @ ( sk2 @ cQ ) ) ),
    inference(rewrite,[status(thm)],[189,1794]) ).

thf(1799,plain,
    ~ ( cQ @ ( sk2 @ cQ ) ),
    inference(simp,[status(thm)],[1798]) ).

thf(1893,plain,
    $false,
    inference(rewrite,[status(thm)],[1889,1799]) ).

thf(1894,plain,
    $false,
    inference(simp,[status(thm)],[1893]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SYO266^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon May 20 09:33:09 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.81/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.94  % [INFO] 	 Parsing done (103ms). 
% 1.21/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.43/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.43/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.79/1.24  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.79/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.79/1.24  % [INFO] 	 Type checking passed. 
% 1.79/1.24  % [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 ... 
% 16.86/3.72  % [INFO] 	 Killing All external provers ... 
% 16.86/3.73  % Time passed: 3216ms (effective reasoning time: 2770ms)
% 16.86/3.73  % 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)>
% 16.86/3.73  % Axioms used in derivation (0): 
% 16.86/3.73  % No. of inferences in proof: 49
% 16.86/3.73  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3216 ms resp. 2770 ms w/o parsing
% 17.01/3.84  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.01/3.84  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------