TSTP Solution File: SEV221^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEV221^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 04:11:08 EDT 2024

% Result   : Theorem 125.24s 18.42s
% Output   : Refutation 125.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   74 (  12 unt;   7 typ;   0 def)
%            Number of atoms       :  267 (  37 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  485 (  99   ~; 102   |;  50   &; 234   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   47 (  47   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   74 (  15   ^  38   !;  21   ?;  74   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(cZ_type,type,
    cZ: a > $o ).

thf(cW_type,type,
    cW: ( a > $o ) > $o ).

thf(sk1_type,type,
    sk1: a ).

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

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

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

thf(1,conjecture,
    ! [A: a] :
      ( ( ? [B: a > $o] :
            ( ( cW @ B )
            & ( B @ A ) )
        & ( cZ @ A ) )
      = ( ? [B: a > $o] :
            ( ? [C: a > $o] :
                ( ( cW @ C )
                & ( B
                  = ( ^ [D: a] :
                        ( ( cZ @ D )
                        & ( C @ D ) ) ) ) )
            & ( B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM61_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: a] :
        ( ( ? [B: a > $o] :
              ( ( cW @ B )
              & ( B @ A ) )
          & ( cZ @ A ) )
        = ( ? [B: a > $o] :
              ( ? [C: a > $o] :
                  ( ( cW @ C )
                  & ( B
                    = ( ^ [D: a] :
                          ( ( cZ @ D )
                          & ( C @ D ) ) ) ) )
              & ( B @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: a] :
        ( ( ? [B: a > $o] :
              ( ( cW @ B )
              & ( B @ A ) )
          & ( cZ @ A ) )
        = ( ? [B: a > $o] :
              ( ? [C: a > $o] :
                  ( ( cW @ C )
                  & ( B
                    = ( ^ [D: a] :
                          ( ( cZ @ D )
                          & ( C @ D ) ) ) ) )
              & ( B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ? [A: a > $o] :
          ( ( cW @ A )
          & ( A @ sk1 ) )
      & ( cZ @ sk1 ) )
   != ( ? [A: a > $o] :
          ( ? [B: a > $o] :
              ( ( cW @ B )
              & ( A
                = ( ^ [C: a] :
                      ( ( cZ @ C )
                      & ( B @ C ) ) ) ) )
          & ( A @ sk1 ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ? [A: a > $o] :
          ( ( cW @ A )
          & ( A @ sk1 ) )
      & ( cZ @ sk1 ) )
   != ( ? [A: a > $o] :
          ( ? [B: a > $o] :
              ( ( cW @ B )
              & ( A
                = ( ^ [C: a] :
                      ( ( cZ @ C )
                      & ( B @ C ) ) ) ) )
          & ( A @ sk1 ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ? [A: a > $o] :
          ( ( cW @ A )
          & ( A @ sk1 ) )
      & ( cZ @ sk1 ) )
    | ? [A: a > $o] :
        ( ? [B: a > $o] :
            ( ( cW @ B )
            & ( A
              = ( ^ [C: a] :
                    ( ( cZ @ C )
                    & ( B @ C ) ) ) ) )
        & ( A @ sk1 ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(19,plain,
    ( ( sk3
      = ( ^ [A: a] :
            ( ( cZ @ A )
            & ( sk4 @ A ) ) ) )
    | ( sk2 @ sk1 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(22,plain,
    ( ( ( ^ [A: a] :
            ( ( cZ @ A )
            & ( sk4 @ A ) ) )
      = sk3 )
    | ( sk2 @ sk1 ) ),
    inference(lifteq,[status(thm)],[19]) ).

thf(174,plain,
    ! [A: a] :
      ( ( ( ( cZ @ A )
          & ( sk4 @ A ) )
        = ( sk3 @ A ) )
      | ( sk2 @ sk1 ) ),
    inference(func_ext,[status(esa)],[22]) ).

thf(353,plain,
    ! [A: a] :
      ( ( sk2 @ sk1 )
      | ( ( cZ @ A )
        & ( sk4 @ A ) )
      | ~ ( sk3 @ A ) ),
    inference(bool_ext,[status(thm)],[174]) ).

thf(378,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( sk4 @ A )
      | ( sk2 @ sk1 ) ),
    inference(cnf,[status(esa)],[353]) ).

thf(12,plain,
    ( ( sk3 @ sk1 )
    | ( cW @ sk2 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(14,plain,
    ( ( sk3
      = ( ^ [A: a] :
            ( ( cZ @ A )
            & ( sk4 @ A ) ) ) )
    | ( cW @ sk2 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(20,plain,
    ( ( ( ^ [A: a] :
            ( ( cZ @ A )
            & ( sk4 @ A ) ) )
      = sk3 )
    | ( cW @ sk2 ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(167,plain,
    ! [A: a] :
      ( ( ( ( cZ @ A )
          & ( sk4 @ A ) )
        = ( sk3 @ A ) )
      | ( cW @ sk2 ) ),
    inference(func_ext,[status(esa)],[20]) ).

thf(248,plain,
    ! [A: a] :
      ( ( cW @ sk2 )
      | ( ( cZ @ A )
        & ( sk4 @ A ) )
      | ~ ( sk3 @ A ) ),
    inference(bool_ext,[status(thm)],[167]) ).

thf(263,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( sk4 @ A )
      | ( cW @ sk2 ) ),
    inference(cnf,[status(esa)],[248]) ).

thf(3201,plain,
    ! [A: a] :
      ( ( cW @ sk2 )
      | ( sk4 @ A )
      | ( ( sk3 @ sk1 )
       != ( sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[12,263]) ).

thf(3202,plain,
    ( ( cW @ sk2 )
    | ( sk4 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[3201:[bind(A,$thf( sk1 ))]]) ).

thf(13,plain,
    ( ( cW @ sk4 )
    | ( cW @ sk2 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(6,plain,
    ( ~ ( ? [A: a > $o] :
            ( ( cW @ A )
            & ( A @ sk1 ) )
        & ( cZ @ sk1 ) )
    | ~ ? [A: a > $o] :
          ( ? [B: a > $o] :
              ( ( cW @ B )
              & ( A
                = ( ^ [C: a] :
                      ( ( cZ @ C )
                      & ( B @ C ) ) ) ) )
          & ( A @ sk1 ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(8,plain,
    ! [C: a > $o,B: a > $o,A: a > $o] :
      ( ~ ( cW @ C )
      | ( B
       != ( ^ [D: a] :
              ( ( cZ @ D )
              & ( C @ D ) ) ) )
      | ~ ( B @ sk1 )
      | ~ ( cW @ A )
      | ~ ( A @ sk1 )
      | ~ ( cZ @ sk1 ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(9,plain,
    ! [C: a > $o,B: a > $o,A: a > $o] :
      ( ( B
       != ( ^ [D: a] :
              ( ( cZ @ D )
              & ( C @ D ) ) ) )
      | ~ ( cW @ C )
      | ~ ( B @ sk1 )
      | ~ ( cW @ A )
      | ~ ( A @ sk1 )
      | ~ ( cZ @ sk1 ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(10,plain,
    ! [B: a > $o,A: a > $o] :
      ( ~ ( cW @ B )
      | ~ ( ( cZ @ sk1 )
          & ( B @ sk1 ) )
      | ~ ( cW @ A )
      | ~ ( A @ sk1 )
      | ~ ( cZ @ sk1 ) ),
    inference(simp,[status(thm)],[9]) ).

thf(23,plain,
    ! [B: a > $o,A: a > $o] :
      ( ~ ( cZ @ sk1 )
      | ~ ( A @ sk1 )
      | ~ ( cW @ A )
      | ~ ( cZ @ sk1 )
      | ~ ( B @ sk1 )
      | ~ ( cW @ B ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(24,plain,
    ! [B: a > $o,A: a > $o] :
      ( ~ ( cZ @ sk1 )
      | ~ ( A @ sk1 )
      | ~ ( cW @ A )
      | ~ ( B @ sk1 )
      | ~ ( cW @ B ) ),
    inference(simp,[status(thm)],[23]) ).

thf(45,plain,
    ! [B: a > $o,A: a > $o] :
      ( ~ ( cZ @ sk1 )
      | ~ ( A @ sk1 )
      | ~ ( cW @ A )
      | ~ ( B @ sk1 )
      | ( ( cW @ B )
       != ( cW @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[24]) ).

thf(85,plain,
    ! [A: a > $o] :
      ( ~ ( cZ @ sk1 )
      | ~ ( A @ sk1 )
      | ~ ( cW @ A )
      | ~ ( A @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( B ))]]) ).

thf(107,plain,
    ! [A: a > $o] :
      ( ~ ( cZ @ sk1 )
      | ~ ( A @ sk1 )
      | ~ ( cW @ A ) ),
    inference(simp,[status(thm)],[85]) ).

thf(191,plain,
    ! [A: a > $o] :
      ( ( cW @ sk2 )
      | ~ ( cZ @ sk1 )
      | ~ ( A @ sk1 )
      | ( ( cW @ sk4 )
       != ( cW @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[13,107]) ).

thf(192,plain,
    ( ( cW @ sk2 )
    | ~ ( cZ @ sk1 )
    | ~ ( sk4 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( sk4 ))]]) ).

thf(3272,plain,
    ( ( cW @ sk2 )
    | ~ ( cZ @ sk1 )
    | ( ( sk4 @ sk1 )
     != ( sk4 @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[3202,192]) ).

thf(3273,plain,
    ( ( cW @ sk2 )
    | ~ ( cZ @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[3272:[]]) ).

thf(3414,plain,
    ! [A: a > $o] :
      ( ~ ( cZ @ sk1 )
      | ~ ( A @ sk1 )
      | ( ( cW @ sk2 )
       != ( cW @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3273,107]) ).

thf(3415,plain,
    ( ~ ( cZ @ sk1 )
    | ~ ( sk2 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[3414:[bind(A,$thf( sk2 ))]]) ).

thf(11,plain,
    ( ( sk3 @ sk1 )
    | ( cZ @ sk1 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(17,plain,
    ( ( sk3
      = ( ^ [A: a] :
            ( ( cZ @ A )
            & ( sk4 @ A ) ) ) )
    | ( cZ @ sk1 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(21,plain,
    ( ( ( ^ [A: a] :
            ( ( cZ @ A )
            & ( sk4 @ A ) ) )
      = sk3 )
    | ( cZ @ sk1 ) ),
    inference(lifteq,[status(thm)],[17]) ).

thf(169,plain,
    ! [A: a] :
      ( ( ( ( cZ @ A )
          & ( sk4 @ A ) )
        = ( sk3 @ A ) )
      | ( cZ @ sk1 ) ),
    inference(func_ext,[status(esa)],[21]) ).

thf(338,plain,
    ! [A: a] :
      ( ( cZ @ sk1 )
      | ( ( cZ @ A )
        & ( sk4 @ A ) )
      | ~ ( sk3 @ A ) ),
    inference(bool_ext,[status(thm)],[169]) ).

thf(350,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( sk4 @ A )
      | ( cZ @ sk1 ) ),
    inference(cnf,[status(esa)],[338]) ).

thf(28240,plain,
    ! [A: a] :
      ( ( cZ @ sk1 )
      | ( sk4 @ A )
      | ( ( sk3 @ sk1 )
       != ( sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[11,350]) ).

thf(28241,plain,
    ( ( cZ @ sk1 )
    | ( sk4 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[28240:[bind(A,$thf( sk1 ))]]) ).

thf(28351,plain,
    ! [A: a] :
      ( ( cZ @ sk1 )
      | ( ( cZ @ A )
        = ( sk3 @ A ) )
      | ( ( sk4 @ sk1 )
       != ( sk4 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[28241,169]) ).

thf(28352,plain,
    ( ( cZ @ sk1 )
    | ( ( sk3 @ sk1 )
      = ( cZ @ sk1 ) ) ),
    inference(pattern_uni,[status(thm)],[28351:[bind(A,$thf( sk1 ))]]) ).

thf(28536,plain,
    ( ( cZ @ sk1 )
    | ( ( sk3 @ sk1 )
     != ( sk3 @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[28352,11]) ).

thf(28537,plain,
    cZ @ sk1,
    inference(pattern_uni,[status(thm)],[28536:[]]) ).

thf(29057,plain,
    ( ~ $true
    | ~ ( sk2 @ sk1 ) ),
    inference(rewrite,[status(thm)],[3415,28537]) ).

thf(29058,plain,
    ~ ( sk2 @ sk1 ),
    inference(simp,[status(thm)],[29057]) ).

thf(29822,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( sk4 @ A )
      | $false ),
    inference(rewrite,[status(thm)],[378,29058]) ).

thf(29823,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( sk4 @ A ) ),
    inference(simp,[status(thm)],[29822]) ).

thf(15,plain,
    ( ( cW @ sk4 )
    | ( sk2 @ sk1 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(202,plain,
    ! [A: a > $o] :
      ( ( cW @ sk4 )
      | ~ ( cZ @ sk1 )
      | ~ ( cW @ A )
      | ( ( sk2 @ sk1 )
       != ( A @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[15,107]) ).

thf(226,plain,
    ( ( cW @ sk4 )
    | ~ ( cZ @ sk1 )
    | ~ ( cW @ sk2 ) ),
    inference(pre_uni,[status(thm)],[202:[bind(A,$thf( sk2 ))]]) ).

thf(543,plain,
    ! [A: a > $o] :
      ( ~ ( cZ @ sk1 )
      | ~ ( cW @ sk2 )
      | ~ ( A @ sk1 )
      | ( ( cW @ sk4 )
       != ( cW @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[226,107]) ).

thf(544,plain,
    ( ~ ( cZ @ sk1 )
    | ~ ( cW @ sk2 )
    | ~ ( sk4 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[543:[bind(A,$thf( sk4 ))]]) ).

thf(3400,plain,
    ( ~ ( cZ @ sk1 )
    | ~ ( sk4 @ sk1 )
    | ( ( cW @ sk2 )
     != ( cW @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[3273,544]) ).

thf(3401,plain,
    ( ~ ( cZ @ sk1 )
    | ~ ( sk4 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[3400:[]]) ).

thf(29091,plain,
    ( ~ $true
    | ~ ( sk4 @ sk1 ) ),
    inference(rewrite,[status(thm)],[3401,28537]) ).

thf(29092,plain,
    ~ ( sk4 @ sk1 ),
    inference(simp,[status(thm)],[29091]) ).

thf(29836,plain,
    ! [A: a] :
      ( ~ ( sk3 @ A )
      | ( ( sk4 @ A )
       != ( sk4 @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[29823,29092]) ).

thf(29837,plain,
    ~ ( sk3 @ sk1 ),
    inference(pattern_uni,[status(thm)],[29836:[bind(A,$thf( sk1 ))]]) ).

thf(16,plain,
    ( ( sk3 @ sk1 )
    | ( sk2 @ sk1 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(29395,plain,
    ( ( sk3 @ sk1 )
    | $false ),
    inference(rewrite,[status(thm)],[16,29058]) ).

thf(29396,plain,
    sk3 @ sk1,
    inference(simp,[status(thm)],[29395]) ).

thf(29880,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[29837,29396]) ).

thf(29881,plain,
    $false,
    inference(simp,[status(thm)],[29880]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV221^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n012.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 18:56:24 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.97/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.16/0.95  % [INFO] 	 Parsing done (101ms). 
% 1.16/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.61/1.18  % [INFO] 	 nitpick registered as external prover. 
% 1.61/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.76/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.76/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.76/1.26  % [INFO] 	 Type checking passed. 
% 1.76/1.26  % [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 ... 
% 125.24/18.40  % [INFO] 	 Killing All external provers ... 
% 125.24/18.41  % Time passed: 17883ms (effective reasoning time: 17438ms)
% 125.24/18.41  % 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)>
% 125.24/18.42  % Axioms used in derivation (0): 
% 125.24/18.42  % No. of inferences in proof: 67
% 125.24/18.42  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17883 ms resp. 17438 ms w/o parsing
% 125.29/18.46  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 125.29/18.46  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------