TSTP Solution File: SEV222^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEV222^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 33.95s 6.06s
% Output   : Refutation 34.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   68 (  16 unt;   7 typ;   0 def)
%            Number of atoms       :  238 (  34 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  413 (  61   ~; 119   |;   7   &; 212   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   51 (  51   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   73 (  15   ^  51   !;   7   ?;  73   :)

% 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/sandbox2/benchmark/theBenchmark.p',cTHM60_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(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(11,plain,
    ( ( cW @ sk4 )
    | ~ ( sk2 @ sk1 ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(16,plain,
    ( ( cW @ sk4 )
    | ( cW @ sk2 ) ),
    inference(cnf,[status(esa)],[6]) ).

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(20,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)],[7]) ).

thf(21,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)],[20]) ).

thf(22,plain,
    ! [B: a > $o,A: a > $o] :
      ( ~ ( cW @ B )
      | ( cZ @ sk1 )
      | ( B @ sk1 )
      | ~ ( cW @ A )
      | ( A @ sk1 )
      | ( cZ @ sk1 ) ),
    inference(simp,[status(thm)],[21]) ).

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)],[22]) ).

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(137,plain,
    ! [B: a > $o,A: a > $o] :
      ( ( cW @ sk2 )
      | ( cZ @ sk1 )
      | ( A @ sk1 )
      | ~ ( cW @ A )
      | ( B @ sk1 )
      | ( ( cW @ sk4 )
       != ( cW @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[16,24]) ).

thf(138,plain,
    ! [A: a > $o] :
      ( ( cW @ sk2 )
      | ( cZ @ sk1 )
      | ( A @ sk1 )
      | ~ ( cW @ A )
      | ( sk4 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).

thf(748,plain,
    ! [A: a > $o] :
      ( ( cW @ sk2 )
      | ( cZ @ sk1 )
      | ( A @ sk1 )
      | ( sk4 @ sk1 )
      | ( ( cW @ sk4 )
       != ( cW @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[16,138]) ).

thf(749,plain,
    ( ( cW @ sk2 )
    | ( cZ @ sk1 )
    | ( sk4 @ sk1 )
    | ( sk4 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[748:[bind(A,$thf( sk4 ))]]) ).

thf(1060,plain,
    ( ( cW @ sk2 )
    | ( cZ @ sk1 )
    | ( sk4 @ sk1 ) ),
    inference(simp,[status(thm)],[749]) ).

thf(14,plain,
    ( ( sk3
      = ( ^ [A: a] :
            ( ( cZ @ A )
            | ( sk4 @ A ) ) ) )
    | ~ ( cZ @ sk1 ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(17,plain,
    ( ( ( ^ [A: a] :
            ( ( cZ @ A )
            | ( sk4 @ A ) ) )
      = sk3 )
    | ~ ( cZ @ sk1 ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(29,plain,
    ! [A: a] :
      ( ( ( ( cZ @ A )
          | ( sk4 @ A ) )
        = ( sk3 @ A ) )
      | ~ ( cZ @ sk1 ) ),
    inference(func_ext,[status(esa)],[17]) ).

thf(53,plain,
    ! [A: a] :
      ( ~ ( cZ @ sk1 )
      | ~ ( ( cZ @ A )
          | ( sk4 @ A ) )
      | ( sk3 @ A ) ),
    inference(bool_ext,[status(thm)],[29]) ).

thf(58,plain,
    ! [A: a] :
      ( ( sk3 @ A )
      | ~ ( cZ @ A )
      | ~ ( cZ @ sk1 ) ),
    inference(cnf,[status(esa)],[53]) ).

thf(8,plain,
    ( ~ ( sk3 @ sk1 )
    | ~ ( cZ @ sk1 ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(1092,plain,
    ! [A: a] :
      ( ~ ( cZ @ A )
      | ~ ( cZ @ sk1 )
      | ( ( sk3 @ A )
       != ( sk3 @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[58,8]) ).

thf(1093,plain,
    ( ~ ( cZ @ sk1 )
    | ~ ( cZ @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[1092:[bind(A,$thf( sk1 ))]]) ).

thf(1105,plain,
    ~ ( cZ @ sk1 ),
    inference(simp,[status(thm)],[1093]) ).

thf(1367,plain,
    ( ( cW @ sk2 )
    | $false
    | ( sk4 @ sk1 ) ),
    inference(rewrite,[status(thm)],[1060,1105]) ).

thf(1368,plain,
    ( ( cW @ sk2 )
    | ( sk4 @ sk1 ) ),
    inference(simp,[status(thm)],[1367]) ).

thf(13,plain,
    ( ( sk3
      = ( ^ [A: a] :
            ( ( cZ @ A )
            | ( sk4 @ A ) ) ) )
    | ( cW @ sk2 ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(19,plain,
    ( ( ( ^ [A: a] :
            ( ( cZ @ A )
            | ( sk4 @ A ) ) )
      = sk3 )
    | ( cW @ sk2 ) ),
    inference(lifteq,[status(thm)],[13]) ).

thf(35,plain,
    ! [A: a] :
      ( ( ( ( cZ @ A )
          | ( sk4 @ A ) )
        = ( sk3 @ A ) )
      | ( cW @ sk2 ) ),
    inference(func_ext,[status(esa)],[19]) ).

thf(1370,plain,
    ! [A: a] :
      ( ( cW @ sk2 )
      | ( sk3 @ A )
      | ( ( sk4 @ sk1 )
       != ( sk4 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1368,35]) ).

thf(1371,plain,
    ( ( cW @ sk2 )
    | ( sk3 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[1370:[bind(A,$thf( sk1 ))]]) ).

thf(10,plain,
    ( ~ ( sk3 @ sk1 )
    | ( cW @ sk2 ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(1381,plain,
    ( ( cW @ sk2 )
    | ( ( sk3 @ sk1 )
     != ( sk3 @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[1371,10]) ).

thf(1382,plain,
    cW @ sk2,
    inference(pattern_uni,[status(thm)],[1381:[]]) ).

thf(206,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(273,plain,
    ! [A: a > $o] :
      ( ( cZ @ sk1 )
      | ( A @ sk1 )
      | ~ ( cW @ A )
      | ( A @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( B ))]]) ).

thf(329,plain,
    ! [A: a > $o] :
      ( ( cZ @ sk1 )
      | ( A @ sk1 )
      | ~ ( cW @ A ) ),
    inference(simp,[status(thm)],[273]) ).

thf(1894,plain,
    ! [A: a > $o] :
      ( $false
      | ( A @ sk1 )
      | ~ ( cW @ A ) ),
    inference(rewrite,[status(thm)],[329,1105]) ).

thf(1895,plain,
    ! [A: a > $o] :
      ( ( A @ sk1 )
      | ~ ( cW @ A ) ),
    inference(simp,[status(thm)],[1894]) ).

thf(1937,plain,
    ! [A: a > $o] :
      ( ( A @ sk1 )
      | ( ( cW @ sk2 )
       != ( cW @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1382,1895]) ).

thf(1938,plain,
    sk2 @ sk1,
    inference(pattern_uni,[status(thm)],[1937:[bind(A,$thf( sk2 ))]]) ).

thf(2313,plain,
    ( ( cW @ sk4 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[11,1938]) ).

thf(2314,plain,
    cW @ sk4,
    inference(simp,[status(thm)],[2313]) ).

thf(2401,plain,
    ! [A: a > $o] :
      ( ( A @ sk1 )
      | ( ( cW @ sk4 )
       != ( cW @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2314,1895]) ).

thf(2402,plain,
    sk4 @ sk1,
    inference(pattern_uni,[status(thm)],[2401:[bind(A,$thf( sk4 ))]]) ).

thf(9,plain,
    ( ( sk3
      = ( ^ [A: a] :
            ( ( cZ @ A )
            | ( sk4 @ A ) ) ) )
    | ~ ( sk2 @ sk1 ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(18,plain,
    ( ( ( ^ [A: a] :
            ( ( cZ @ A )
            | ( sk4 @ A ) ) )
      = sk3 )
    | ~ ( sk2 @ sk1 ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(30,plain,
    ! [A: a] :
      ( ( ( ( cZ @ A )
          | ( sk4 @ A ) )
        = ( sk3 @ A ) )
      | ~ ( sk2 @ sk1 ) ),
    inference(func_ext,[status(esa)],[18]) ).

thf(2315,plain,
    ! [A: a] :
      ( ( ( ( cZ @ A )
          | ( sk4 @ A ) )
        = ( sk3 @ A ) )
      | ~ $true ),
    inference(rewrite,[status(thm)],[30,1938]) ).

thf(2316,plain,
    ! [A: a] :
      ( ( ( cZ @ A )
        | ( sk4 @ A ) )
      = ( sk3 @ A ) ),
    inference(simp,[status(thm)],[2315]) ).

thf(3464,plain,
    ! [A: a] :
      ( ( sk3 @ A )
      | ( ( sk4 @ sk1 )
       != ( sk4 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2402,2316]) ).

thf(3465,plain,
    sk3 @ sk1,
    inference(pattern_uni,[status(thm)],[3464:[bind(A,$thf( sk1 ))]]) ).

thf(12,plain,
    ( ~ ( sk3 @ sk1 )
    | ~ ( sk2 @ sk1 ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(2309,plain,
    ( ~ ( sk3 @ sk1 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[12,1938]) ).

thf(2310,plain,
    ~ ( sk3 @ sk1 ),
    inference(simp,[status(thm)],[2309]) ).

thf(3492,plain,
    $false,
    inference(rewrite,[status(thm)],[3465,2310]) ).

thf(3493,plain,
    $false,
    inference(simp,[status(thm)],[3492]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12  % Problem  : SEV222^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n009.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sun May 19 18:38:38 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.82/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.95  % [INFO] 	 Parsing done (105ms). 
% 1.18/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.62/1.18  % [INFO] 	 nitpick registered as external prover. 
% 1.62/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.77/1.26  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.77/1.26  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.77/1.26  % [INFO] 	 Type checking passed. 
% 1.77/1.27  % [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 ... 
% 33.95/6.05  % [INFO] 	 Killing All external provers ... 
% 33.95/6.06  % Time passed: 5539ms (effective reasoning time: 5089ms)
% 33.95/6.06  % 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)>
% 33.95/6.06  % Axioms used in derivation (0): 
% 33.95/6.06  % No. of inferences in proof: 61
% 33.95/6.06  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5539 ms resp. 5089 ms w/o parsing
% 34.05/6.13  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.05/6.13  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------