TSTP Solution File: SEU948^5 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEU948^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% 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 : Mon Jun 24 15:29:30 EDT 2024

% Result   : Theorem 56.94s 12.82s
% Output   : Refutation 56.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   32 (   7 unt;   0 typ;   0 def)
%            Number of atoms       :   57 (   6 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  313 (  36   ~;  36   |;  12   &; 208   @)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   66 (  66   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  108 (  67   ^  41   !;   0   ?; 108   :)

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

thf(sk1_type,type,
    sk1: a > a ).

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

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

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

thf(sk5_type,type,
    sk5: ( ( a > a ) > $o ) > a > a ).

thf(sk6_type,type,
    sk6: ( a > a ) > $o ).

thf(1,conjecture,
    ! [A: a > a,B: a > a,C: a > a] :
      ( ( ! [D: ( a > a ) > $o] :
            ( ( ( D
                @ ^ [E: a] : E )
              & ! [E: a > a] :
                  ( ( D @ E )
                 => ( D
                    @ ^ [F: a] : ( A @ ( E @ F ) ) ) ) )
           => ( D @ B ) )
        & ! [D: ( a > a ) > $o] :
            ( ( ( D
                @ ^ [E: a] : E )
              & ! [E: a > a] :
                  ( ( D @ E )
                 => ( D
                    @ ^ [F: a] : ( A @ ( E @ F ) ) ) ) )
           => ( D @ C ) ) )
     => ! [D: ( a > a ) > $o] :
          ( ( ( D
              @ ^ [E: a] : E )
            & ! [E: a > a] :
                ( ( D @ E )
               => ( D
                  @ ^ [F: a] : ( A @ ( E @ F ) ) ) ) )
         => ( D
            @ ^ [E: a] : ( B @ ( C @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM135_pme) ).

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

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

thf(8,plain,
    ! [A: ( a > a ) > $o] :
      ( ~ ( A
          @ ^ [B: a] : B )
      | ( A @ ( sk4 @ A ) )
      | ( A @ sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: a > a] :
      ( ~ ( sk6 @ A )
      | ( sk6
        @ ^ [B: a] : ( sk1 @ ( A @ B ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(19,plain,
    ! [A: a > a] :
      ( ~ ( sk6 @ A )
      | ( sk6
        @ ^ [B: a] : ( sk1 @ ( A @ B ) ) ) ),
    inference(simp,[status(thm)],[9]) ).

thf(7,plain,
    ! [A: ( a > a ) > $o] :
      ( ~ ( A
          @ ^ [B: a] : B )
      | ~ ( A
          @ ^ [B: a] : ( sk1 @ ( sk4 @ A @ B ) ) )
      | ( A @ sk2 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( sk6
      @ ^ [A: a] : ( sk2 @ ( sk3 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(33,plain,
    ! [A: ( a > a ) > $o] :
      ( ~ ( A
          @ ^ [B: a] : B )
      | ~ ( A
          @ ^ [B: a] : ( sk1 @ ( sk4 @ A @ B ) ) )
      | ( ( A @ sk2 )
       != ( sk6
          @ ^ [B: a] : ( sk2 @ ( sk3 @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7,4]) ).

thf(59,plain,
    ( ~ ( sk6 @ sk3 )
    | ~ ( sk6
        @ ^ [A: a] :
            ( sk1
            @ ( sk4
              @ ^ [B: a > a] :
                  ( sk6
                  @ ^ [C: a] : ( B @ ( sk3 @ C ) ) )
              @ ( sk3 @ A ) ) ) ) ),
    inference(pre_uni,[status(thm)],[33:[bind(A,$thf( ^ [B: a > a] : ( sk6 @ ^ [C: a] : ( B @ ( sk3 @ C ) ) ) ))]]) ).

thf(6,plain,
    ( sk6
    @ ^ [A: a] : A ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ! [A: ( a > a ) > $o] :
      ( ~ ( A
          @ ^ [B: a] : B )
      | ( A @ ( sk5 @ A ) )
      | ( A @ sk3 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(15,plain,
    ! [A: ( a > a ) > $o] :
      ( ~ ( A
          @ ^ [B: a] : B )
      | ( A @ ( sk5 @ A ) )
      | ( A @ sk3 ) ),
    inference(simp,[status(thm)],[5]) ).

thf(233,plain,
    ! [A: ( a > a ) > $o] :
      ( ( A @ ( sk5 @ A ) )
      | ( A @ sk3 )
      | ( ( sk6
          @ ^ [B: a] : B )
       != ( A
          @ ^ [B: a] : B ) ) ),
    inference(paramod_ordered,[status(thm)],[6,15]) ).

thf(286,plain,
    ( ( sk6 @ ( sk5 @ sk6 ) )
    | ( sk6 @ sk3 ) ),
    inference(pre_uni,[status(thm)],[233:[bind(A,$thf( sk6 ))]]) ).

thf(791,plain,
    ! [A: a > a] :
      ( ( sk6 @ sk3 )
      | ( sk6
        @ ^ [B: a] : ( sk1 @ ( A @ B ) ) )
      | ( ( sk6 @ ( sk5 @ sk6 ) )
       != ( sk6 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[286,19]) ).

thf(792,plain,
    ( ( sk6 @ sk3 )
    | ( sk6
      @ ^ [A: a] : ( sk1 @ ( sk5 @ sk6 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[791:[bind(A,$thf( sk5 @ sk6 ))]]) ).

thf(10,plain,
    ! [A: ( a > a ) > $o] :
      ( ~ ( A
          @ ^ [B: a] : B )
      | ~ ( A
          @ ^ [B: a] : ( sk1 @ ( sk5 @ A @ B ) ) )
      | ( A @ sk3 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(16,plain,
    ! [A: ( a > a ) > $o] :
      ( ~ ( A
          @ ^ [B: a] : B )
      | ~ ( A
          @ ^ [B: a] : ( sk1 @ ( sk5 @ A @ B ) ) )
      | ( A @ sk3 ) ),
    inference(simp,[status(thm)],[10]) ).

thf(1666,plain,
    ! [A: ( a > a ) > $o] :
      ( ( sk6 @ sk3 )
      | ~ ( A
          @ ^ [B: a] : B )
      | ( A @ sk3 )
      | ( ( sk6
          @ ^ [B: a] : ( sk1 @ ( sk5 @ sk6 @ B ) ) )
       != ( A
          @ ^ [B: a] : ( sk1 @ ( sk5 @ A @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[792,16]) ).

thf(1720,plain,
    ( ( sk6 @ sk3 )
    | ~ ( sk6
        @ ^ [A: a] : A )
    | ( sk6 @ sk3 ) ),
    inference(pre_uni,[status(thm)],[1666:[bind(A,$thf( sk6 ))]]) ).

thf(1744,plain,
    ( ( sk6 @ sk3 )
    | ~ ( sk6
        @ ^ [A: a] : A ) ),
    inference(simp,[status(thm)],[1720]) ).

thf(1745,plain,
    ( ( sk6 @ sk3 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[1744,6]) ).

thf(1746,plain,
    sk6 @ sk3,
    inference(simp,[status(thm)],[1745]) ).

thf(1749,plain,
    ( ~ $true
    | ~ ( sk6
        @ ^ [A: a] :
            ( sk1
            @ ( sk4
              @ ^ [B: a > a] :
                  ( sk6
                  @ ^ [C: a] : ( B @ ( sk3 @ C ) ) )
              @ ( sk3 @ A ) ) ) ) ),
    inference(rewrite,[status(thm)],[59,1746]) ).

thf(1750,plain,
    ~ ( sk6
      @ ^ [A: a] :
          ( sk1
          @ ( sk4
            @ ^ [B: a > a] :
                ( sk6
                @ ^ [C: a] : ( B @ ( sk3 @ C ) ) )
            @ ( sk3 @ A ) ) ) ),
    inference(simp,[status(thm)],[1749]) ).

thf(3113,plain,
    ! [A: a > a] :
      ( ~ ( sk6 @ A )
      | ( ( sk6
          @ ^ [B: a] : ( sk1 @ ( A @ B ) ) )
       != ( sk6
          @ ^ [B: a] :
              ( sk1
              @ ( sk4
                @ ^ [C: a > a] :
                    ( sk6
                    @ ^ [D: a] : ( C @ ( sk3 @ D ) ) )
                @ ( sk3 @ B ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[19,1750]) ).

thf(3114,plain,
    ~ ( sk6
      @ ^ [A: a] :
          ( sk4
          @ ^ [B: a > a] :
              ( sk6
              @ ^ [C: a] : ( B @ ( sk3 @ C ) ) )
          @ ( sk3 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[3113:[bind(A,$thf( ^ [B: a] : ( sk4 @ ^ [C: a > a] : ( sk6 @ ^ [D: a] : ( C @ ( sk3 @ D ) ) ) @ ( sk3 @ B ) ) ))]]) ).

thf(3160,plain,
    ! [A: ( a > a ) > $o] :
      ( ~ ( A
          @ ^ [B: a] : B )
      | ( A @ sk2 )
      | ( ( A @ ( sk4 @ A ) )
       != ( sk6
          @ ^ [B: a] :
              ( sk4
              @ ^ [C: a > a] :
                  ( sk6
                  @ ^ [D: a] : ( C @ ( sk3 @ D ) ) )
              @ ( sk3 @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,3114]) ).

thf(3183,plain,
    ( ~ ( sk6 @ sk3 )
    | ( sk6
      @ ^ [A: a] : ( sk2 @ ( sk3 @ A ) ) ) ),
    inference(pre_uni,[status(thm)],[3160:[bind(A,$thf( ^ [B: a > a] : ( sk6 @ ^ [C: a] : ( B @ ( sk3 @ C ) ) ) ))]]) ).

thf(4874,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[3183,1746,4]) ).

thf(4875,plain,
    $false,
    inference(simp,[status(thm)],[4874]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU948^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_Leo-III %s %d THM
% 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 : Fri Jun 21 17:11:55 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.92/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.00/0.93  % [INFO] 	 Parsing done (107ms). 
% 1.00/0.94  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.59/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.72/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.92/1.24  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.92/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.92/1.24  % [INFO] 	 Type checking passed. 
% 1.92/1.25  % [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 ... 
% 56.94/12.81  % [INFO] 	 Killing All external provers ... 
% 56.94/12.82  % Time passed: 12321ms (effective reasoning time: 11874ms)
% 56.94/12.82  % 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)>
% 56.94/12.82  % Axioms used in derivation (0): 
% 56.94/12.82  % No. of inferences in proof: 32
% 56.94/12.82  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12321 ms resp. 11874 ms w/o parsing
% 56.94/12.87  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 56.94/12.87  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------