TSTP Solution File: SEV121^5 by Leo-III---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV121^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n001.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 15:58:16 EDT 2024

% Result   : Theorem 4.59s 1.95s
% Output   : Refutation 4.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   25 (  13 unt;   0 typ;   0 def)
%            Number of atoms       :   47 (  38 equ;   4 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  238 (  32   ~;  43   |;   0   &; 154   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  42   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   4 usr;   5 con; 0-2 aty)
%            Number of variables   :   69 (  36   ^  33   !;   0   ?;  69   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sk1_type,type,
    sk1: $i ).

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

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

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

thf(1,conjecture,
    ( ( (=) @ $i )
    = ( ^ [A: $i,B: $i] :
        ! [C: $i > $i > $o] :
          ( ! [D: $i] : ( C @ D @ D )
         => ( C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM47C_pme) ).

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

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

thf(4,plain,
    ( ( (=) @ $i )
   != ( ^ [A: $i,B: $i] :
        ! [C: $i > $i > $o] :
          ( ! [D: $i] : ( C @ D @ D )
         => ( C @ A @ B ) ) ) ),
    inference(lifteq,[status(thm)],[3]) ).

thf(5,plain,
    ( ( sk1 = sk2 )
   != ( ! [A: $i > $i > $o] :
          ( ! [B: $i] : ( A @ B @ B )
         => ( A @ sk1 @ sk2 ) ) ) ),
    inference(func_ext,[status(esa)],[4]) ).

thf(7,plain,
    ( ( sk1 = sk2 )
    | ! [A: $i > $i > $o] :
        ( ! [B: $i] : ( A @ B @ B )
       => ( A @ sk1 @ sk2 ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(9,plain,
    ( ( sk2 = sk1 )
    | ! [A: $i > $i > $o] :
        ( ! [B: $i] : ( A @ B @ B )
       => ( A @ sk1 @ sk2 ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(12,plain,
    ! [A: $i > $i > $o] :
      ( ~ ( A @ ( sk4 @ A ) @ ( sk4 @ A ) )
      | ( A @ sk1 @ sk2 )
      | ( sk2 = sk1 ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(6,plain,
    ( ( sk1 != sk2 )
    | ~ ! [A: $i > $i > $o] :
          ( ! [B: $i] : ( A @ B @ B )
         => ( A @ sk1 @ sk2 ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(8,plain,
    ( ( sk2 != sk1 )
    | ~ ! [A: $i > $i > $o] :
          ( ! [B: $i] : ( A @ B @ B )
         => ( A @ sk1 @ sk2 ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(11,plain,
    ! [A: $i] :
      ( ( sk3 @ A @ A )
      | ( sk2 != sk1 ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(10,plain,
    ( ~ ( sk3 @ sk1 @ sk2 )
    | ( sk2 != sk1 ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(13,plain,
    ! [A: $i] :
      ( ( sk2 != sk1 )
      | ( ( sk3 @ A @ A )
       != ( sk3 @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,10]) ).

thf(14,plain,
    ! [A: $i] :
      ( ( sk2 != sk1 )
      | ( A != sk1 )
      | ( A != sk2 ) ),
    inference(simp,[status(thm)],[13]) ).

thf(15,plain,
    sk2 != sk1,
    inference(simp,[status(thm)],[14]) ).

thf(16,plain,
    ! [A: $i > $i > $o] :
      ( ~ ( A @ ( sk4 @ A ) @ ( sk4 @ A ) )
      | ( A @ sk1 @ sk2 ) ),
    inference(simplifyReflect,[status(thm)],[12,15]) ).

thf(19,plain,
    ! [B: $i > $i > $o,A: $i > $i > $o] :
      ( ~ ( ( A
            @ ( sk4
              @ ^ [C: $i,D: $i] :
                  ( ( A @ C @ D )
                  | ( B @ C @ D ) ) )
            @ ( sk4
              @ ^ [C: $i,D: $i] :
                  ( ( A @ C @ D )
                  | ( B @ C @ D ) ) ) )
          | ( B
            @ ( sk4
              @ ^ [C: $i,D: $i] :
                  ( ( A @ C @ D )
                  | ( B @ C @ D ) ) )
            @ ( sk4
              @ ^ [C: $i,D: $i] :
                  ( ( A @ C @ D )
                  | ( B @ C @ D ) ) ) ) )
      | ( A @ sk1 @ sk2 )
      | ( B @ sk1 @ sk2 ) ),
    inference(prim_subst,[status(thm)],[16:[bind(A,$thf( ^ [D: $i] : ^ [E: $i] : ( ( B @ D @ E ) | ( C @ D @ E ) ) ))]]) ).

thf(25,plain,
    ! [B: $i > $i > $o,A: $i > $i > $o] :
      ( ( A @ sk1 @ sk2 )
      | ( B @ sk1 @ sk2 )
      | ~ ( A
          @ ( sk4
            @ ^ [C: $i,D: $i] :
                ( ( A @ C @ D )
                | ( B @ C @ D ) ) )
          @ ( sk4
            @ ^ [C: $i,D: $i] :
                ( ( A @ C @ D )
                | ( B @ C @ D ) ) ) ) ),
    inference(cnf,[status(esa)],[19]) ).

thf(27,plain,
    ! [B: $i > $i > $o,A: $i > $i > $o] :
      ( ( A @ sk1 @ sk2 )
      | ( B @ sk1 @ sk2 )
      | ~ ( A
          @ ( sk4
            @ ^ [C: $i,D: $i] :
                ( ( A @ C @ D )
                | ( B @ C @ D ) ) )
          @ ( sk4
            @ ^ [C: $i,D: $i] :
                ( ( A @ C @ D )
                | ( B @ C @ D ) ) ) ) ),
    inference(simp,[status(thm)],[25]) ).

thf(36,plain,
    ! [B: $i > $i > $o,A: $i > $i > $o] :
      ( ( A @ sk1 @ sk2 )
      | ~ ( A
          @ ( sk4
            @ ^ [C: $i,D: $i] :
                ( ( A @ C @ D )
                | ( B @ C @ D ) ) )
          @ ( sk4
            @ ^ [C: $i,D: $i] :
                ( ( A @ C @ D )
                | ( B @ C @ D ) ) ) )
      | ( ( B @ sk1 @ sk2 )
       != ( A @ sk1 @ sk2 ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[27]) ).

thf(63,plain,
    ! [A: $i > $i > $o] :
      ( ( sk1 = sk2 )
      | ( ( sk4
          @ ^ [B: $i,C: $i] :
              ( ( B = C )
              | ( A @ B @ C ) ) )
       != ( sk4
          @ ^ [B: $i,C: $i] :
              ( ( B = C )
              | ( A @ B @ C ) ) ) )
      | ( ( A @ sk1 @ sk2 )
       != ( sk1 = sk2 ) )
      | ~ $true ),
    inference(replace_andrewseq,[status(thm)],[36:[bind(A,$thf( (=) @ $i ))]]) ).

thf(74,plain,
    ! [A: $i > $i > $o] :
      ( ( sk2 = sk1 )
      | ( ( sk4
          @ ^ [B: $i,C: $i] :
              ( ( B = C )
              | ( A @ B @ C ) ) )
       != ( sk4
          @ ^ [B: $i,C: $i] :
              ( ( B = C )
              | ( A @ B @ C ) ) ) )
      | ( ( A @ sk1 @ sk2 )
       != ( sk1 = sk2 ) )
      | ~ $true ),
    inference(lifteq,[status(thm)],[63]) ).

thf(78,plain,
    ( ~ $true
    | ( sk2 = sk1 ) ),
    inference(pre_uni,[status(thm)],[74:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 = sk2 ) ))]]) ).

thf(107,plain,
    sk2 = sk1,
    inference(simp,[status(thm)],[78]) ).

thf(149,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[107,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SEV121^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.13  % Command  : run_Leo-III %s %d THM
% 0.12/0.34  % Computer : n001.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Jun 21 18:21:40 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.96/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.14/0.97  % [INFO] 	 Parsing done (93ms). 
% 1.25/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.66/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.66/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.82/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.82/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.82/1.25  % [INFO] 	 Type checking passed. 
% 1.82/1.25  % [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 ... 
% 4.59/1.95  % [INFO] 	 Killing All external provers ... 
% 4.59/1.95  % Time passed: 1407ms (effective reasoning time: 966ms)
% 4.59/1.95  % 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)>
% 4.59/1.95  % Axioms used in derivation (0): 
% 4.59/1.95  % No. of inferences in proof: 25
% 4.59/1.95  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1407 ms resp. 966 ms w/o parsing
% 4.59/1.99  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.59/1.99  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------