TSTP Solution File: SEU890^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU890^5 : 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 03:44:10 EDT 2024

% Result   : Theorem 3.73s 2.07s
% Output   : Refutation 3.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   52 (  15 unt;  10 typ;   0 def)
%            Number of atoms       :  122 (  69 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  255 (  47   ~;  41   |;  21   &; 146   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   40 (   0   ^  19   !;  21   ?;  40   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_type,type,
    c: $tType ).

thf(b_type,type,
    b: $tType ).

thf(a_type,type,
    a: $tType ).

thf(cG_type,type,
    cG: c > b ).

thf(cF_type,type,
    cF: b > a ).

thf(cS_type,type,
    cS: c > $o ).

thf(sk1_type,type,
    sk1: a ).

thf(sk2_type,type,
    sk2: b ).

thf(sk3_type,type,
    sk3: c ).

thf(sk4_type,type,
    sk4: c ).

thf(1,conjecture,
    ! [A: a] :
      ( ( ? [B: b] :
            ( ? [C: c] :
                ( ( cS @ C )
                & ( B
                  = ( cG @ C ) ) )
            & ( A
              = ( cF @ B ) ) ) )
      = ( ? [B: c] :
            ( ( cS @ B )
            & ( A
              = ( cF @ ( cG @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM29_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: a] :
        ( ( ? [B: b] :
              ( ? [C: c] :
                  ( ( cS @ C )
                  & ( B
                    = ( cG @ C ) ) )
              & ( A
                = ( cF @ B ) ) ) )
        = ( ? [B: c] :
              ( ( cS @ B )
              & ( A
                = ( cF @ ( cG @ B ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: a] :
        ( ( ? [B: b] :
              ( ? [C: c] :
                  ( ( cS @ C )
                  & ( B
                    = ( cG @ C ) ) )
              & ( A
                = ( cF @ B ) ) ) )
        = ( ? [B: c] :
              ( ( cS @ B )
              & ( A
                = ( cF @ ( cG @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ? [A: b] :
          ( ? [B: c] :
              ( ( cS @ B )
              & ( A
                = ( cG @ B ) ) )
          & ( sk1
            = ( cF @ A ) ) ) )
   != ( ? [A: c] :
          ( ( cS @ A )
          & ( sk1
            = ( cF @ ( cG @ A ) ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ? [A: b] :
          ( ? [B: c] :
              ( ( cS @ B )
              & ( A
                = ( cG @ B ) ) )
          & ( sk1
            = ( cF @ A ) ) ) )
   != ( ? [A: c] :
          ( ( cS @ A )
          & ( sk1
            = ( cF @ ( cG @ A ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(7,plain,
    ( ? [A: b] :
        ( ? [B: c] :
            ( ( cS @ B )
            & ( A
              = ( cG @ B ) ) )
        & ( sk1
          = ( cF @ A ) ) )
    | ? [A: c] :
        ( ( cS @ A )
        & ( sk1
          = ( cF @ ( cG @ A ) ) ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(16,plain,
    ( ( sk1
      = ( cF @ ( cG @ sk4 ) ) )
    | ( sk2
      = ( cG @ sk3 ) ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(20,plain,
    ( ( ( cF @ ( cG @ sk4 ) )
      = sk1 )
    | ( ( cG @ sk3 )
      = sk2 ) ),
    inference(lifteq,[status(thm)],[16]) ).

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

thf(21,plain,
    ( ( ( cF @ sk2 )
      = sk1 )
    | ( cS @ sk4 ) ),
    inference(lifteq,[status(thm)],[15]) ).

thf(12,plain,
    ( ( sk1
      = ( cF @ ( cG @ sk4 ) ) )
    | ( sk1
      = ( cF @ sk2 ) ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(19,plain,
    ( ( ( cF @ ( cG @ sk4 ) )
      = sk1 )
    | ( ( cF @ sk2 )
      = sk1 ) ),
    inference(lifteq,[status(thm)],[12]) ).

thf(6,plain,
    ( ~ ? [A: b] :
          ( ? [B: c] :
              ( ( cS @ B )
              & ( A
                = ( cG @ B ) ) )
          & ( sk1
            = ( cF @ A ) ) )
    | ~ ? [A: c] :
          ( ( cS @ A )
          & ( sk1
            = ( cF @ ( cG @ A ) ) ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(8,plain,
    ! [C: c,B: c,A: b] :
      ( ~ ( cS @ C )
      | ( sk1
       != ( cF @ ( cG @ C ) ) )
      | ~ ( cS @ B )
      | ( A
       != ( cG @ B ) )
      | ( sk1
       != ( cF @ A ) ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(9,plain,
    ! [C: c,B: c,A: b] :
      ( ( ( cF @ ( cG @ C ) )
       != sk1 )
      | ( A
       != ( cG @ B ) )
      | ( ( cF @ A )
       != sk1 )
      | ~ ( cS @ C )
      | ~ ( cS @ B ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(10,plain,
    ! [B: c,A: c] :
      ( ( ( cF @ ( cG @ B ) )
       != sk1 )
      | ( ( cF @ ( cG @ A ) )
       != sk1 )
      | ~ ( cS @ B )
      | ~ ( cS @ A ) ),
    inference(simp,[status(thm)],[9]) ).

thf(42,plain,
    ! [B: c,A: c] :
      ( ( ( cF @ ( cG @ B ) )
       != sk1 )
      | ( ( cF @ ( cG @ A ) )
       != sk1 )
      | ~ ( cS @ B )
      | ( ( cS @ A )
       != ( cS @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[10]) ).

thf(43,plain,
    ! [A: c] :
      ( ( ( cF @ ( cG @ A ) )
       != sk1 )
      | ( ( cF @ ( cG @ A ) )
       != sk1 )
      | ~ ( cS @ A ) ),
    inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(48,plain,
    ! [A: c] :
      ( ( ( cF @ ( cG @ A ) )
       != sk1 )
      | ~ ( cS @ A ) ),
    inference(simp,[status(thm)],[43]) ).

thf(88,plain,
    ! [A: c] :
      ( ( ( cF @ sk2 )
        = sk1 )
      | ~ ( cS @ A )
      | ( ( cF @ ( cG @ sk4 ) )
       != ( cF @ ( cG @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[19,48]) ).

thf(89,plain,
    ( ( ( cF @ sk2 )
      = sk1 )
    | ~ ( cS @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk4 ))]]) ).

thf(123,plain,
    ( ( ( cF @ sk2 )
      = sk1 )
    | ( ( cS @ sk4 )
     != ( cS @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[21,89]) ).

thf(124,plain,
    ( ( cF @ sk2 )
    = sk1 ),
    inference(pattern_uni,[status(thm)],[123:[]]) ).

thf(11,plain,
    ( ( cS @ sk4 )
    | ( cS @ sk3 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(14,plain,
    ( ( sk1
      = ( cF @ ( cG @ sk4 ) ) )
    | ( cS @ sk3 ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(17,plain,
    ( ( ( cF @ ( cG @ sk4 ) )
      = sk1 )
    | ( cS @ sk3 ) ),
    inference(lifteq,[status(thm)],[14]) ).

thf(65,plain,
    ! [A: c] :
      ( ( cS @ sk3 )
      | ~ ( cS @ A )
      | ( ( cF @ ( cG @ sk4 ) )
       != ( cF @ ( cG @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[17,48]) ).

thf(66,plain,
    ( ( cS @ sk3 )
    | ~ ( cS @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( sk4 ))]]) ).

thf(75,plain,
    ( ( cS @ sk3 )
    | ( ( cS @ sk4 )
     != ( cS @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,66]) ).

thf(76,plain,
    cS @ sk3,
    inference(pattern_uni,[status(thm)],[75:[]]) ).

thf(95,plain,
    ! [A: c] :
      ( ( ( cF @ ( cG @ A ) )
       != sk1 )
      | ( ( cS @ sk3 )
       != ( cS @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[76,48]) ).

thf(96,plain,
    ( ( cF @ ( cG @ sk3 ) )
   != sk1 ),
    inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( sk3 ))]]) ).

thf(137,plain,
    ( ( cF @ ( cG @ sk3 ) )
   != ( cF @ sk2 ) ),
    inference(paramod_ordered,[status(thm)],[124,96]) ).

thf(139,plain,
    ( ( cG @ sk3 )
   != sk2 ),
    inference(simp,[status(thm)],[137]) ).

thf(142,plain,
    ( ( cF @ ( cG @ sk4 ) )
    = sk1 ),
    inference(simplifyReflect,[status(thm)],[20,139]) ).

thf(146,plain,
    ! [A: c] :
      ( ~ ( cS @ A )
      | ( ( cF @ ( cG @ sk4 ) )
       != ( cF @ ( cG @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[142,48]) ).

thf(147,plain,
    ~ ( cS @ sk4 ),
    inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( sk4 ))]]) ).

thf(13,plain,
    ( ( cS @ sk4 )
    | ( sk2
      = ( cG @ sk3 ) ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(18,plain,
    ( ( ( cG @ sk3 )
      = sk2 )
    | ( cS @ sk4 ) ),
    inference(lifteq,[status(thm)],[13]) ).

thf(143,plain,
    cS @ sk4,
    inference(simplifyReflect,[status(thm)],[18,139]) ).

thf(152,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[147,143]) ).

thf(153,plain,
    $false,
    inference(simp,[status(thm)],[152]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU890^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n023.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 15:22:54 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.94/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.17/1.04  % [INFO] 	 Parsing done (116ms). 
% 1.17/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.27  % [INFO] 	 nitpick registered as external prover. 
% 1.74/1.27  % [INFO] 	 Scanning for conjecture ... 
% 1.74/1.33  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.94/1.35  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.94/1.35  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.94/1.35  % [INFO] 	 Type checking passed. 
% 1.94/1.36  % [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 ... 
% 3.73/2.07  % [INFO] 	 Killing All external provers ... 
% 3.73/2.07  % Time passed: 1537ms (effective reasoning time: 1020ms)
% 3.73/2.07  % 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)>
% 3.73/2.07  % Axioms used in derivation (0): 
% 3.73/2.07  % No. of inferences in proof: 42
% 3.73/2.07  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1537 ms resp. 1020 ms w/o parsing
% 3.76/2.13  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.76/2.13  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------