TSTP Solution File: SWC097+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWC097+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 04:34:02 EDT 2024

% Result   : Theorem 5.67s 2.24s
% Output   : Refutation 5.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   40 (  10 unt;  12 typ;   0 def)
%            Number of atoms       :   84 (  27 equ;   0 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  218 (  41   ~;  33   |;   6   &; 123   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :   23 (   0   ^  20   !;   3   ?;  23   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ssList_type,type,
    ssList: $i > $o ).

thf(neq_type,type,
    neq: $i > $i > $o ).

thf(nil_type,type,
    nil: $i ).

thf(ssItem_type,type,
    ssItem: $i > $o ).

thf(app_type,type,
    app: $i > $i > $i ).

thf(cons_type,type,
    cons: $i > $i > $i ).

thf(sk1_type,type,
    sk1: $i ).

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

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

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

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

thf(sk6_type,type,
    sk6: $i ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ! [D: $i] :
                  ( ( ssList @ D )
                 => ( ( B != D )
                    | ( A != C )
                    | ( ( ~ ( neq @ B @ nil )
                        | ? [E: $i] :
                            ( ( ssItem @ E )
                            & ( ( app @ A @ ( cons @ E @ nil ) )
                              = B ) )
                        | ! [E: $i] :
                            ( ( ssItem @ E )
                           => ( ( app @ C @ ( cons @ E @ nil ) )
                             != D ) ) )
                      & ( ~ ( neq @ B @ nil )
                        | ( neq @ D @ nil ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ssList @ A )
       => ! [B: $i] :
            ( ( ssList @ B )
           => ! [C: $i] :
                ( ( ssList @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ( ( B != D )
                      | ( A != C )
                      | ( ( ~ ( neq @ B @ nil )
                          | ? [E: $i] :
                              ( ( ssItem @ E )
                              & ( ( app @ A @ ( cons @ E @ nil ) )
                                = B ) )
                          | ! [E: $i] :
                              ( ( ssItem @ E )
                             => ( ( app @ C @ ( cons @ E @ nil ) )
                               != D ) ) )
                        & ( ~ ( neq @ B @ nil )
                          | ( neq @ D @ nil ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(98,plain,
    ~ ! [A: $i] :
        ( ( ssList @ A )
       => ! [B: $i] :
            ( ( ssList @ B )
           => ! [C: $i] :
                ( ( ssList @ C )
               => ! [D: $i] :
                    ( ( ssList @ D )
                   => ( ( B != D )
                      | ( A != C )
                      | ( ( ~ ( neq @ B @ nil )
                          | ? [E: $i] :
                              ( ( ssItem @ E )
                              & ( ( app @ A @ ( cons @ E @ nil ) )
                                = B ) )
                          | ! [E: $i] :
                              ( ( ssItem @ E )
                             => ( ( app @ C @ ( cons @ E @ nil ) )
                               != D ) ) )
                        & ( ~ ( neq @ B @ nil )
                          | ( neq @ D @ nil ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(109,plain,
    ( ( ( app @ sk3 @ ( cons @ sk6 @ nil ) )
      = sk4 )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(112,plain,
    ( ( ( app @ sk3 @ ( cons @ sk6 @ nil ) )
      = sk4 )
    | ~ sk5 ),
    inference(lifteq,[status(thm)],[109]) ).

thf(105,plain,
    sk1 = sk3,
    inference(cnf,[status(esa)],[98]) ).

thf(113,plain,
    sk3 = sk1,
    inference(lifteq,[status(thm)],[105]) ).

thf(106,plain,
    sk2 = sk4,
    inference(cnf,[status(esa)],[98]) ).

thf(111,plain,
    sk4 = sk2,
    inference(lifteq,[status(thm)],[106]) ).

thf(514,plain,
    ( ( ( app @ sk1 @ ( cons @ sk6 @ nil ) )
      = sk2 )
    | ~ sk5 ),
    inference(rewrite,[status(thm)],[112,113,111]) ).

thf(107,plain,
    ( sk5
    | ( neq @ sk2 @ nil ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(110,plain,
    ( sk5
    | ~ ( neq @ sk4 @ nil ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(509,plain,
    ( sk5
    | ~ ( neq @ sk2 @ nil ) ),
    inference(rewrite,[status(thm)],[110,111]) ).

thf(512,plain,
    ( sk5
    | ( ( neq @ sk2 @ nil )
     != ( neq @ sk2 @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[107,509]) ).

thf(513,plain,
    sk5,
    inference(pattern_uni,[status(thm)],[512:[]]) ).

thf(515,plain,
    ( ( ( app @ sk1 @ ( cons @ sk6 @ nil ) )
      = sk2 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[514,513]) ).

thf(516,plain,
    ( ( app @ sk1 @ ( cons @ sk6 @ nil ) )
    = sk2 ),
    inference(simp,[status(thm)],[515]) ).

thf(99,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( ( app @ sk1 @ ( cons @ A @ nil ) )
       != sk2 )
      | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(114,plain,
    ! [A: $i] :
      ( ( ( app @ sk1 @ ( cons @ A @ nil ) )
       != sk2 )
      | ~ ( ssItem @ A )
      | ~ sk5 ),
    inference(lifteq,[status(thm)],[99]) ).

thf(529,plain,
    ! [A: $i] :
      ( ( ( app @ sk1 @ ( cons @ A @ nil ) )
       != sk2 )
      | ~ ( ssItem @ A )
      | ~ $true ),
    inference(rewrite,[status(thm)],[114,513]) ).

thf(530,plain,
    ! [A: $i] :
      ( ( ( app @ sk1 @ ( cons @ A @ nil ) )
       != sk2 )
      | ~ ( ssItem @ A ) ),
    inference(simp,[status(thm)],[529]) ).

thf(537,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( ( app @ sk1 @ ( cons @ sk6 @ nil ) )
       != ( app @ sk1 @ ( cons @ A @ nil ) ) ) ),
    inference(paramod_ordered,[status(thm)],[516,530]) ).

thf(538,plain,
    ~ ( ssItem @ sk6 ),
    inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( sk6 ))]]) ).

thf(100,plain,
    ( ( ssItem @ sk6 )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(521,plain,
    ( ( ssItem @ sk6 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[100,513]) ).

thf(522,plain,
    ssItem @ sk6,
    inference(simp,[status(thm)],[521]) ).

thf(539,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[538,522]) ).

thf(540,plain,
    $false,
    inference(simp,[status(thm)],[539]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SWC097+1 : TPTP v8.2.0. Released v2.4.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun May 19 03:53:39 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.64/0.70  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.27/0.86  % [INFO] 	 Parsing done (160ms). 
% 1.30/0.87  % [INFO] 	 Running in sequential loop mode. 
% 1.62/1.07  % [INFO] 	 nitpick registered as external prover. 
% 1.62/1.08  % [INFO] 	 Scanning for conjecture ... 
% 1.81/1.15  % [INFO] 	 Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ... 
% 2.09/1.22  % [INFO] 	 Axiom selection finished. Selected 95 axioms (removed 0 axioms). 
% 2.29/1.30  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.29/1.31  % [INFO] 	 Type checking passed. 
% 2.51/1.31  % [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 ... 
% 5.67/2.23  % [INFO] 	 Killing All external provers ... 
% 5.67/2.24  % Time passed: 1806ms (effective reasoning time: 1357ms)
% 5.67/2.24  % 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)>
% 5.67/2.24  % Axioms used in derivation (0): 
% 5.67/2.24  % No. of inferences in proof: 28
% 5.67/2.24  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1806 ms resp. 1357 ms w/o parsing
% 5.67/2.26  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.67/2.26  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------