TSTP Solution File: SWC001+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWC001+1 : TPTP v8.2.0. Released v2.4.0.
% 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 04:33:38 EDT 2024

% Result   : Theorem 8.02s 3.64s
% Output   : Refutation 8.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   42 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :  120 (  12 equ;   0 cnn)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  301 (  59   ~;  50   |;  18   &; 159   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   24 (   0   ^  21   !;   3   ?;  24   :)

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

thf(duplicatefreeP_type,type,
    duplicatefreeP: $i > $o ).

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

thf(memberP_type,type,
    memberP: $i > $i > $o ).

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: $i ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ! [D: $i] :
                  ( ( ssList @ D )
                 => ( ( B != D )
                    | ( A != C )
                    | ~ ( duplicatefreeP @ C )
                    | ? [E: $i] :
                        ( ( ssItem @ E )
                        & ( ( ~ ( memberP @ D @ E )
                            & ( memberP @ C @ E ) )
                          | ( ~ ( memberP @ C @ E )
                            & ( memberP @ D @ E ) ) ) )
                    | ( ! [E: $i] :
                          ( ( ssItem @ E )
                         => ( ( ~ ( memberP @ B @ E )
                              & ~ ( memberP @ A @ E ) )
                            | ( ( memberP @ B @ E )
                              & ( memberP @ A @ E ) ) ) )
                      & ( duplicatefreeP @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/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 )
                      | ~ ( duplicatefreeP @ C )
                      | ? [E: $i] :
                          ( ( ssItem @ E )
                          & ( ( ~ ( memberP @ D @ E )
                              & ( memberP @ C @ E ) )
                            | ( ~ ( memberP @ C @ E )
                              & ( memberP @ D @ E ) ) ) )
                      | ( ! [E: $i] :
                            ( ( ssItem @ E )
                           => ( ( ~ ( memberP @ B @ E )
                                & ~ ( memberP @ A @ E ) )
                              | ( ( memberP @ B @ E )
                                & ( memberP @ A @ E ) ) ) )
                        & ( duplicatefreeP @ A ) ) ) ) ) ) ),
    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 )
                      | ~ ( duplicatefreeP @ C )
                      | ? [E: $i] :
                          ( ( ssItem @ E )
                          & ( ( ~ ( memberP @ D @ E )
                              & ( memberP @ C @ E ) )
                            | ( ~ ( memberP @ C @ E )
                              & ( memberP @ D @ E ) ) ) )
                      | ( ! [E: $i] :
                            ( ( ssItem @ E )
                           => ( ( ~ ( memberP @ B @ E )
                                & ~ ( memberP @ A @ E ) )
                              | ( ( memberP @ B @ E )
                                & ( memberP @ A @ E ) ) ) )
                        & ( duplicatefreeP @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(100,plain,
    ( ( memberP @ sk2 @ sk5 )
    | ( memberP @ sk1 @ sk5 )
    | ~ ( duplicatefreeP @ sk1 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(103,plain,
    duplicatefreeP @ sk3,
    inference(cnf,[status(esa)],[98]) ).

thf(107,plain,
    sk1 = sk3,
    inference(cnf,[status(esa)],[98]) ).

thf(111,plain,
    sk3 = sk1,
    inference(lifteq,[status(thm)],[107]) ).

thf(504,plain,
    duplicatefreeP @ sk1,
    inference(rewrite,[status(thm)],[103,111]) ).

thf(523,plain,
    ( ( memberP @ sk2 @ sk5 )
    | ( memberP @ sk1 @ sk5 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[100,504]) ).

thf(524,plain,
    ( ( memberP @ sk2 @ sk5 )
    | ( memberP @ sk1 @ sk5 ) ),
    inference(simp,[status(thm)],[523]) ).

thf(104,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( memberP @ sk4 @ A )
      | ~ ( memberP @ sk3 @ A ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(108,plain,
    sk2 = sk4,
    inference(cnf,[status(esa)],[98]) ).

thf(112,plain,
    sk4 = sk2,
    inference(lifteq,[status(thm)],[108]) ).

thf(548,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( memberP @ sk2 @ A )
      | ~ ( memberP @ sk1 @ A ) ),
    inference(rewrite,[status(thm)],[104,112,111]) ).

thf(99,plain,
    ( ~ ( memberP @ sk2 @ sk5 )
    | ~ ( memberP @ sk1 @ sk5 )
    | ~ ( duplicatefreeP @ sk1 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(517,plain,
    ( ~ ( memberP @ sk2 @ sk5 )
    | ~ ( memberP @ sk1 @ sk5 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[99,504]) ).

thf(518,plain,
    ( ~ ( memberP @ sk2 @ sk5 )
    | ~ ( memberP @ sk1 @ sk5 ) ),
    inference(simp,[status(thm)],[517]) ).

thf(549,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ~ ( memberP @ sk1 @ A )
      | ~ ( memberP @ sk1 @ sk5 )
      | ( ( memberP @ sk2 @ A )
       != ( memberP @ sk2 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[548,518]) ).

thf(550,plain,
    ( ~ ( ssItem @ sk5 )
    | ~ ( memberP @ sk1 @ sk5 )
    | ~ ( memberP @ sk1 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[549:[bind(A,$thf( sk5 ))]]) ).

thf(566,plain,
    ( ~ ( ssItem @ sk5 )
    | ~ ( memberP @ sk1 @ sk5 ) ),
    inference(simp,[status(thm)],[550]) ).

thf(110,plain,
    ( ( ssItem @ sk5 )
    | ~ ( duplicatefreeP @ sk1 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(521,plain,
    ( ( ssItem @ sk5 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[110,504]) ).

thf(522,plain,
    ssItem @ sk5,
    inference(simp,[status(thm)],[521]) ).

thf(573,plain,
    ( ~ $true
    | ~ ( memberP @ sk1 @ sk5 ) ),
    inference(rewrite,[status(thm)],[566,522]) ).

thf(574,plain,
    ~ ( memberP @ sk1 @ sk5 ),
    inference(simp,[status(thm)],[573]) ).

thf(575,plain,
    ( ( memberP @ sk2 @ sk5 )
    | $false ),
    inference(rewrite,[status(thm)],[524,574]) ).

thf(576,plain,
    memberP @ sk2 @ sk5,
    inference(simp,[status(thm)],[575]) ).

thf(109,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( memberP @ sk3 @ A )
      | ~ ( memberP @ sk4 @ A ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(600,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( memberP @ sk1 @ A )
      | ~ ( memberP @ sk2 @ A ) ),
    inference(rewrite,[status(thm)],[109,112,111]) ).

thf(607,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( memberP @ sk1 @ A )
      | ( ( memberP @ sk2 @ sk5 )
       != ( memberP @ sk2 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[576,600]) ).

thf(608,plain,
    ( ~ ( ssItem @ sk5 )
    | ( memberP @ sk1 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[607:[bind(A,$thf( sk5 ))]]) ).

thf(613,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[608,522,574]) ).

thf(614,plain,
    $false,
    inference(simp,[status(thm)],[613]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SWC001+1 : TPTP v8.2.0. Released v2.4.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n023.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Sun May 19 03:13:24 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 1.00/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.67/1.19  % [INFO] 	 Parsing done (257ms). 
% 1.67/1.21  % [INFO] 	 Running in sequential loop mode. 
% 2.16/1.56  % [INFO] 	 nitpick registered as external prover. 
% 2.16/1.57  % [INFO] 	 Scanning for conjecture ... 
% 2.47/1.70  % [INFO] 	 Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ... 
% 2.74/1.80  % [INFO] 	 Axiom selection finished. Selected 95 axioms (removed 0 axioms). 
% 3.02/1.93  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 3.02/1.96  % [INFO] 	 Type checking passed. 
% 3.02/1.96  % [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 ... 
% 8.02/3.63  % [INFO] 	 Killing All external provers ... 
% 8.02/3.63  % Time passed: 3165ms (effective reasoning time: 2417ms)
% 8.02/3.63  % 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)>
% 8.02/3.63  % Axioms used in derivation (0): 
% 8.02/3.63  % No. of inferences in proof: 33
% 8.02/3.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3165 ms resp. 2417 ms w/o parsing
% 8.02/3.66  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.02/3.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------