TSTP Solution File: SWC050+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWC050+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 04:33:51 EDT 2024

% Result   : Theorem 14.23s 4.34s
% Output   : Refutation 14.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   41 (  10 unt;  10 typ;   0 def)
%            Number of atoms       :  113 (  12 equ;   0 cnn)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :  274 (  58   ~;  51   |;  12   &; 138   @)
%                                         (   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     :   13 (  10 usr;   9 con; 0-2 aty)
%            Number of variables   :   22 (   0   ^  19   !;   3   ?;  22   :)

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

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

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

thf(rearsegP_type,type,
    rearsegP: $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: $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] :
                            ( ( ssList @ E )
                            & ( neq @ E @ nil )
                            & ( rearsegP @ B @ E )
                            & ( rearsegP @ A @ E ) )
                        | ! [E: $i] :
                            ( ( ssList @ E )
                           => ( ~ ( neq @ E @ nil )
                              | ~ ( rearsegP @ D @ E )
                              | ~ ( rearsegP @ C @ E ) ) ) )
                      & ( ~ ( 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] :
                              ( ( ssList @ E )
                              & ( neq @ E @ nil )
                              & ( rearsegP @ B @ E )
                              & ( rearsegP @ A @ E ) )
                          | ! [E: $i] :
                              ( ( ssList @ E )
                             => ( ~ ( neq @ E @ nil )
                                | ~ ( rearsegP @ D @ E )
                                | ~ ( rearsegP @ C @ E ) ) ) )
                        & ( ~ ( 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] :
                              ( ( ssList @ E )
                              & ( neq @ E @ nil )
                              & ( rearsegP @ B @ E )
                              & ( rearsegP @ A @ E ) )
                          | ! [E: $i] :
                              ( ( ssList @ E )
                             => ( ~ ( neq @ E @ nil )
                                | ~ ( rearsegP @ D @ E )
                                | ~ ( rearsegP @ C @ E ) ) ) )
                        & ( ~ ( neq @ B @ nil )
                          | ( neq @ D @ nil ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(99,plain,
    ( ( neq @ sk6 @ nil )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(106,plain,
    ( sk5
    | ( neq @ sk2 @ nil ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(102,plain,
    ( sk5
    | ~ ( neq @ sk4 @ nil ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(105,plain,
    sk2 = sk4,
    inference(cnf,[status(esa)],[98]) ).

thf(113,plain,
    sk4 = sk2,
    inference(lifteq,[status(thm)],[105]) ).

thf(511,plain,
    ( sk5
    | ~ ( neq @ sk2 @ nil ) ),
    inference(rewrite,[status(thm)],[102,113]) ).

thf(515,plain,
    ( sk5
    | ( ( neq @ sk2 @ nil )
     != ( neq @ sk2 @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[106,511]) ).

thf(516,plain,
    sk5,
    inference(pattern_uni,[status(thm)],[515:[]]) ).

thf(519,plain,
    ( ( neq @ sk6 @ nil )
    | ~ $true ),
    inference(rewrite,[status(thm)],[99,516]) ).

thf(520,plain,
    neq @ sk6 @ nil,
    inference(simp,[status(thm)],[519]) ).

thf(108,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( neq @ A @ nil )
      | ~ ( rearsegP @ sk2 @ A )
      | ~ ( rearsegP @ sk1 @ A )
      | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(527,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( neq @ A @ nil )
      | ~ ( rearsegP @ sk2 @ A )
      | ~ ( rearsegP @ sk1 @ A )
      | ~ $true ),
    inference(rewrite,[status(thm)],[108,516]) ).

thf(528,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( neq @ A @ nil )
      | ~ ( rearsegP @ sk2 @ A )
      | ~ ( rearsegP @ sk1 @ A ) ),
    inference(simp,[status(thm)],[527]) ).

thf(543,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( rearsegP @ sk2 @ A )
      | ~ ( rearsegP @ sk1 @ A )
      | ( ( neq @ sk6 @ nil )
       != ( neq @ A @ nil ) ) ),
    inference(paramod_ordered,[status(thm)],[520,528]) ).

thf(544,plain,
    ( ~ ( ssList @ sk6 )
    | ~ ( rearsegP @ sk2 @ sk6 )
    | ~ ( rearsegP @ sk1 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[543:[bind(A,$thf( sk6 ))]]) ).

thf(112,plain,
    ( ( rearsegP @ sk3 @ sk6 )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(111,plain,
    sk1 = sk3,
    inference(cnf,[status(esa)],[98]) ).

thf(114,plain,
    sk3 = sk1,
    inference(lifteq,[status(thm)],[111]) ).

thf(580,plain,
    ( ( rearsegP @ sk1 @ sk6 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[112,114,516]) ).

thf(581,plain,
    rearsegP @ sk1 @ sk6,
    inference(simp,[status(thm)],[580]) ).

thf(109,plain,
    ( ( rearsegP @ sk4 @ sk6 )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(565,plain,
    ( ( rearsegP @ sk2 @ sk6 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[109,113,516]) ).

thf(566,plain,
    rearsegP @ sk2 @ sk6,
    inference(simp,[status(thm)],[565]) ).

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

thf(521,plain,
    ( ( ssList @ sk6 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[100,516]) ).

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

thf(1334,plain,
    ( ~ $true
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[544,581,566,522]) ).

thf(1335,plain,
    $false,
    inference(simp,[status(thm)],[1334]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : SWC050+1 : TPTP v8.2.0. Released v2.4.0.
% 0.04/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n019.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 03:33:54 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.90/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.36/1.15  % [INFO] 	 Parsing done (246ms). 
% 1.61/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.10/1.51  % [INFO] 	 nitpick registered as external prover. 
% 2.10/1.51  % [INFO] 	 Scanning for conjecture ... 
% 2.38/1.64  % [INFO] 	 Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ... 
% 2.53/1.73  % [INFO] 	 Axiom selection finished. Selected 95 axioms (removed 0 axioms). 
% 2.92/1.86  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.92/1.88  % [INFO] 	 Type checking passed. 
% 2.92/1.89  % [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 ... 
% 14.23/4.32  % [INFO] 	 Killing All external provers ... 
% 14.23/4.33  % Time passed: 3875ms (effective reasoning time: 3160ms)
% 14.23/4.33  % 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)>
% 14.23/4.34  % Axioms used in derivation (0): 
% 14.23/4.34  % No. of inferences in proof: 31
% 14.23/4.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3875 ms resp. 3160 ms w/o parsing
% 14.23/4.37  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.23/4.37  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------