TSTP Solution File: SWC020+1 by Leo-III-SAT---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWC020+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 04:33:43 EDT 2024

% Result   : Theorem 18.92s 4.18s
% Output   : Refutation 18.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   52 (  11 unt;   8 typ;   0 def)
%            Number of atoms       :  131 (  48 equ;   0 cnn)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  273 (  56   ~;  54   |;  15   &; 134   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :   21 (   0   ^  18   !;   3   ?;  21   :)

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

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

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

thf(frontsegP_type,type,
    frontsegP: $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(81,axiom,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( frontsegP @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).

thf(444,plain,
    ! [A: $i] :
      ( ( ssList @ A )
     => ( frontsegP @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(445,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( frontsegP @ A @ A ) ),
    inference(cnf,[status(esa)],[444]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ssList @ A )
     => ! [B: $i] :
          ( ( ssList @ B )
         => ! [C: $i] :
              ( ( ssList @ C )
             => ! [D: $i] :
                  ( ( ssList @ D )
                 => ( ( B != D )
                    | ( A != C )
                    | ? [E: $i] :
                        ( ( ssList @ E )
                        & ( neq @ E @ nil )
                        & ( frontsegP @ B @ E )
                        & ( frontsegP @ A @ E ) )
                    | ( ( nil = B )
                      & ( nil = A ) )
                    | ( ( ( nil != D )
                        | ( nil != C ) )
                      & ( ~ ( neq @ C @ nil )
                        | ~ ( frontsegP @ D @ C ) ) ) ) ) ) ) ),
    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 )
                      | ? [E: $i] :
                          ( ( ssList @ E )
                          & ( neq @ E @ nil )
                          & ( frontsegP @ B @ E )
                          & ( frontsegP @ A @ E ) )
                      | ( ( nil = B )
                        & ( nil = A ) )
                      | ( ( ( nil != D )
                          | ( nil != C ) )
                        & ( ~ ( neq @ C @ nil )
                          | ~ ( frontsegP @ D @ C ) ) ) ) ) ) ) ),
    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 )
                      | ? [E: $i] :
                          ( ( ssList @ E )
                          & ( neq @ E @ nil )
                          & ( frontsegP @ B @ E )
                          & ( frontsegP @ A @ E ) )
                      | ( ( nil = B )
                        & ( nil = A ) )
                      | ( ( ( nil != D )
                          | ( nil != C ) )
                        & ( ~ ( neq @ C @ nil )
                          | ~ ( frontsegP @ D @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(105,plain,
    ssList @ sk1,
    inference(cnf,[status(esa)],[98]) ).

thf(100,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ~ ( neq @ A @ nil )
      | ~ ( frontsegP @ sk2 @ A )
      | ~ ( frontsegP @ sk1 @ A ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(510,plain,
    ! [A: $i] :
      ( ~ ( neq @ A @ nil )
      | ~ ( frontsegP @ sk2 @ A )
      | ~ ( frontsegP @ sk1 @ A )
      | ( ( ssList @ sk1 )
       != ( ssList @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[105,100]) ).

thf(511,plain,
    ( ~ ( neq @ sk1 @ nil )
    | ~ ( frontsegP @ sk2 @ sk1 )
    | ~ ( frontsegP @ sk1 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[510:[bind(A,$thf( sk1 ))]]) ).

thf(99,plain,
    ( ( nil = sk3 )
    | ( neq @ sk3 @ nil ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(117,plain,
    ( ( sk3 = nil )
    | ( neq @ sk3 @ nil ) ),
    inference(lifteq,[status(thm)],[99]) ).

thf(106,plain,
    sk1 = sk3,
    inference(cnf,[status(esa)],[98]) ).

thf(112,plain,
    sk3 = sk1,
    inference(lifteq,[status(thm)],[106]) ).

thf(677,plain,
    ( ( sk1 = nil )
    | ( neq @ sk1 @ nil ) ),
    inference(rewrite,[status(thm)],[117,112]) ).

thf(110,plain,
    ( ( nil = sk4 )
    | ( neq @ sk3 @ nil ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(111,plain,
    ( ( sk4 = nil )
    | ( neq @ sk3 @ nil ) ),
    inference(lifteq,[status(thm)],[110]) ).

thf(109,plain,
    sk2 = sk4,
    inference(cnf,[status(esa)],[98]) ).

thf(114,plain,
    sk4 = sk2,
    inference(lifteq,[status(thm)],[109]) ).

thf(522,plain,
    ( ( sk2 = nil )
    | ( neq @ sk1 @ nil ) ),
    inference(rewrite,[status(thm)],[111,112,114]) ).

thf(102,plain,
    ( ( nil != sk2 )
    | ( nil != sk1 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(113,plain,
    ( ( sk2 != nil )
    | ( sk1 != nil ) ),
    inference(lifteq,[status(thm)],[102]) ).

thf(527,plain,
    ( ( neq @ sk1 @ nil )
    | ( sk1 != nil )
    | ( sk2 != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[522,113]) ).

thf(528,plain,
    ( ( neq @ sk1 @ nil )
    | ( sk1 != nil ) ),
    inference(pattern_uni,[status(thm)],[527:[]]) ).

thf(737,plain,
    ( ( neq @ sk1 @ nil )
    | ( sk1 != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[677,528]) ).

thf(738,plain,
    neq @ sk1 @ nil,
    inference(pattern_uni,[status(thm)],[737:[]]) ).

thf(758,plain,
    ( ~ $true
    | ~ ( frontsegP @ sk2 @ sk1 )
    | ~ ( frontsegP @ sk1 @ sk1 ) ),
    inference(rewrite,[status(thm)],[511,738]) ).

thf(759,plain,
    ( ~ ( frontsegP @ sk2 @ sk1 )
    | ~ ( frontsegP @ sk1 @ sk1 ) ),
    inference(simp,[status(thm)],[758]) ).

thf(103,plain,
    ( ( nil = sk4 )
    | ( frontsegP @ sk4 @ sk3 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(116,plain,
    ( ( sk4 = nil )
    | ( frontsegP @ sk4 @ sk3 ) ),
    inference(lifteq,[status(thm)],[103]) ).

thf(579,plain,
    ( ( sk2 = nil )
    | ( frontsegP @ sk2 @ sk1 ) ),
    inference(rewrite,[status(thm)],[116,112,114]) ).

thf(107,plain,
    ( ( nil = sk3 )
    | ( frontsegP @ sk4 @ sk3 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(115,plain,
    ( ( sk3 = nil )
    | ( frontsegP @ sk4 @ sk3 ) ),
    inference(lifteq,[status(thm)],[107]) ).

thf(539,plain,
    ( ( sk1 = nil )
    | ( frontsegP @ sk2 @ sk1 ) ),
    inference(rewrite,[status(thm)],[115,112,114]) ).

thf(557,plain,
    ( ( frontsegP @ sk2 @ sk1 )
    | ( sk2 != nil )
    | ( sk1 != sk1 ) ),
    inference(paramod_ordered,[status(thm)],[539,113]) ).

thf(558,plain,
    ( ( frontsegP @ sk2 @ sk1 )
    | ( sk2 != nil ) ),
    inference(pattern_uni,[status(thm)],[557:[]]) ).

thf(834,plain,
    ( ( frontsegP @ sk2 @ sk1 )
    | ( sk2 != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[579,558]) ).

thf(835,plain,
    frontsegP @ sk2 @ sk1,
    inference(pattern_uni,[status(thm)],[834:[]]) ).

thf(905,plain,
    ( ~ $true
    | ~ ( frontsegP @ sk1 @ sk1 ) ),
    inference(rewrite,[status(thm)],[759,835]) ).

thf(906,plain,
    ~ ( frontsegP @ sk1 @ sk1 ),
    inference(simp,[status(thm)],[905]) ).

thf(3997,plain,
    ! [A: $i] :
      ( ~ ( ssList @ A )
      | ( ( frontsegP @ A @ A )
       != ( frontsegP @ sk1 @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[445,906]) ).

thf(3998,plain,
    ~ ( ssList @ sk1 ),
    inference(pattern_uni,[status(thm)],[3997:[bind(A,$thf( sk1 ))]]) ).

thf(4012,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[3998,105]) ).

thf(4013,plain,
    $false,
    inference(simp,[status(thm)],[4012]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC020+1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.36  % Computer : n027.cluster.edu
% 0.17/0.36  % Model    : x86_64 x86_64
% 0.17/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36  % Memory   : 8042.1875MB
% 0.17/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Sun May 19 03:40:24 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.98/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.52/1.02  % [INFO] 	 Parsing done (155ms). 
% 1.52/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.83/1.23  % [INFO] 	 nitpick registered as external prover. 
% 1.95/1.23  % [INFO] 	 Scanning for conjecture ... 
% 2.17/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ... 
% 2.38/1.37  % [INFO] 	 Axiom selection finished. Selected 95 axioms (removed 0 axioms). 
% 2.38/1.45  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.71/1.47  % [INFO] 	 Type checking passed. 
% 2.71/1.47  % [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 ... 
% 18.92/4.17  % [INFO] 	 Killing All external provers ... 
% 18.92/4.17  % Time passed: 3636ms (effective reasoning time: 3135ms)
% 18.92/4.17  % 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)>
% 18.92/4.18  % Axioms used in derivation (1): ax42
% 18.92/4.18  % No. of inferences in proof: 44
% 18.92/4.18  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3636 ms resp. 3135 ms w/o parsing
% 18.92/4.19  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.92/4.19  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------