TSTP Solution File: SWC257+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SWC257+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 04:34:39 EDT 2024

% Result   : Theorem 30.55s 6.73s
% Output   : Refutation 30.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   40 (  14 unt;  11 typ;   0 def)
%            Number of atoms       :   90 (  30 equ;   0 cnn)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  179 (  40   ~;  34   |;  12   &;  82   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   22 (   0   ^  19   !;   3   ?;  22   :)

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

thf(totalorderedP_type,type,
    totalorderedP: $i > $o ).

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

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

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

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

thf(leq_type,type,
    leq: $i > $i > $o ).

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

thf(sk3_type,type,
    sk3: $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 )
                  | ( totalorderedP @ A )
                  | ( ! [E: $i] :
                        ( ~ ( ssItem @ E )
                        | ( ( cons @ E @ nil )
                         != C )
                        | ~ ( memberP @ D @ E )
                        | ? [F: $i] :
                            ( ( ssItem @ F )
                            & ( E != F )
                            & ( memberP @ D @ F )
                            & ( leq @ E @ F ) ) )
                    & ( ( nil != D )
                      | ( nil != 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 )
                    | ( totalorderedP @ A )
                    | ( ! [E: $i] :
                          ( ~ ( ssItem @ E )
                          | ( ( cons @ E @ nil )
                           != C )
                          | ~ ( memberP @ D @ E )
                          | ? [F: $i] :
                              ( ( ssItem @ F )
                              & ( E != F )
                              & ( memberP @ D @ F )
                              & ( leq @ E @ F ) ) )
                      & ( ( nil != D )
                        | ( nil != 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 )
                    | ( totalorderedP @ A )
                    | ( ! [E: $i] :
                          ( ~ ( ssItem @ E )
                          | ( ( cons @ E @ nil )
                           != C )
                          | ~ ( memberP @ D @ E )
                          | ? [F: $i] :
                              ( ( ssItem @ F )
                              & ( E != F )
                              & ( memberP @ D @ F )
                              & ( leq @ E @ F ) ) )
                      & ( ( nil != D )
                        | ( nil != C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(109,plain,
    ~ ( totalorderedP @ sk1 ),
    inference(cnf,[status(esa)],[98]) ).

thf(102,plain,
    ( ( ssItem @ sk6 )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(111,plain,
    ( sk5
    | ( nil = sk3 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(116,plain,
    ( ( sk3 = nil )
    | sk5 ),
    inference(lifteq,[status(thm)],[111]) ).

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

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

thf(522,plain,
    ( ( sk1 = nil )
    | sk5 ),
    inference(rewrite,[status(thm)],[116,113]) ).

thf(8,axiom,
    totalorderedP @ nil,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).

thf(131,plain,
    totalorderedP @ nil,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(511,plain,
    ( ( totalorderedP @ sk1 )
   != ( totalorderedP @ nil ) ),
    inference(paramod_ordered,[status(thm)],[131,109]) ).

thf(512,plain,
    sk1 != nil,
    inference(simp,[status(thm)],[511]) ).

thf(523,plain,
    sk5,
    inference(simplifyReflect,[status(thm)],[522,512]) ).

thf(526,plain,
    ( ( ssItem @ sk6 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[102,523]) ).

thf(527,plain,
    ssItem @ sk6,
    inference(simp,[status(thm)],[526]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( totalorderedP @ ( cons @ A @ nil ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).

thf(193,plain,
    ! [A: $i] :
      ( ( ssItem @ A )
     => ( totalorderedP @ ( cons @ A @ nil ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(194,plain,
    ! [A: $i] :
      ( ~ ( ssItem @ A )
      | ( totalorderedP @ ( cons @ A @ nil ) ) ),
    inference(cnf,[status(esa)],[193]) ).

thf(3695,plain,
    ! [A: $i] :
      ( ( totalorderedP @ ( cons @ A @ nil ) )
      | ( ( ssItem @ sk6 )
       != ( ssItem @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[527,194]) ).

thf(3696,plain,
    totalorderedP @ ( cons @ sk6 @ nil ),
    inference(pattern_uni,[status(thm)],[3695:[bind(A,$thf( sk6 ))]]) ).

thf(100,plain,
    ( ( ( cons @ sk6 @ nil )
      = sk3 )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[98]) ).

thf(117,plain,
    ( ( ( cons @ sk6 @ nil )
      = sk3 )
    | ~ sk5 ),
    inference(lifteq,[status(thm)],[100]) ).

thf(591,plain,
    ( ( ( cons @ sk6 @ nil )
      = sk1 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[117,113,523]) ).

thf(592,plain,
    ( ( cons @ sk6 @ nil )
    = sk1 ),
    inference(simp,[status(thm)],[591]) ).

thf(3785,plain,
    totalorderedP @ sk1,
    inference(rewrite,[status(thm)],[3696,592]) ).

thf(3786,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[109,3785]) ).

thf(3787,plain,
    $false,
    inference(simp,[status(thm)],[3786]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10  % Problem  : SWC257+1 : TPTP v8.2.0. Released v2.4.0.
% 0.04/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun May 19 03:14:24 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 1.03/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.72/1.24  % [INFO] 	 Parsing done (251ms). 
% 1.75/1.26  % [INFO] 	 Running in sequential loop mode. 
% 2.29/1.65  % [INFO] 	 nitpick registered as external prover. 
% 2.29/1.66  % [INFO] 	 Scanning for conjecture ... 
% 2.64/1.80  % [INFO] 	 Found a conjecture (or negated_conjecture) and 95 axioms. Running axiom selection ... 
% 2.76/1.91  % [INFO] 	 Axiom selection finished. Selected 95 axioms (removed 0 axioms). 
% 3.14/2.04  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 3.35/2.07  % [INFO] 	 Type checking passed. 
% 3.35/2.07  % [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 ... 
% 30.55/6.72  % [INFO] 	 Killing All external provers ... 
% 30.55/6.72  % Time passed: 6233ms (effective reasoning time: 5459ms)
% 30.55/6.72  % 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)>
% 30.55/6.73  % Axioms used in derivation (2): ax66, ax65
% 30.55/6.73  % No. of inferences in proof: 29
% 30.55/6.73  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6233 ms resp. 5459 ms w/o parsing
% 30.55/6.76  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.55/6.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------