TSTP Solution File: SWC179+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC179+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n028.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 : Wed Aug 31 18:39:23 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   43 (   8 unt;   0 def)
%            Number of atoms       :  321 (  91 equ)
%            Maximal formula atoms :   22 (   7 avg)
%            Number of connectives :  396 ( 118   ~;  94   |; 160   &)
%                                         (   2 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   8 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   3 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  119 (  63   !;  56   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f733,plain,
    $false,
    inference(avatar_sat_refutation,[],[f646,f726,f732]) ).

fof(f732,plain,
    ~ spl61_8,
    inference(avatar_contradiction_clause,[],[f731]) ).

fof(f731,plain,
    ( $false
    | ~ spl61_8 ),
    inference(subsumption_resolution,[],[f730,f519]) ).

fof(f519,plain,
    duplicatefreeP(nil),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,axiom,
    duplicatefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).

fof(f730,plain,
    ( ~ duplicatefreeP(nil)
    | ~ spl61_8 ),
    inference(backward_demodulation,[],[f436,f645]) ).

fof(f645,plain,
    ( nil = sK33
    | ~ spl61_8 ),
    inference(avatar_component_clause,[],[f643]) ).

fof(f643,plain,
    ( spl61_8
  <=> nil = sK33 ),
    introduced(avatar_definition,[new_symbols(naming,[spl61_8])]) ).

fof(f436,plain,
    ~ duplicatefreeP(sK33),
    inference(cnf_transformation,[],[f291]) ).

fof(f291,plain,
    ( ssList(sK33)
    & ssList(sK35)
    & sK36 = sK34
    & ( ( nil = sK35
        & nil = sK36 )
      | sP2(sK36,sK35) )
    & ssList(sK36)
    & sK35 = sK33
    & ~ duplicatefreeP(sK33)
    & ssList(sK34) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36])],[f227,f290,f289,f288,f287]) ).

fof(f287,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( X1 = X3
                    & ( ( nil = X2
                        & nil = X3 )
                      | sP2(X3,X2) )
                    & ssList(X3)
                    & X0 = X2
                    & ~ duplicatefreeP(X0) ) )
            & ssList(X1) ) )
   => ( ssList(sK33)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ( ( nil = X2
                      & nil = X3 )
                    | sP2(X3,X2) )
                  & ssList(X3)
                  & sK33 = X2
                  & ~ duplicatefreeP(sK33) ) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f288,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( X1 = X3
                & ( ( nil = X2
                    & nil = X3 )
                  | sP2(X3,X2) )
                & ssList(X3)
                & sK33 = X2
                & ~ duplicatefreeP(sK33) ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( sK34 = X3
              & ( ( nil = X2
                  & nil = X3 )
                | sP2(X3,X2) )
              & ssList(X3)
              & sK33 = X2
              & ~ duplicatefreeP(sK33) ) )
      & ssList(sK34) ) ),
    introduced(choice_axiom,[]) ).

fof(f289,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( sK34 = X3
            & ( ( nil = X2
                & nil = X3 )
              | sP2(X3,X2) )
            & ssList(X3)
            & sK33 = X2
            & ~ duplicatefreeP(sK33) ) )
   => ( ssList(sK35)
      & ? [X3] :
          ( sK34 = X3
          & ( ( nil = sK35
              & nil = X3 )
            | sP2(X3,sK35) )
          & ssList(X3)
          & sK35 = sK33
          & ~ duplicatefreeP(sK33) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f290,plain,
    ( ? [X3] :
        ( sK34 = X3
        & ( ( nil = sK35
            & nil = X3 )
          | sP2(X3,sK35) )
        & ssList(X3)
        & sK35 = sK33
        & ~ duplicatefreeP(sK33) )
   => ( sK36 = sK34
      & ( ( nil = sK35
          & nil = sK36 )
        | sP2(sK36,sK35) )
      & ssList(sK36)
      & sK35 = sK33
      & ~ duplicatefreeP(sK33) ) ),
    introduced(choice_axiom,[]) ).

fof(f227,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ( ( nil = X2
                      & nil = X3 )
                    | sP2(X3,X2) )
                  & ssList(X3)
                  & X0 = X2
                  & ~ duplicatefreeP(X0) ) )
          & ssList(X1) ) ),
    inference(definition_folding,[],[f141,f226]) ).

fof(f226,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ssItem(X4)
          & ? [X5] :
              ( ssList(X5)
              & ? [X6] :
                  ( app(app(X5,X2),X6) = X3
                  & cons(X4,nil) = X2
                  & ! [X8] :
                      ( ~ lt(X8,X4)
                      | ~ memberP(X6,X8)
                      | ~ ssItem(X8) )
                  & ! [X7] :
                      ( ~ ssItem(X7)
                      | ~ lt(X4,X7)
                      | ~ memberP(X5,X7) )
                  & ssList(X6) ) ) )
      | ~ sP2(X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f141,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ssItem(X4)
                        & ? [X5] :
                            ( ssList(X5)
                            & ? [X6] :
                                ( app(app(X5,X2),X6) = X3
                                & cons(X4,nil) = X2
                                & ! [X8] :
                                    ( ~ lt(X8,X4)
                                    | ~ memberP(X6,X8)
                                    | ~ ssItem(X8) )
                                & ! [X7] :
                                    ( ~ ssItem(X7)
                                    | ~ lt(X4,X7)
                                    | ~ memberP(X5,X7) )
                                & ssList(X6) ) ) ) )
                  & ssList(X3)
                  & X0 = X2
                  & ~ duplicatefreeP(X0) ) )
          & ssList(X1) ) ),
    inference(flattening,[],[f140]) ).

fof(f140,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( app(app(X5,X2),X6) = X3
                                & ! [X7] :
                                    ( ~ ssItem(X7)
                                    | ~ lt(X4,X7)
                                    | ~ memberP(X5,X7) )
                                & ! [X8] :
                                    ( ~ lt(X8,X4)
                                    | ~ memberP(X6,X8)
                                    | ~ ssItem(X8) )
                                & cons(X4,nil) = X2
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & X0 = X2
                  & ~ duplicatefreeP(X0)
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( X1 != X3
                      | ( ( nil != X2
                          | nil != X3 )
                        & ! [X4] :
                            ( ssItem(X4)
                           => ! [X5] :
                                ( ssList(X5)
                               => ! [X6] :
                                    ( ssList(X6)
                                   => ( app(app(X5,X2),X6) != X3
                                      | ? [X7] :
                                          ( ssItem(X7)
                                          & lt(X4,X7)
                                          & memberP(X5,X7) )
                                      | ? [X8] :
                                          ( lt(X8,X4)
                                          & memberP(X6,X8)
                                          & ssItem(X8) )
                                      | cons(X4,nil) != X2 ) ) ) ) )
                      | X0 != X2
                      | duplicatefreeP(X0) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( X1 != X3
                    | ( ( nil != X2
                        | nil != X3 )
                      & ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ! [X6] :
                                  ( ssList(X6)
                                 => ( app(app(X5,X2),X6) != X3
                                    | ? [X7] :
                                        ( ssItem(X7)
                                        & lt(X4,X7)
                                        & memberP(X5,X7) )
                                    | ? [X8] :
                                        ( lt(X8,X4)
                                        & memberP(X6,X8)
                                        & ssItem(X8) )
                                    | cons(X4,nil) != X2 ) ) ) ) )
                    | X0 != X2
                    | duplicatefreeP(X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f726,plain,
    ~ spl61_7,
    inference(avatar_contradiction_clause,[],[f725]) ).

fof(f725,plain,
    ( $false
    | ~ spl61_7 ),
    inference(subsumption_resolution,[],[f724,f436]) ).

fof(f724,plain,
    ( duplicatefreeP(sK33)
    | ~ spl61_7 ),
    inference(resolution,[],[f709,f638]) ).

fof(f638,plain,
    ( sP2(sK34,sK33)
    | ~ spl61_7 ),
    inference(avatar_component_clause,[],[f636]) ).

fof(f636,plain,
    ( spl61_7
  <=> sP2(sK34,sK33) ),
    introduced(avatar_definition,[new_symbols(naming,[spl61_7])]) ).

fof(f709,plain,
    ! [X8,X9] :
      ( ~ sP2(X8,X9)
      | duplicatefreeP(X9) ),
    inference(subsumption_resolution,[],[f701,f434]) ).

fof(f434,plain,
    ! [X0,X1] :
      ( ssItem(sK30(X0,X1))
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f286]) ).

fof(f286,plain,
    ! [X0,X1] :
      ( ( ssItem(sK30(X0,X1))
        & ssList(sK31(X0,X1))
        & app(app(sK31(X0,X1),X1),sK32(X0,X1)) = X0
        & cons(sK30(X0,X1),nil) = X1
        & ! [X5] :
            ( ~ lt(X5,sK30(X0,X1))
            | ~ memberP(sK32(X0,X1),X5)
            | ~ ssItem(X5) )
        & ! [X6] :
            ( ~ ssItem(X6)
            | ~ lt(sK30(X0,X1),X6)
            | ~ memberP(sK31(X0,X1),X6) )
        & ssList(sK32(X0,X1)) )
      | ~ sP2(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32])],[f282,f285,f284,f283]) ).

fof(f283,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ssItem(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( app(app(X3,X1),X4) = X0
                  & cons(X2,nil) = X1
                  & ! [X5] :
                      ( ~ lt(X5,X2)
                      | ~ memberP(X4,X5)
                      | ~ ssItem(X5) )
                  & ! [X6] :
                      ( ~ ssItem(X6)
                      | ~ lt(X2,X6)
                      | ~ memberP(X3,X6) )
                  & ssList(X4) ) ) )
     => ( ssItem(sK30(X0,X1))
        & ? [X3] :
            ( ssList(X3)
            & ? [X4] :
                ( app(app(X3,X1),X4) = X0
                & cons(sK30(X0,X1),nil) = X1
                & ! [X5] :
                    ( ~ lt(X5,sK30(X0,X1))
                    | ~ memberP(X4,X5)
                    | ~ ssItem(X5) )
                & ! [X6] :
                    ( ~ ssItem(X6)
                    | ~ lt(sK30(X0,X1),X6)
                    | ~ memberP(X3,X6) )
                & ssList(X4) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f284,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ssList(X3)
          & ? [X4] :
              ( app(app(X3,X1),X4) = X0
              & cons(sK30(X0,X1),nil) = X1
              & ! [X5] :
                  ( ~ lt(X5,sK30(X0,X1))
                  | ~ memberP(X4,X5)
                  | ~ ssItem(X5) )
              & ! [X6] :
                  ( ~ ssItem(X6)
                  | ~ lt(sK30(X0,X1),X6)
                  | ~ memberP(X3,X6) )
              & ssList(X4) ) )
     => ( ssList(sK31(X0,X1))
        & ? [X4] :
            ( app(app(sK31(X0,X1),X1),X4) = X0
            & cons(sK30(X0,X1),nil) = X1
            & ! [X5] :
                ( ~ lt(X5,sK30(X0,X1))
                | ~ memberP(X4,X5)
                | ~ ssItem(X5) )
            & ! [X6] :
                ( ~ ssItem(X6)
                | ~ lt(sK30(X0,X1),X6)
                | ~ memberP(sK31(X0,X1),X6) )
            & ssList(X4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f285,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( app(app(sK31(X0,X1),X1),X4) = X0
          & cons(sK30(X0,X1),nil) = X1
          & ! [X5] :
              ( ~ lt(X5,sK30(X0,X1))
              | ~ memberP(X4,X5)
              | ~ ssItem(X5) )
          & ! [X6] :
              ( ~ ssItem(X6)
              | ~ lt(sK30(X0,X1),X6)
              | ~ memberP(sK31(X0,X1),X6) )
          & ssList(X4) )
     => ( app(app(sK31(X0,X1),X1),sK32(X0,X1)) = X0
        & cons(sK30(X0,X1),nil) = X1
        & ! [X5] :
            ( ~ lt(X5,sK30(X0,X1))
            | ~ memberP(sK32(X0,X1),X5)
            | ~ ssItem(X5) )
        & ! [X6] :
            ( ~ ssItem(X6)
            | ~ lt(sK30(X0,X1),X6)
            | ~ memberP(sK31(X0,X1),X6) )
        & ssList(sK32(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f282,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ssItem(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( app(app(X3,X1),X4) = X0
                  & cons(X2,nil) = X1
                  & ! [X5] :
                      ( ~ lt(X5,X2)
                      | ~ memberP(X4,X5)
                      | ~ ssItem(X5) )
                  & ! [X6] :
                      ( ~ ssItem(X6)
                      | ~ lt(X2,X6)
                      | ~ memberP(X3,X6) )
                  & ssList(X4) ) ) )
      | ~ sP2(X0,X1) ),
    inference(rectify,[],[f281]) ).

fof(f281,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ssItem(X4)
          & ? [X5] :
              ( ssList(X5)
              & ? [X6] :
                  ( app(app(X5,X2),X6) = X3
                  & cons(X4,nil) = X2
                  & ! [X8] :
                      ( ~ lt(X8,X4)
                      | ~ memberP(X6,X8)
                      | ~ ssItem(X8) )
                  & ! [X7] :
                      ( ~ ssItem(X7)
                      | ~ lt(X4,X7)
                      | ~ memberP(X5,X7) )
                  & ssList(X6) ) ) )
      | ~ sP2(X3,X2) ),
    inference(nnf_transformation,[],[f226]) ).

fof(f701,plain,
    ! [X8,X9] :
      ( ~ ssItem(sK30(X8,X9))
      | duplicatefreeP(X9)
      | ~ sP2(X8,X9) ),
    inference(superposition,[],[f537,f431]) ).

fof(f431,plain,
    ! [X0,X1] :
      ( cons(sK30(X0,X1),nil) = X1
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f286]) ).

fof(f537,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f211]) ).

fof(f211,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f71]) ).

fof(f71,axiom,
    ! [X0] :
      ( ssItem(X0)
     => duplicatefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).

fof(f646,plain,
    ( spl61_8
    | spl61_7 ),
    inference(avatar_split_clause,[],[f572,f636,f643]) ).

fof(f572,plain,
    ( sP2(sK34,sK33)
    | nil = sK33 ),
    inference(definition_unfolding,[],[f440,f437,f441,f437]) ).

fof(f441,plain,
    sK36 = sK34,
    inference(cnf_transformation,[],[f291]) ).

fof(f437,plain,
    sK35 = sK33,
    inference(cnf_transformation,[],[f291]) ).

fof(f440,plain,
    ( nil = sK35
    | sP2(sK36,sK35) ),
    inference(cnf_transformation,[],[f291]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC179+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 18:40:34 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (13877)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.51  % (13877)Instruction limit reached!
% 0.20/0.51  % (13877)------------------------------
% 0.20/0.51  % (13877)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (13876)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.51  % (13887)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52  % (13876)First to succeed.
% 0.20/0.52  % (13877)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (13877)Termination reason: Unknown
% 0.20/0.52  % (13877)Termination phase: Saturation
% 0.20/0.52  
% 0.20/0.52  % (13877)Memory used [KB]: 6396
% 0.20/0.52  % (13877)Time elapsed: 0.096 s
% 0.20/0.52  % (13877)Instructions burned: 13 (million)
% 0.20/0.52  % (13877)------------------------------
% 0.20/0.52  % (13877)------------------------------
% 0.20/0.53  % (13876)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (13876)------------------------------
% 0.20/0.53  % (13876)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (13876)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (13876)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (13876)Memory used [KB]: 6524
% 0.20/0.53  % (13876)Time elapsed: 0.102 s
% 0.20/0.53  % (13876)Instructions burned: 16 (million)
% 0.20/0.53  % (13876)------------------------------
% 0.20/0.53  % (13876)------------------------------
% 0.20/0.53  % (13875)Success in time 0.177 s
%------------------------------------------------------------------------------