TSTP Solution File: SWC023+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC023+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 : 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 : Wed Aug 31 18:38:16 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   54 (   8 unt;   0 def)
%            Number of atoms       :  336 (  69 equ)
%            Maximal formula atoms :   34 (   6 avg)
%            Number of connectives :  400 ( 118   ~; 110   |; 147   &)
%                                         (   8 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   7 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   76 (  34   !;  42   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f818,plain,
    $false,
    inference(avatar_sat_refutation,[],[f611,f621,f659,f667,f668,f805,f817]) ).

fof(f817,plain,
    ( ~ spl58_1
    | ~ spl58_5 ),
    inference(avatar_contradiction_clause,[],[f816]) ).

fof(f816,plain,
    ( $false
    | ~ spl58_1
    | ~ spl58_5 ),
    inference(subsumption_resolution,[],[f814,f624]) ).

fof(f624,plain,
    ( ssList(nil)
    | ~ spl58_5 ),
    inference(avatar_component_clause,[],[f623]) ).

fof(f623,plain,
    ( spl58_5
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl58_5])]) ).

fof(f814,plain,
    ( ~ ssList(nil)
    | ~ spl58_1 ),
    inference(resolution,[],[f808,f602]) ).

fof(f602,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f592]) ).

fof(f592,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f538]) ).

fof(f538,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f331]) ).

fof(f331,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f117]) ).

fof(f117,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( X0 != X1
          <=> neq(X0,X1) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( X0 != X1
          <=> neq(X0,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).

fof(f808,plain,
    ( neq(nil,nil)
    | ~ spl58_1 ),
    inference(backward_demodulation,[],[f567,f606]) ).

fof(f606,plain,
    ( nil = sK35
    | ~ spl58_1 ),
    inference(avatar_component_clause,[],[f604]) ).

fof(f604,plain,
    ( spl58_1
  <=> nil = sK35 ),
    introduced(avatar_definition,[new_symbols(naming,[spl58_1])]) ).

fof(f567,plain,
    neq(sK35,nil),
    inference(definition_unfolding,[],[f483,f482]) ).

fof(f482,plain,
    sK33 = sK35,
    inference(cnf_transformation,[],[f305]) ).

fof(f305,plain,
    ( ssList(sK33)
    & ssList(sK34)
    & ssList(sK35)
    & ( ( ssList(sK36)
        & frontsegP(sK34,sK36)
        & neq(sK36,nil)
        & frontsegP(sK35,sK36) )
      | ( nil = sK34
        & nil = sK35 ) )
    & ! [X5] :
        ( ~ neq(X5,nil)
        | ~ frontsegP(sK32,X5)
        | ~ frontsegP(sK33,X5)
        | ~ ssList(X5) )
    & neq(sK33,nil)
    & sK33 = sK35
    & sK32 = sK34
    & ssList(sK32) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35,sK36])],[f299,f304,f303,f302,f301,f300]) ).

fof(f300,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( ssList(X3)
                    & ( ? [X4] :
                          ( ssList(X4)
                          & frontsegP(X2,X4)
                          & neq(X4,nil)
                          & frontsegP(X3,X4) )
                      | ( nil = X2
                        & nil = X3 ) )
                    & ! [X5] :
                        ( ~ neq(X5,nil)
                        | ~ frontsegP(X0,X5)
                        | ~ frontsegP(X1,X5)
                        | ~ ssList(X5) )
                    & neq(X1,nil)
                    & X1 = X3
                    & X0 = X2 ) ) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( ? [X4] :
                        ( ssList(X4)
                        & frontsegP(X2,X4)
                        & neq(X4,nil)
                        & frontsegP(X3,X4) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ! [X5] :
                      ( ~ neq(X5,nil)
                      | ~ frontsegP(sK32,X5)
                      | ~ frontsegP(X1,X5)
                      | ~ ssList(X5) )
                  & neq(X1,nil)
                  & X1 = X3
                  & sK32 = X2 ) ) )
      & ssList(sK32) ) ),
    introduced(choice_axiom,[]) ).

fof(f301,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssList(X3)
                & ( ? [X4] :
                      ( ssList(X4)
                      & frontsegP(X2,X4)
                      & neq(X4,nil)
                      & frontsegP(X3,X4) )
                  | ( nil = X2
                    & nil = X3 ) )
                & ! [X5] :
                    ( ~ neq(X5,nil)
                    | ~ frontsegP(sK32,X5)
                    | ~ frontsegP(X1,X5)
                    | ~ ssList(X5) )
                & neq(X1,nil)
                & X1 = X3
                & sK32 = X2 ) ) )
   => ( ssList(sK33)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ( ? [X4] :
                    ( ssList(X4)
                    & frontsegP(X2,X4)
                    & neq(X4,nil)
                    & frontsegP(X3,X4) )
                | ( nil = X2
                  & nil = X3 ) )
              & ! [X5] :
                  ( ~ neq(X5,nil)
                  | ~ frontsegP(sK32,X5)
                  | ~ frontsegP(sK33,X5)
                  | ~ ssList(X5) )
              & neq(sK33,nil)
              & sK33 = X3
              & sK32 = X2 ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f302,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( ssList(X3)
            & ( ? [X4] :
                  ( ssList(X4)
                  & frontsegP(X2,X4)
                  & neq(X4,nil)
                  & frontsegP(X3,X4) )
              | ( nil = X2
                & nil = X3 ) )
            & ! [X5] :
                ( ~ neq(X5,nil)
                | ~ frontsegP(sK32,X5)
                | ~ frontsegP(sK33,X5)
                | ~ ssList(X5) )
            & neq(sK33,nil)
            & sK33 = X3
            & sK32 = X2 ) )
   => ( ssList(sK34)
      & ? [X3] :
          ( ssList(X3)
          & ( ? [X4] :
                ( ssList(X4)
                & frontsegP(sK34,X4)
                & neq(X4,nil)
                & frontsegP(X3,X4) )
            | ( nil = sK34
              & nil = X3 ) )
          & ! [X5] :
              ( ~ neq(X5,nil)
              | ~ frontsegP(sK32,X5)
              | ~ frontsegP(sK33,X5)
              | ~ ssList(X5) )
          & neq(sK33,nil)
          & sK33 = X3
          & sK32 = sK34 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f303,plain,
    ( ? [X3] :
        ( ssList(X3)
        & ( ? [X4] :
              ( ssList(X4)
              & frontsegP(sK34,X4)
              & neq(X4,nil)
              & frontsegP(X3,X4) )
          | ( nil = sK34
            & nil = X3 ) )
        & ! [X5] :
            ( ~ neq(X5,nil)
            | ~ frontsegP(sK32,X5)
            | ~ frontsegP(sK33,X5)
            | ~ ssList(X5) )
        & neq(sK33,nil)
        & sK33 = X3
        & sK32 = sK34 )
   => ( ssList(sK35)
      & ( ? [X4] :
            ( ssList(X4)
            & frontsegP(sK34,X4)
            & neq(X4,nil)
            & frontsegP(sK35,X4) )
        | ( nil = sK34
          & nil = sK35 ) )
      & ! [X5] :
          ( ~ neq(X5,nil)
          | ~ frontsegP(sK32,X5)
          | ~ frontsegP(sK33,X5)
          | ~ ssList(X5) )
      & neq(sK33,nil)
      & sK33 = sK35
      & sK32 = sK34 ) ),
    introduced(choice_axiom,[]) ).

fof(f304,plain,
    ( ? [X4] :
        ( ssList(X4)
        & frontsegP(sK34,X4)
        & neq(X4,nil)
        & frontsegP(sK35,X4) )
   => ( ssList(sK36)
      & frontsegP(sK34,sK36)
      & neq(sK36,nil)
      & frontsegP(sK35,sK36) ) ),
    introduced(choice_axiom,[]) ).

fof(f299,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( ? [X4] :
                        ( ssList(X4)
                        & frontsegP(X2,X4)
                        & neq(X4,nil)
                        & frontsegP(X3,X4) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ! [X5] :
                      ( ~ neq(X5,nil)
                      | ~ frontsegP(X0,X5)
                      | ~ frontsegP(X1,X5)
                      | ~ ssList(X5) )
                  & neq(X1,nil)
                  & X1 = X3
                  & X0 = X2 ) ) )
      & ssList(X0) ),
    inference(rectify,[],[f176]) ).

fof(f176,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ssList(X3)
                  & ( ? [X5] :
                        ( ssList(X5)
                        & frontsegP(X2,X5)
                        & neq(X5,nil)
                        & frontsegP(X3,X5) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ! [X4] :
                      ( ~ neq(X4,nil)
                      | ~ frontsegP(X0,X4)
                      | ~ frontsegP(X1,X4)
                      | ~ ssList(X4) )
                  & neq(X1,nil)
                  & X1 = X3
                  & X0 = X2 ) ) )
      & ssList(X0) ),
    inference(flattening,[],[f175]) ).

fof(f175,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & X1 = X3
                  & ! [X4] :
                      ( ~ neq(X4,nil)
                      | ~ frontsegP(X0,X4)
                      | ~ frontsegP(X1,X4)
                      | ~ ssList(X4) )
                  & ( ? [X5] :
                        ( neq(X5,nil)
                        & frontsegP(X3,X5)
                        & frontsegP(X2,X5)
                        & ssList(X5) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & neq(X1,nil)
                  & 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)
                   => ( X0 != X2
                      | X1 != X3
                      | ? [X4] :
                          ( frontsegP(X0,X4)
                          & frontsegP(X1,X4)
                          & ssList(X4)
                          & neq(X4,nil) )
                      | ( ! [X5] :
                            ( ssList(X5)
                           => ( ~ neq(X5,nil)
                              | ~ frontsegP(X3,X5)
                              | ~ frontsegP(X2,X5) ) )
                        & ( nil != X3
                          | nil != X2 ) )
                      | ~ neq(X1,nil) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( X0 != X2
                    | X1 != X3
                    | ? [X4] :
                        ( frontsegP(X0,X4)
                        & frontsegP(X1,X4)
                        & ssList(X4)
                        & neq(X4,nil) )
                    | ( ! [X5] :
                          ( ssList(X5)
                         => ( ~ neq(X5,nil)
                            | ~ frontsegP(X3,X5)
                            | ~ frontsegP(X2,X5) ) )
                      & ( nil != X3
                        | nil != X2 ) )
                    | ~ neq(X1,nil) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f483,plain,
    neq(sK33,nil),
    inference(cnf_transformation,[],[f305]) ).

fof(f805,plain,
    ( ~ spl58_11
    | ~ spl58_2
    | ~ spl58_3
    | ~ spl58_10 ),
    inference(avatar_split_clause,[],[f804,f646,f613,f608,f651]) ).

fof(f651,plain,
    ( spl58_11
  <=> frontsegP(sK34,sK36) ),
    introduced(avatar_definition,[new_symbols(naming,[spl58_11])]) ).

fof(f608,plain,
    ( spl58_2
  <=> neq(sK36,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl58_2])]) ).

fof(f613,plain,
    ( spl58_3
  <=> frontsegP(sK35,sK36) ),
    introduced(avatar_definition,[new_symbols(naming,[spl58_3])]) ).

fof(f646,plain,
    ( spl58_10
  <=> ssList(sK36) ),
    introduced(avatar_definition,[new_symbols(naming,[spl58_10])]) ).

fof(f804,plain,
    ( ~ frontsegP(sK34,sK36)
    | ~ spl58_2
    | ~ spl58_3
    | ~ spl58_10 ),
    inference(subsumption_resolution,[],[f798,f648]) ).

fof(f648,plain,
    ( ssList(sK36)
    | ~ spl58_10 ),
    inference(avatar_component_clause,[],[f646]) ).

fof(f798,plain,
    ( ~ frontsegP(sK34,sK36)
    | ~ ssList(sK36)
    | ~ spl58_2
    | ~ spl58_3 ),
    inference(subsumption_resolution,[],[f794,f610]) ).

fof(f610,plain,
    ( neq(sK36,nil)
    | ~ spl58_2 ),
    inference(avatar_component_clause,[],[f608]) ).

fof(f794,plain,
    ( ~ neq(sK36,nil)
    | ~ ssList(sK36)
    | ~ frontsegP(sK34,sK36)
    | ~ spl58_3 ),
    inference(resolution,[],[f566,f615]) ).

fof(f615,plain,
    ( frontsegP(sK35,sK36)
    | ~ spl58_3 ),
    inference(avatar_component_clause,[],[f613]) ).

fof(f566,plain,
    ! [X5] :
      ( ~ frontsegP(sK35,X5)
      | ~ neq(X5,nil)
      | ~ ssList(X5)
      | ~ frontsegP(sK34,X5) ),
    inference(definition_unfolding,[],[f484,f481,f482]) ).

fof(f481,plain,
    sK32 = sK34,
    inference(cnf_transformation,[],[f305]) ).

fof(f484,plain,
    ! [X5] :
      ( ~ neq(X5,nil)
      | ~ frontsegP(sK32,X5)
      | ~ frontsegP(sK33,X5)
      | ~ ssList(X5) ),
    inference(cnf_transformation,[],[f305]) ).

fof(f668,plain,
    spl58_5,
    inference(avatar_split_clause,[],[f409,f623]) ).

fof(f409,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).

fof(f667,plain,
    ( spl58_11
    | spl58_1 ),
    inference(avatar_split_clause,[],[f489,f604,f651]) ).

fof(f489,plain,
    ( nil = sK35
    | frontsegP(sK34,sK36) ),
    inference(cnf_transformation,[],[f305]) ).

fof(f659,plain,
    ( spl58_10
    | spl58_1 ),
    inference(avatar_split_clause,[],[f491,f604,f646]) ).

fof(f491,plain,
    ( nil = sK35
    | ssList(sK36) ),
    inference(cnf_transformation,[],[f305]) ).

fof(f621,plain,
    ( spl58_3
    | spl58_1 ),
    inference(avatar_split_clause,[],[f485,f604,f613]) ).

fof(f485,plain,
    ( nil = sK35
    | frontsegP(sK35,sK36) ),
    inference(cnf_transformation,[],[f305]) ).

fof(f611,plain,
    ( spl58_1
    | spl58_2 ),
    inference(avatar_split_clause,[],[f487,f608,f604]) ).

fof(f487,plain,
    ( neq(sK36,nil)
    | nil = sK35 ),
    inference(cnf_transformation,[],[f305]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWC023+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 18:01:05 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.47  % (26523)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.49  % (26523)First to succeed.
% 0.19/0.50  % (26531)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.50  % (26524)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)
% 0.19/0.50  % (26549)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.50  % (26523)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (26523)------------------------------
% 0.19/0.50  % (26523)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (26523)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (26523)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (26523)Memory used [KB]: 6524
% 0.19/0.50  % (26523)Time elapsed: 0.103 s
% 0.19/0.50  % (26523)Instructions burned: 19 (million)
% 0.19/0.50  % (26523)------------------------------
% 0.19/0.50  % (26523)------------------------------
% 0.19/0.50  % (26517)Success in time 0.156 s
%------------------------------------------------------------------------------