TSTP Solution File: SWC037+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC037+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 : n022.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 18:38:21 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   53 (   8 unt;   0 def)
%            Number of atoms       :  286 ( 102 equ)
%            Maximal formula atoms :   28 (   5 avg)
%            Number of connectives :  316 (  83   ~;  76   |; 130   &)
%                                         (   9 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   6 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   59 (  24   !;  35   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f269,plain,
    $false,
    inference(avatar_sat_refutation,[],[f188,f189,f190,f194,f198,f261]) ).

fof(f261,plain,
    ( ~ spl7_1
    | ~ spl7_3
    | ~ spl7_4
    | ~ spl7_6 ),
    inference(avatar_contradiction_clause,[],[f260]) ).

fof(f260,plain,
    ( $false
    | ~ spl7_1
    | ~ spl7_3
    | ~ spl7_4
    | ~ spl7_6 ),
    inference(subsumption_resolution,[],[f242,f236]) ).

fof(f236,plain,
    ( neq(nil,nil)
    | ~ spl7_1
    | ~ spl7_3
    | ~ spl7_4
    | ~ spl7_6 ),
    inference(backward_demodulation,[],[f176,f223]) ).

fof(f223,plain,
    ( nil = sK6
    | ~ spl7_1
    | ~ spl7_3
    | ~ spl7_6 ),
    inference(unit_resulting_resolution,[],[f186,f200,f126]) ).

fof(f126,plain,
    ! [X0] :
      ( ~ segmentP(nil,X0)
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( nil = X0
          | ~ segmentP(nil,X0) )
        & ( segmentP(nil,X0)
          | nil != X0 ) ) ),
    inference(nnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( nil = X0
      <=> segmentP(nil,X0) ) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil = X0
      <=> segmentP(nil,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

fof(f200,plain,
    ( segmentP(nil,sK6)
    | ~ spl7_1
    | ~ spl7_3 ),
    inference(forward_demodulation,[],[f171,f162]) ).

fof(f162,plain,
    ( nil = sK5
    | ~ spl7_1 ),
    inference(avatar_component_clause,[],[f160]) ).

fof(f160,plain,
    ( spl7_1
  <=> nil = sK5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

fof(f171,plain,
    ( segmentP(sK5,sK6)
    | ~ spl7_3 ),
    inference(avatar_component_clause,[],[f169]) ).

fof(f169,plain,
    ( spl7_3
  <=> segmentP(sK5,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).

fof(f186,plain,
    ( ssList(sK6)
    | ~ spl7_6 ),
    inference(avatar_component_clause,[],[f184]) ).

fof(f184,plain,
    ( spl7_6
  <=> ssList(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).

fof(f176,plain,
    ( neq(sK6,nil)
    | ~ spl7_4 ),
    inference(avatar_component_clause,[],[f174]) ).

fof(f174,plain,
    ( spl7_4
  <=> neq(sK6,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).

fof(f242,plain,
    ( ~ neq(nil,nil)
    | ~ spl7_1
    | ~ spl7_3
    | ~ spl7_6 ),
    inference(backward_demodulation,[],[f203,f223]) ).

fof(f203,plain,
    ( ~ neq(sK6,sK6)
    | ~ spl7_6 ),
    inference(unit_resulting_resolution,[],[f186,f158]) ).

fof(f158,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f156]) ).

fof(f156,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f129]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( X0 != X1
          <=> neq(X0,X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( X0 != X1
          <=> neq(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f198,plain,
    ~ spl7_5,
    inference(avatar_contradiction_clause,[],[f197]) ).

fof(f197,plain,
    ( $false
    | ~ spl7_5 ),
    inference(subsumption_resolution,[],[f196,f139]) ).

fof(f139,plain,
    nil != sK2,
    inference(cnf_transformation,[],[f124]) ).

fof(f124,plain,
    ( ssList(sK2)
    & ssList(sK4)
    & nil = sK3
    & ( ( neq(sK6,nil)
        & segmentP(sK4,sK6)
        & ssList(sK6)
        & segmentP(sK5,sK6) )
      | ( nil = sK4
        & nil = sK5 ) )
    & sK2 = sK4
    & nil != sK2
    & ssList(sK5)
    & sK3 = sK5
    & ssList(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f109,f123,f122,f121,f120,f119]) ).

fof(f119,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( nil = X1
                    & ( ? [X4] :
                          ( neq(X4,nil)
                          & segmentP(X2,X4)
                          & ssList(X4)
                          & segmentP(X3,X4) )
                      | ( nil = X2
                        & nil = X3 ) )
                    & X0 = X2
                    & nil != X0
                    & ssList(X3)
                    & X1 = X3 ) )
            & ssList(X1) ) )
   => ( ssList(sK2)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( nil = X1
                  & ( ? [X4] :
                        ( neq(X4,nil)
                        & segmentP(X2,X4)
                        & ssList(X4)
                        & segmentP(X3,X4) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & sK2 = X2
                  & nil != sK2
                  & ssList(X3)
                  & X1 = X3 ) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f120,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( nil = X1
                & ( ? [X4] :
                      ( neq(X4,nil)
                      & segmentP(X2,X4)
                      & ssList(X4)
                      & segmentP(X3,X4) )
                  | ( nil = X2
                    & nil = X3 ) )
                & sK2 = X2
                & nil != sK2
                & ssList(X3)
                & X1 = X3 ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( nil = sK3
              & ( ? [X4] :
                    ( neq(X4,nil)
                    & segmentP(X2,X4)
                    & ssList(X4)
                    & segmentP(X3,X4) )
                | ( nil = X2
                  & nil = X3 ) )
              & sK2 = X2
              & nil != sK2
              & ssList(X3)
              & sK3 = X3 ) )
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f121,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( nil = sK3
            & ( ? [X4] :
                  ( neq(X4,nil)
                  & segmentP(X2,X4)
                  & ssList(X4)
                  & segmentP(X3,X4) )
              | ( nil = X2
                & nil = X3 ) )
            & sK2 = X2
            & nil != sK2
            & ssList(X3)
            & sK3 = X3 ) )
   => ( ssList(sK4)
      & ? [X3] :
          ( nil = sK3
          & ( ? [X4] :
                ( neq(X4,nil)
                & segmentP(sK4,X4)
                & ssList(X4)
                & segmentP(X3,X4) )
            | ( nil = sK4
              & nil = X3 ) )
          & sK2 = sK4
          & nil != sK2
          & ssList(X3)
          & sK3 = X3 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f122,plain,
    ( ? [X3] :
        ( nil = sK3
        & ( ? [X4] :
              ( neq(X4,nil)
              & segmentP(sK4,X4)
              & ssList(X4)
              & segmentP(X3,X4) )
          | ( nil = sK4
            & nil = X3 ) )
        & sK2 = sK4
        & nil != sK2
        & ssList(X3)
        & sK3 = X3 )
   => ( nil = sK3
      & ( ? [X4] :
            ( neq(X4,nil)
            & segmentP(sK4,X4)
            & ssList(X4)
            & segmentP(sK5,X4) )
        | ( nil = sK4
          & nil = sK5 ) )
      & sK2 = sK4
      & nil != sK2
      & ssList(sK5)
      & sK3 = sK5 ) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ( ? [X4] :
        ( neq(X4,nil)
        & segmentP(sK4,X4)
        & ssList(X4)
        & segmentP(sK5,X4) )
   => ( neq(sK6,nil)
      & segmentP(sK4,sK6)
      & ssList(sK6)
      & segmentP(sK5,sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f109,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( nil = X1
                  & ( ? [X4] :
                        ( neq(X4,nil)
                        & segmentP(X2,X4)
                        & ssList(X4)
                        & segmentP(X3,X4) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & X0 = X2
                  & nil != X0
                  & ssList(X3)
                  & X1 = X3 ) )
          & ssList(X1) ) ),
    inference(flattening,[],[f108]) ).

fof(f108,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & nil = X1
                  & nil != X0
                  & X1 = X3
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( neq(X4,nil)
                        & segmentP(X2,X4)
                        & segmentP(X3,X4)
                        & ssList(X4) ) )
                  & 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
                      | nil != X1
                      | nil = X0
                      | X1 != X3
                      | ( ( nil != X3
                          | nil != X2 )
                        & ! [X4] :
                            ( ssList(X4)
                           => ( ~ neq(X4,nil)
                              | ~ segmentP(X2,X4)
                              | ~ segmentP(X3,X4) ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( X0 != X2
                    | nil != X1
                    | nil = X0
                    | X1 != X3
                    | ( ( nil != X3
                        | nil != X2 )
                      & ! [X4] :
                          ( ssList(X4)
                         => ( ~ neq(X4,nil)
                            | ~ segmentP(X2,X4)
                            | ~ segmentP(X3,X4) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f196,plain,
    ( nil = sK2
    | ~ spl7_5 ),
    inference(backward_demodulation,[],[f140,f181]) ).

fof(f181,plain,
    ( nil = sK4
    | ~ spl7_5 ),
    inference(avatar_component_clause,[],[f179]) ).

fof(f179,plain,
    ( spl7_5
  <=> nil = sK4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).

fof(f140,plain,
    sK2 = sK4,
    inference(cnf_transformation,[],[f124]) ).

fof(f194,plain,
    spl7_1,
    inference(avatar_split_clause,[],[f193,f160]) ).

fof(f193,plain,
    nil = sK5,
    inference(forward_demodulation,[],[f137,f149]) ).

fof(f149,plain,
    nil = sK3,
    inference(cnf_transformation,[],[f124]) ).

fof(f137,plain,
    sK3 = sK5,
    inference(cnf_transformation,[],[f124]) ).

fof(f190,plain,
    ( spl7_5
    | spl7_4 ),
    inference(avatar_split_clause,[],[f148,f174,f179]) ).

fof(f148,plain,
    ( neq(sK6,nil)
    | nil = sK4 ),
    inference(cnf_transformation,[],[f124]) ).

fof(f189,plain,
    ( spl7_3
    | spl7_5 ),
    inference(avatar_split_clause,[],[f142,f179,f169]) ).

fof(f142,plain,
    ( nil = sK4
    | segmentP(sK5,sK6) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f188,plain,
    ( spl7_6
    | spl7_5 ),
    inference(avatar_split_clause,[],[f144,f179,f184]) ).

fof(f144,plain,
    ( nil = sK4
    | ssList(sK6) ),
    inference(cnf_transformation,[],[f124]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC037+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % 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 : n022.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 18:02:41 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (9444)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50  % (9437)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (9420)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)
% 0.19/0.51  % (9427)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)
% 0.19/0.51  % (9439)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.19/0.51  % (9437)Instruction limit reached!
% 0.19/0.51  % (9437)------------------------------
% 0.19/0.51  % (9437)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (9431)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.51  % (9437)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (9437)Termination reason: Unknown
% 0.19/0.51  % (9437)Termination phase: Naming
% 0.19/0.51  
% 0.19/0.51  % (9437)Memory used [KB]: 1663
% 0.19/0.51  % (9437)Time elapsed: 0.004 s
% 0.19/0.51  % (9437)Instructions burned: 3 (million)
% 0.19/0.51  % (9437)------------------------------
% 0.19/0.51  % (9437)------------------------------
% 0.19/0.51  % (9422)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (9426)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.52  % (9422)First to succeed.
% 0.19/0.52  % (9443)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.52  % (9432)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (9422)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Theorem for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (9422)------------------------------
% 0.19/0.52  % (9422)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (9422)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (9422)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (9422)Memory used [KB]: 6140
% 0.19/0.52  % (9422)Time elapsed: 0.122 s
% 0.19/0.52  % (9422)Instructions burned: 5 (million)
% 0.19/0.52  % (9422)------------------------------
% 0.19/0.52  % (9422)------------------------------
% 0.19/0.52  % (9415)Success in time 0.168 s
%------------------------------------------------------------------------------