TSTP Solution File: SWC254+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC254+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 : n029.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 18:39:54 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   46 (   6 unt;   0 def)
%            Number of atoms       :  280 (  76 equ)
%            Maximal formula atoms :   28 (   6 avg)
%            Number of connectives :  312 (  78   ~;  66   |; 142   &)
%                                         (   6 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :   77 (  24   !;  53   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f290,plain,
    $false,
    inference(avatar_sat_refutation,[],[f235,f236,f243,f244,f288]) ).

fof(f288,plain,
    ( spl11_3
    | ~ spl11_5
    | ~ spl11_6 ),
    inference(avatar_contradiction_clause,[],[f287]) ).

fof(f287,plain,
    ( $false
    | spl11_3
    | ~ spl11_5
    | ~ spl11_6 ),
    inference(subsumption_resolution,[],[f286,f233]) ).

fof(f233,plain,
    ( ssItem(sK9)
    | ~ spl11_5 ),
    inference(avatar_component_clause,[],[f231]) ).

fof(f231,plain,
    ( spl11_5
  <=> ssItem(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_5])]) ).

fof(f286,plain,
    ( ~ ssItem(sK9)
    | spl11_3
    | ~ spl11_6 ),
    inference(subsumption_resolution,[],[f285,f189]) ).

fof(f189,plain,
    ssList(sK7),
    inference(cnf_transformation,[],[f141]) ).

fof(f141,plain,
    ( ssList(sK6)
    & ssList(sK7)
    & sK5 = sK7
    & ssList(sK8)
    & sK6 = sK8
    & ( ( ssItem(sK9)
        & cons(sK9,nil) = sK7
        & sK8 = app(sK10,cons(sK9,nil))
        & ssList(sK10)
        & neq(sK6,nil)
        & ~ singletonP(sK5) )
      | ( ~ neq(sK8,nil)
        & neq(sK6,nil) ) )
    & ssList(sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10])],[f112,f140,f139,f138,f137,f136,f135]) ).

fof(f135,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( X0 = X2
                    & ssList(X3)
                    & X1 = X3
                    & ( ( ? [X4] :
                            ( ssItem(X4)
                            & ? [X5] :
                                ( cons(X4,nil) = X2
                                & app(X5,cons(X4,nil)) = X3
                                & ssList(X5) ) )
                        & neq(X1,nil)
                        & ~ singletonP(X0) )
                      | ( ~ neq(X3,nil)
                        & neq(X1,nil) ) ) ) ) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( sK5 = X2
                  & ssList(X3)
                  & X1 = X3
                  & ( ( ? [X4] :
                          ( ssItem(X4)
                          & ? [X5] :
                              ( cons(X4,nil) = X2
                              & app(X5,cons(X4,nil)) = X3
                              & ssList(X5) ) )
                      & neq(X1,nil)
                      & ~ singletonP(sK5) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) ) ) ) )
      & ssList(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( sK5 = X2
                & ssList(X3)
                & X1 = X3
                & ( ( ? [X4] :
                        ( ssItem(X4)
                        & ? [X5] :
                            ( cons(X4,nil) = X2
                            & app(X5,cons(X4,nil)) = X3
                            & ssList(X5) ) )
                    & neq(X1,nil)
                    & ~ singletonP(sK5) )
                  | ( ~ neq(X3,nil)
                    & neq(X1,nil) ) ) ) ) )
   => ( ssList(sK6)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( sK5 = X2
              & ssList(X3)
              & sK6 = X3
              & ( ( ? [X4] :
                      ( ssItem(X4)
                      & ? [X5] :
                          ( cons(X4,nil) = X2
                          & app(X5,cons(X4,nil)) = X3
                          & ssList(X5) ) )
                  & neq(sK6,nil)
                  & ~ singletonP(sK5) )
                | ( ~ neq(X3,nil)
                  & neq(sK6,nil) ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f137,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( sK5 = X2
            & ssList(X3)
            & sK6 = X3
            & ( ( ? [X4] :
                    ( ssItem(X4)
                    & ? [X5] :
                        ( cons(X4,nil) = X2
                        & app(X5,cons(X4,nil)) = X3
                        & ssList(X5) ) )
                & neq(sK6,nil)
                & ~ singletonP(sK5) )
              | ( ~ neq(X3,nil)
                & neq(sK6,nil) ) ) ) )
   => ( ssList(sK7)
      & ? [X3] :
          ( sK5 = sK7
          & ssList(X3)
          & sK6 = X3
          & ( ( ? [X4] :
                  ( ssItem(X4)
                  & ? [X5] :
                      ( cons(X4,nil) = sK7
                      & app(X5,cons(X4,nil)) = X3
                      & ssList(X5) ) )
              & neq(sK6,nil)
              & ~ singletonP(sK5) )
            | ( ~ neq(X3,nil)
              & neq(sK6,nil) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f138,plain,
    ( ? [X3] :
        ( sK5 = sK7
        & ssList(X3)
        & sK6 = X3
        & ( ( ? [X4] :
                ( ssItem(X4)
                & ? [X5] :
                    ( cons(X4,nil) = sK7
                    & app(X5,cons(X4,nil)) = X3
                    & ssList(X5) ) )
            & neq(sK6,nil)
            & ~ singletonP(sK5) )
          | ( ~ neq(X3,nil)
            & neq(sK6,nil) ) ) )
   => ( sK5 = sK7
      & ssList(sK8)
      & sK6 = sK8
      & ( ( ? [X4] :
              ( ssItem(X4)
              & ? [X5] :
                  ( cons(X4,nil) = sK7
                  & app(X5,cons(X4,nil)) = sK8
                  & ssList(X5) ) )
          & neq(sK6,nil)
          & ~ singletonP(sK5) )
        | ( ~ neq(sK8,nil)
          & neq(sK6,nil) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f139,plain,
    ( ? [X4] :
        ( ssItem(X4)
        & ? [X5] :
            ( cons(X4,nil) = sK7
            & app(X5,cons(X4,nil)) = sK8
            & ssList(X5) ) )
   => ( ssItem(sK9)
      & ? [X5] :
          ( cons(sK9,nil) = sK7
          & app(X5,cons(sK9,nil)) = sK8
          & ssList(X5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f140,plain,
    ( ? [X5] :
        ( cons(sK9,nil) = sK7
        & app(X5,cons(sK9,nil)) = sK8
        & ssList(X5) )
   => ( cons(sK9,nil) = sK7
      & sK8 = app(sK10,cons(sK9,nil))
      & ssList(sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f112,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X0 = X2
                  & ssList(X3)
                  & X1 = X3
                  & ( ( ? [X4] :
                          ( ssItem(X4)
                          & ? [X5] :
                              ( cons(X4,nil) = X2
                              & app(X5,cons(X4,nil)) = X3
                              & ssList(X5) ) )
                      & neq(X1,nil)
                      & ~ singletonP(X0) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) ) ) ) )
      & ssList(X0) ),
    inference(flattening,[],[f111]) ).

fof(f111,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( neq(X1,nil)
                      & ? [X4] :
                          ( ? [X5] :
                              ( cons(X4,nil) = X2
                              & app(X5,cons(X4,nil)) = X3
                              & ssList(X5) )
                          & ssItem(X4) )
                      & ~ singletonP(X0) ) )
                  & X0 = X2
                  & X1 = X3
                  & 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)
                   => ( ( ( ~ neq(X1,nil)
                          | neq(X3,nil) )
                        & ( ~ neq(X1,nil)
                          | ! [X4] :
                              ( ssItem(X4)
                             => ! [X5] :
                                  ( ssList(X5)
                                 => ( cons(X4,nil) != X2
                                    | app(X5,cons(X4,nil)) != X3 ) ) )
                          | singletonP(X0) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( ~ neq(X1,nil)
                        | neq(X3,nil) )
                      & ( ~ neq(X1,nil)
                        | ! [X4] :
                            ( ssItem(X4)
                           => ! [X5] :
                                ( ssList(X5)
                               => ( cons(X4,nil) != X2
                                  | app(X5,cons(X4,nil)) != X3 ) ) )
                        | singletonP(X0) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f285,plain,
    ( ~ ssList(sK7)
    | ~ ssItem(sK9)
    | spl11_3
    | ~ spl11_6 ),
    inference(subsumption_resolution,[],[f283,f222]) ).

fof(f222,plain,
    ( ~ singletonP(sK7)
    | spl11_3 ),
    inference(avatar_component_clause,[],[f220]) ).

fof(f220,plain,
    ( spl11_3
  <=> singletonP(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).

fof(f283,plain,
    ( singletonP(sK7)
    | ~ ssItem(sK9)
    | ~ ssList(sK7)
    | ~ spl11_6 ),
    inference(superposition,[],[f201,f241]) ).

fof(f241,plain,
    ( cons(sK9,nil) = sK7
    | ~ spl11_6 ),
    inference(avatar_component_clause,[],[f239]) ).

fof(f239,plain,
    ( spl11_6
  <=> cons(sK9,nil) = sK7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_6])]) ).

fof(f201,plain,
    ! [X1] :
      ( ~ ssList(cons(X1,nil))
      | ~ ssItem(X1)
      | singletonP(cons(X1,nil)) ),
    inference(equality_resolution,[],[f150]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK2(X0),nil) = X0
            & ssItem(sK2(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f125,f126]) ).

fof(f126,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK2(X0),nil) = X0
        & ssItem(sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f124]) ).

fof(f124,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X1] :
              ( cons(X1,nil) = X0
              & ssItem(X1) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

fof(f244,plain,
    ( ~ spl11_2
    | spl11_5 ),
    inference(avatar_split_clause,[],[f185,f231,f215]) ).

fof(f215,plain,
    ( spl11_2
  <=> neq(sK8,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).

fof(f185,plain,
    ( ssItem(sK9)
    | ~ neq(sK8,nil) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f243,plain,
    ( spl11_6
    | ~ spl11_2 ),
    inference(avatar_split_clause,[],[f183,f215,f239]) ).

fof(f183,plain,
    ( ~ neq(sK8,nil)
    | cons(sK9,nil) = sK7 ),
    inference(cnf_transformation,[],[f141]) ).

fof(f236,plain,
    spl11_2,
    inference(avatar_split_clause,[],[f206,f215]) ).

fof(f206,plain,
    neq(sK8,nil),
    inference(duplicate_literal_removal,[],[f197]) ).

fof(f197,plain,
    ( neq(sK8,nil)
    | neq(sK8,nil) ),
    inference(definition_unfolding,[],[f176,f186,f186]) ).

fof(f186,plain,
    sK6 = sK8,
    inference(cnf_transformation,[],[f141]) ).

fof(f176,plain,
    ( neq(sK6,nil)
    | neq(sK6,nil) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f235,plain,
    ( ~ spl11_3
    | ~ spl11_2 ),
    inference(avatar_split_clause,[],[f198,f215,f220]) ).

fof(f198,plain,
    ( ~ neq(sK8,nil)
    | ~ singletonP(sK7) ),
    inference(definition_unfolding,[],[f175,f188]) ).

fof(f188,plain,
    sK5 = sK7,
    inference(cnf_transformation,[],[f141]) ).

fof(f175,plain,
    ( ~ singletonP(sK5)
    | ~ neq(sK8,nil) ),
    inference(cnf_transformation,[],[f141]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC254+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 : n029.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 18:49:27 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (16149)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51  % (16160)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.19/0.51  % (16137)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51  % (16142)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.51  % (16136)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)
% 0.19/0.51  % (16137)First to succeed.
% 0.19/0.52  % (16155)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.52  % (16161)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.52  % (16137)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  % (16137)------------------------------
% 0.19/0.52  % (16137)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (16137)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (16137)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (16137)Memory used [KB]: 6140
% 0.19/0.52  % (16137)Time elapsed: 0.115 s
% 0.19/0.52  % (16137)Instructions burned: 5 (million)
% 0.19/0.52  % (16137)------------------------------
% 0.19/0.52  % (16137)------------------------------
% 0.19/0.52  % (16132)Success in time 0.171 s
%------------------------------------------------------------------------------