TSTP Solution File: SWC369+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC369+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 : n025.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 18:40:45 EDT 2022

% Result   : Theorem 0.52s 0.70s
% Output   : Refutation 0.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   46 (  10 unt;   0 def)
%            Number of atoms       :  230 (  73 equ)
%            Maximal formula atoms :   24 (   5 avg)
%            Number of connectives :  270 (  86   ~;  69   |;  93   &)
%                                         (   7 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   4 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   44 (  20   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f198,plain,
    $false,
    inference(avatar_sat_refutation,[],[f172,f174,f181,f197]) ).

fof(f197,plain,
    ( ~ spl6_3
    | ~ spl6_4 ),
    inference(avatar_contradiction_clause,[],[f196]) ).

fof(f196,plain,
    ( $false
    | ~ spl6_3
    | ~ spl6_4 ),
    inference(subsumption_resolution,[],[f189,f146]) ).

fof(f146,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f189,plain,
    ( ~ ssList(nil)
    | ~ spl6_3
    | ~ spl6_4 ),
    inference(resolution,[],[f185,f153]) ).

fof(f153,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f144]) ).

fof(f144,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f123]) ).

fof(f123,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

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

fof(f185,plain,
    ( ~ segmentP(nil,nil)
    | ~ spl6_3
    | ~ spl6_4 ),
    inference(backward_demodulation,[],[f184,f167]) ).

fof(f167,plain,
    ( nil = sK2
    | ~ spl6_3 ),
    inference(avatar_component_clause,[],[f165]) ).

fof(f165,plain,
    ( spl6_3
  <=> nil = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).

fof(f184,plain,
    ( ~ segmentP(nil,sK2)
    | ~ spl6_4 ),
    inference(backward_demodulation,[],[f149,f170]) ).

fof(f170,plain,
    ( nil = sK3
    | ~ spl6_4 ),
    inference(avatar_component_clause,[],[f169]) ).

fof(f169,plain,
    ( spl6_4
  <=> nil = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).

fof(f149,plain,
    ~ segmentP(sK3,sK2),
    inference(definition_unfolding,[],[f130,f129,f126]) ).

fof(f126,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ( ssList(sK0)
    & ( ~ neq(sK3,nil)
      | ( neq(sK2,nil)
        & segmentP(sK3,sK2) ) )
    & ~ segmentP(sK1,sK0)
    & sK1 = sK3
    & ssList(sK3)
    & ( nil != sK3
      | nil = sK2 )
    & sK0 = sK2
    & ssList(sK2)
    & ssList(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f104,f115,f114,f113,f112]) ).

fof(f112,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ neq(X3,nil)
                      | ( neq(X2,nil)
                        & segmentP(X3,X2) ) )
                    & ~ segmentP(X1,X0)
                    & X1 = X3
                    & ssList(X3)
                    & ( nil != X3
                      | nil = X2 )
                    & X0 = X2 )
                & ssList(X2) )
            & ssList(X1) ) )
   => ( ssList(sK0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ( neq(X2,nil)
                      & segmentP(X3,X2) ) )
                  & ~ segmentP(X1,sK0)
                  & X1 = X3
                  & ssList(X3)
                  & ( nil != X3
                    | nil = X2 )
                  & sK0 = X2 )
              & ssList(X2) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f113,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ neq(X3,nil)
                  | ( neq(X2,nil)
                    & segmentP(X3,X2) ) )
                & ~ segmentP(X1,sK0)
                & X1 = X3
                & ssList(X3)
                & ( nil != X3
                  | nil = X2 )
                & sK0 = X2 )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ neq(X3,nil)
                | ( neq(X2,nil)
                  & segmentP(X3,X2) ) )
              & ~ segmentP(sK1,sK0)
              & sK1 = X3
              & ssList(X3)
              & ( nil != X3
                | nil = X2 )
              & sK0 = X2 )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ neq(X3,nil)
              | ( neq(X2,nil)
                & segmentP(X3,X2) ) )
            & ~ segmentP(sK1,sK0)
            & sK1 = X3
            & ssList(X3)
            & ( nil != X3
              | nil = X2 )
            & sK0 = X2 )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ neq(X3,nil)
            | ( neq(sK2,nil)
              & segmentP(X3,sK2) ) )
          & ~ segmentP(sK1,sK0)
          & sK1 = X3
          & ssList(X3)
          & ( nil != X3
            | nil = sK2 )
          & sK0 = sK2 )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f115,plain,
    ( ? [X3] :
        ( ( ~ neq(X3,nil)
          | ( neq(sK2,nil)
            & segmentP(X3,sK2) ) )
        & ~ segmentP(sK1,sK0)
        & sK1 = X3
        & ssList(X3)
        & ( nil != X3
          | nil = sK2 )
        & sK0 = sK2 )
   => ( ( ~ neq(sK3,nil)
        | ( neq(sK2,nil)
          & segmentP(sK3,sK2) ) )
      & ~ segmentP(sK1,sK0)
      & sK1 = sK3
      & ssList(sK3)
      & ( nil != sK3
        | nil = sK2 )
      & sK0 = sK2 ) ),
    introduced(choice_axiom,[]) ).

fof(f104,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ neq(X3,nil)
                    | ( neq(X2,nil)
                      & segmentP(X3,X2) ) )
                  & ~ segmentP(X1,X0)
                  & X1 = X3
                  & ssList(X3)
                  & ( nil != X3
                    | nil = X2 )
                  & X0 = X2 )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(flattening,[],[f103]) ).

fof(f103,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & ( nil != X3
                    | nil = X2 )
                  & ~ segmentP(X1,X0)
                  & ( ~ neq(X3,nil)
                    | ( neq(X2,nil)
                      & segmentP(X3,X2) ) )
                  & X0 = X2
                  & 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 = X3
                        & nil != X2 )
                      | segmentP(X1,X0)
                      | ( ( ~ segmentP(X3,X2)
                          | ~ neq(X2,nil) )
                        & neq(X3,nil) )
                      | X0 != X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f129,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f116]) ).

fof(f130,plain,
    ~ segmentP(sK1,sK0),
    inference(cnf_transformation,[],[f116]) ).

fof(f181,plain,
    ( spl6_4
    | spl6_2 ),
    inference(avatar_split_clause,[],[f180,f160,f169]) ).

fof(f160,plain,
    ( spl6_2
  <=> neq(sK3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f180,plain,
    ( nil = sK3
    | spl6_2 ),
    inference(subsumption_resolution,[],[f176,f128]) ).

fof(f128,plain,
    ssList(sK3),
    inference(cnf_transformation,[],[f116]) ).

fof(f176,plain,
    ( ~ ssList(sK3)
    | nil = sK3
    | spl6_2 ),
    inference(subsumption_resolution,[],[f175,f146]) ).

fof(f175,plain,
    ( ~ ssList(nil)
    | nil = sK3
    | ~ ssList(sK3)
    | spl6_2 ),
    inference(resolution,[],[f162,f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X0)
      | X0 = X1
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) )
          | ~ ssList(X1) ) ),
    inference(nnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( X0 != X1
          <=> neq(X0,X1) )
          | ~ ssList(X1) ) ),
    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(f162,plain,
    ( ~ neq(sK3,nil)
    | spl6_2 ),
    inference(avatar_component_clause,[],[f160]) ).

fof(f174,plain,
    ~ spl6_2,
    inference(avatar_split_clause,[],[f173,f160]) ).

fof(f173,plain,
    ~ neq(sK3,nil),
    inference(subsumption_resolution,[],[f131,f149]) ).

fof(f131,plain,
    ( segmentP(sK3,sK2)
    | ~ neq(sK3,nil) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f172,plain,
    ( spl6_3
    | ~ spl6_4 ),
    inference(avatar_split_clause,[],[f127,f169,f165]) ).

fof(f127,plain,
    ( nil != sK3
    | nil = sK2 ),
    inference(cnf_transformation,[],[f116]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SWC369+1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.36  % Computer : n025.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Aug 30 18:59:15 EDT 2022
% 0.14/0.36  % CPUTime    : 
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% 0.38/0.67  % (19532)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.38/0.67  % (19532)Instruction limit reached!
% 0.38/0.67  % (19532)------------------------------
% 0.38/0.67  % (19532)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.38/0.67  % (19532)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.38/0.67  % (19532)Termination reason: Unknown
% 0.38/0.67  % (19532)Termination phase: Preprocessing 3
% 0.38/0.67  
% 0.38/0.67  % (19532)Memory used [KB]: 1663
% 0.38/0.67  % (19532)Time elapsed: 0.003 s
% 0.38/0.67  % (19532)Instructions burned: 4 (million)
% 0.38/0.67  % (19532)------------------------------
% 0.38/0.67  % (19532)------------------------------
% 0.38/0.68  % (19547)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.38/0.68  % (19552)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 (2998ds/82Mi)
% 0.38/0.69  % (19545)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/7Mi)
% 0.38/0.69  % (19544)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.38/0.69  % (19555)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 (2998ds/95Mi)
% 0.38/0.69  % (19544)Instruction limit reached!
% 0.38/0.69  % (19544)------------------------------
% 0.38/0.69  % (19544)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.38/0.69  % (19544)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.38/0.69  % (19544)Termination reason: Unknown
% 0.38/0.69  % (19544)Termination phase: Preprocessing 3
% 0.38/0.69  
% 0.38/0.69  % (19544)Memory used [KB]: 1535
% 0.38/0.69  % (19544)Time elapsed: 0.005 s
% 0.38/0.69  % (19544)Instructions burned: 3 (million)
% 0.38/0.69  % (19544)------------------------------
% 0.38/0.69  % (19544)------------------------------
% 0.38/0.69  % (19537)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 (2998ds/39Mi)
% 0.38/0.69  % (19536)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/39Mi)
% 0.38/0.69  % (19531)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 (2998ds/13Mi)
% 0.38/0.69  % (19539)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 (2998ds/33Mi)
% 0.38/0.69  % (19550)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.38/0.69  % (19531)First to succeed.
% 0.52/0.70  % (19531)Refutation found. Thanks to Tanya!
% 0.52/0.70  % SZS status Theorem for theBenchmark
% 0.52/0.70  % SZS output start Proof for theBenchmark
% See solution above
% 0.52/0.70  % (19531)------------------------------
% 0.52/0.70  % (19531)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.52/0.70  % (19531)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.52/0.70  % (19531)Termination reason: Refutation
% 0.52/0.70  
% 0.52/0.70  % (19531)Memory used [KB]: 6012
% 0.52/0.70  % (19531)Time elapsed: 0.106 s
% 0.52/0.70  % (19531)Instructions burned: 3 (million)
% 0.52/0.70  % (19531)------------------------------
% 0.52/0.70  % (19531)------------------------------
% 0.52/0.70  % (19396)Success in time 0.328 s
%------------------------------------------------------------------------------