TSTP Solution File: SWC206+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC206+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_sat --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 18:42:23 EDT 2022

% Result   : Theorem 1.43s 0.53s
% Output   : Refutation 1.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   56 (  21 unt;   3 typ;   0 def)
%            Number of atoms       :  276 (  71 equ)
%            Maximal formula atoms :   30 (   5 avg)
%            Number of connectives :  307 (  84   ~;  69   |; 132   &)
%                                         (   4 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   60 (  25   !;  35   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_27,type,
    sQ59_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_28,type,
    sQ60_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_29,type,
    sQ61_eqProxy: ( $real * $real ) > $o ).

fof(f1208,plain,
    $false,
    inference(subsumption_resolution,[],[f1201,f1177]) ).

fof(f1177,plain,
    ~ neq(nil,nil),
    inference(backward_demodulation,[],[f617,f1176]) ).

fof(f1176,plain,
    nil = sK53,
    inference(subsumption_resolution,[],[f1175,f726]) ).

fof(f726,plain,
    ssList(nil),
    inference(literal_reordering,[],[f478]) ).

fof(f478,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f1175,plain,
    ( nil = sK53
    | ~ ssList(nil) ),
    inference(subsumption_resolution,[],[f1170,f653]) ).

fof(f653,plain,
    ssList(sK53),
    inference(literal_reordering,[],[f567]) ).

fof(f567,plain,
    ssList(sK53),
    inference(definition_unfolding,[],[f549,f558]) ).

fof(f558,plain,
    sK55 = sK53,
    inference(cnf_transformation,[],[f348]) ).

fof(f348,plain,
    ( ( nil = sK55
      | nil != sK56 )
    & sK55 = sK53
    & sK56 = sK54
    & neq(sK54,nil)
    & ~ neq(sK53,nil)
    & ssList(sK56)
    & ( ~ neq(sK56,nil)
      | ( ssList(sK57)
        & segmentP(sK55,sK57)
        & segmentP(sK56,sK57)
        & neq(sK57,nil) ) )
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f168,f347,f346,f345,f344,f343]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( nil = X2
                      | nil != X3 )
                    & X0 = X2
                    & X1 = X3
                    & neq(X1,nil)
                    & ~ neq(X0,nil)
                    & ssList(X3)
                    & ( ~ neq(X3,nil)
                      | ? [X4] :
                          ( ssList(X4)
                          & segmentP(X2,X4)
                          & segmentP(X3,X4)
                          & neq(X4,nil) ) ) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil = X2
                    | nil != X3 )
                  & sK53 = X2
                  & X1 = X3
                  & neq(X1,nil)
                  & ~ neq(sK53,nil)
                  & ssList(X3)
                  & ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ssList(X4)
                        & segmentP(X2,X4)
                        & segmentP(X3,X4)
                        & neq(X4,nil) ) ) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( nil = X2
                  | nil != X3 )
                & sK53 = X2
                & X1 = X3
                & neq(X1,nil)
                & ~ neq(sK53,nil)
                & ssList(X3)
                & ( ~ neq(X3,nil)
                  | ? [X4] :
                      ( ssList(X4)
                      & segmentP(X2,X4)
                      & segmentP(X3,X4)
                      & neq(X4,nil) ) ) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil = X2
                | nil != X3 )
              & sK53 = X2
              & sK54 = X3
              & neq(sK54,nil)
              & ~ neq(sK53,nil)
              & ssList(X3)
              & ( ~ neq(X3,nil)
                | ? [X4] :
                    ( ssList(X4)
                    & segmentP(X2,X4)
                    & segmentP(X3,X4)
                    & neq(X4,nil) ) ) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( nil = X2
              | nil != X3 )
            & sK53 = X2
            & sK54 = X3
            & neq(sK54,nil)
            & ~ neq(sK53,nil)
            & ssList(X3)
            & ( ~ neq(X3,nil)
              | ? [X4] :
                  ( ssList(X4)
                  & segmentP(X2,X4)
                  & segmentP(X3,X4)
                  & neq(X4,nil) ) ) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( nil = sK55
            | nil != X3 )
          & sK55 = sK53
          & sK54 = X3
          & neq(sK54,nil)
          & ~ neq(sK53,nil)
          & ssList(X3)
          & ( ~ neq(X3,nil)
            | ? [X4] :
                ( ssList(X4)
                & segmentP(sK55,X4)
                & segmentP(X3,X4)
                & neq(X4,nil) ) ) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( nil = sK55
          | nil != X3 )
        & sK55 = sK53
        & sK54 = X3
        & neq(sK54,nil)
        & ~ neq(sK53,nil)
        & ssList(X3)
        & ( ~ neq(X3,nil)
          | ? [X4] :
              ( ssList(X4)
              & segmentP(sK55,X4)
              & segmentP(X3,X4)
              & neq(X4,nil) ) ) )
   => ( ( nil = sK55
        | nil != sK56 )
      & sK55 = sK53
      & sK56 = sK54
      & neq(sK54,nil)
      & ~ neq(sK53,nil)
      & ssList(sK56)
      & ( ~ neq(sK56,nil)
        | ? [X4] :
            ( ssList(X4)
            & segmentP(sK55,X4)
            & segmentP(sK56,X4)
            & neq(X4,nil) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X4] :
        ( ssList(X4)
        & segmentP(sK55,X4)
        & segmentP(sK56,X4)
        & neq(X4,nil) )
   => ( ssList(sK57)
      & segmentP(sK55,sK57)
      & segmentP(sK56,sK57)
      & neq(sK57,nil) ) ),
    introduced(choice_axiom,[]) ).

fof(f168,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil = X2
                    | nil != X3 )
                  & X0 = X2
                  & X1 = X3
                  & neq(X1,nil)
                  & ~ neq(X0,nil)
                  & ssList(X3)
                  & ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( ssList(X4)
                        & segmentP(X2,X4)
                        & segmentP(X3,X4)
                        & neq(X4,nil) ) ) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f167]) ).

fof(f167,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ neq(X0,nil)
                  & X0 = X2
                  & neq(X1,nil)
                  & ( ~ neq(X3,nil)
                    | ? [X4] :
                        ( segmentP(X2,X4)
                        & segmentP(X3,X4)
                        & neq(X4,nil)
                        & ssList(X4) ) )
                  & X1 = X3
                  & ( nil = X2
                    | nil != 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(X0,nil)
                      | X0 != X2
                      | ~ neq(X1,nil)
                      | ( neq(X3,nil)
                        & ! [X4] :
                            ( ssList(X4)
                           => ( ~ segmentP(X2,X4)
                              | ~ segmentP(X3,X4)
                              | ~ neq(X4,nil) ) ) )
                      | X1 != X3
                      | ( nil != X2
                        & nil = X3 ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f549,plain,
    ssList(sK55),
    inference(cnf_transformation,[],[f348]) ).

fof(f1170,plain,
    ( ~ ssList(sK53)
    | nil = sK53
    | ~ ssList(nil) ),
    inference(resolution,[],[f606,f617]) ).

fof(f606,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | X0 = X1 ),
    inference(literal_reordering,[],[f414]) ).

fof(f414,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | neq(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f263]) ).

fof(f263,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) ) ) ),
    inference(nnf_transformation,[],[f196]) ).

fof(f196,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ( X0 != X1
          <=> neq(X0,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(f617,plain,
    ~ neq(sK53,nil),
    inference(literal_reordering,[],[f555]) ).

fof(f555,plain,
    ~ neq(sK53,nil),
    inference(cnf_transformation,[],[f348]) ).

fof(f1201,plain,
    neq(nil,nil),
    inference(backward_demodulation,[],[f985,f1198]) ).

fof(f1198,plain,
    nil = sK57,
    inference(subsumption_resolution,[],[f1197,f981]) ).

fof(f981,plain,
    ssList(sK57),
    inference(subsumption_resolution,[],[f793,f723]) ).

fof(f723,plain,
    neq(sK54,nil),
    inference(literal_reordering,[],[f556]) ).

fof(f556,plain,
    neq(sK54,nil),
    inference(cnf_transformation,[],[f348]) ).

fof(f793,plain,
    ( ~ neq(sK54,nil)
    | ssList(sK57) ),
    inference(literal_reordering,[],[f563]) ).

fof(f563,plain,
    ( ssList(sK57)
    | ~ neq(sK54,nil) ),
    inference(definition_unfolding,[],[f553,f557]) ).

fof(f557,plain,
    sK56 = sK54,
    inference(cnf_transformation,[],[f348]) ).

fof(f553,plain,
    ( ~ neq(sK56,nil)
    | ssList(sK57) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f1197,plain,
    ( nil = sK57
    | ~ ssList(sK57) ),
    inference(resolution,[],[f1179,f765]) ).

fof(f765,plain,
    ! [X0] :
      ( ~ segmentP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(literal_reordering,[],[f356]) ).

fof(f356,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ~ segmentP(nil,X0) ),
    inference(cnf_transformation,[],[f234]) ).

fof(f234,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f164]) ).

fof(f164,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(f1179,plain,
    segmentP(nil,sK57),
    inference(backward_demodulation,[],[f984,f1176]) ).

fof(f984,plain,
    segmentP(sK53,sK57),
    inference(subsumption_resolution,[],[f737,f723]) ).

fof(f737,plain,
    ( ~ neq(sK54,nil)
    | segmentP(sK53,sK57) ),
    inference(literal_reordering,[],[f564]) ).

fof(f564,plain,
    ( segmentP(sK53,sK57)
    | ~ neq(sK54,nil) ),
    inference(definition_unfolding,[],[f552,f557,f558]) ).

fof(f552,plain,
    ( ~ neq(sK56,nil)
    | segmentP(sK55,sK57) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f985,plain,
    neq(sK57,nil),
    inference(subsumption_resolution,[],[f796,f723]) ).

fof(f796,plain,
    ( neq(sK57,nil)
    | ~ neq(sK54,nil) ),
    inference(literal_reordering,[],[f566]) ).

fof(f566,plain,
    ( neq(sK57,nil)
    | ~ neq(sK54,nil) ),
    inference(definition_unfolding,[],[f550,f557]) ).

fof(f550,plain,
    ( ~ neq(sK56,nil)
    | neq(sK57,nil) ),
    inference(cnf_transformation,[],[f348]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC206+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33  % Computer : n025.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 18:43:30 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.19/0.49  % (19249)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.49  % (19241)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.49  % (19242)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.49  % (19233)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (19239)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.50  % (19229)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.29/0.51  % (19234)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.29/0.51  % (19234)Instruction limit reached!
% 1.29/0.51  % (19234)------------------------------
% 1.29/0.51  % (19234)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.29/0.51  % (19234)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.29/0.51  % (19234)Termination reason: Unknown
% 1.29/0.51  % (19234)Termination phase: Property scanning
% 1.29/0.51  
% 1.29/0.51  % (19234)Memory used [KB]: 1279
% 1.29/0.51  % (19234)Time elapsed: 0.006 s
% 1.29/0.51  % (19234)Instructions burned: 7 (million)
% 1.29/0.51  % (19234)------------------------------
% 1.29/0.51  % (19234)------------------------------
% 1.29/0.51  % (19250)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.29/0.52  TRYING [1]
% 1.29/0.52  % (19230)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.29/0.52  TRYING [2]
% 1.29/0.52  % (19231)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.29/0.52  % (19253)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.29/0.52  % (19252)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.29/0.52  % (19232)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.29/0.52  % (19228)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.29/0.52  % (19227)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.29/0.52  % (19240)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.29/0.53  % (19241)First to succeed.
% 1.43/0.53  % (19254)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.43/0.53  % (19249)Also succeeded, but the first one will report.
% 1.43/0.53  % (19241)Refutation found. Thanks to Tanya!
% 1.43/0.53  % SZS status Theorem for theBenchmark
% 1.43/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.43/0.53  % (19241)------------------------------
% 1.43/0.53  % (19241)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.43/0.53  % (19241)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.43/0.53  % (19241)Termination reason: Refutation
% 1.43/0.53  
% 1.43/0.53  % (19241)Memory used [KB]: 6652
% 1.43/0.53  % (19241)Time elapsed: 0.028 s
% 1.43/0.53  % (19241)Instructions burned: 28 (million)
% 1.43/0.53  % (19241)------------------------------
% 1.43/0.53  % (19241)------------------------------
% 1.43/0.53  % (19226)Success in time 0.189 s
%------------------------------------------------------------------------------