TSTP Solution File: SWC408+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC408+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 : n009.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 18:43:41 EDT 2022

% Result   : Theorem 1.44s 0.55s
% Output   : Refutation 1.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   34 (  15 unt;   0 def)
%            Number of atoms       :  185 (  47 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  200 (  49   ~;  36   |;  95   &)
%                                         (   2 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   63 (  28   !;  35   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1368,plain,
    $false,
    inference(subsumption_resolution,[],[f1367,f543]) ).

fof(f543,plain,
    ~ memberP(sK53,sK57),
    inference(cnf_transformation,[],[f346]) ).

fof(f346,plain,
    ( ssList(sK55)
    & memberP(sK54,sK57)
    & ~ memberP(sK53,sK57)
    & ssItem(sK57)
    & ssList(sK56)
    & sK55 = app(sK56,sK56)
    & sK54 = sK56
    & sK55 = sK53
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f173,f345,f344,f343,f342,f341]) ).

fof(f341,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( ? [X4] :
                        ( memberP(X1,X4)
                        & ~ memberP(X0,X4)
                        & ssItem(X4) )
                    & ssList(X3)
                    & app(X3,X3) = X2
                    & X1 = X3
                    & X0 = X2 ) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ? [X4] :
                      ( memberP(X1,X4)
                      & ~ memberP(sK53,X4)
                      & ssItem(X4) )
                  & ssList(X3)
                  & app(X3,X3) = X2
                  & X1 = X3
                  & sK53 = X2 ) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f342,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ? [X4] :
                    ( memberP(X1,X4)
                    & ~ memberP(sK53,X4)
                    & ssItem(X4) )
                & ssList(X3)
                & app(X3,X3) = X2
                & X1 = X3
                & sK53 = X2 ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ? [X4] :
                  ( memberP(sK54,X4)
                  & ~ memberP(sK53,X4)
                  & ssItem(X4) )
              & ssList(X3)
              & app(X3,X3) = X2
              & sK54 = X3
              & sK53 = X2 ) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f343,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( ? [X4] :
                ( memberP(sK54,X4)
                & ~ memberP(sK53,X4)
                & ssItem(X4) )
            & ssList(X3)
            & app(X3,X3) = X2
            & sK54 = X3
            & sK53 = X2 ) )
   => ( ssList(sK55)
      & ? [X3] :
          ( ? [X4] :
              ( memberP(sK54,X4)
              & ~ memberP(sK53,X4)
              & ssItem(X4) )
          & ssList(X3)
          & app(X3,X3) = sK55
          & sK54 = X3
          & sK55 = sK53 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( memberP(sK54,X4)
            & ~ memberP(sK53,X4)
            & ssItem(X4) )
        & ssList(X3)
        & app(X3,X3) = sK55
        & sK54 = X3
        & sK55 = sK53 )
   => ( ? [X4] :
          ( memberP(sK54,X4)
          & ~ memberP(sK53,X4)
          & ssItem(X4) )
      & ssList(sK56)
      & sK55 = app(sK56,sK56)
      & sK54 = sK56
      & sK55 = sK53 ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X4] :
        ( memberP(sK54,X4)
        & ~ memberP(sK53,X4)
        & ssItem(X4) )
   => ( memberP(sK54,sK57)
      & ~ memberP(sK53,sK57)
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f173,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ? [X4] :
                      ( memberP(X1,X4)
                      & ~ memberP(X0,X4)
                      & ssItem(X4) )
                  & ssList(X3)
                  & app(X3,X3) = X2
                  & X1 = X3
                  & X0 = X2 ) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f172]) ).

fof(f172,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & X0 = X2
                  & app(X3,X3) = X2
                  & ? [X4] :
                      ( ~ memberP(X0,X4)
                      & memberP(X1,X4)
                      & ssItem(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)
                   => ( X1 != X3
                      | X0 != X2
                      | app(X3,X3) != X2
                      | ! [X4] :
                          ( ssItem(X4)
                         => ( memberP(X0,X4)
                            | ~ memberP(X1,X4) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f1367,plain,
    memberP(sK53,sK57),
    inference(subsumption_resolution,[],[f1364,f597]) ).

fof(f597,plain,
    ssList(sK54),
    inference(backward_demodulation,[],[f541,f539]) ).

fof(f539,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f346]) ).

fof(f541,plain,
    ssList(sK56),
    inference(cnf_transformation,[],[f346]) ).

fof(f1364,plain,
    ( ~ ssList(sK54)
    | memberP(sK53,sK57) ),
    inference(superposition,[],[f1346,f598]) ).

fof(f598,plain,
    sK53 = app(sK54,sK54),
    inference(backward_demodulation,[],[f595,f539]) ).

fof(f595,plain,
    sK53 = app(sK56,sK56),
    inference(backward_demodulation,[],[f594,f538]) ).

fof(f538,plain,
    sK55 = sK53,
    inference(cnf_transformation,[],[f346]) ).

fof(f594,plain,
    sK55 = app(sK56,sK56),
    inference(forward_demodulation,[],[f585,f586]) ).

fof(f586,plain,
    sK55 = sF58,
    inference(definition_folding,[],[f540,f585]) ).

fof(f540,plain,
    sK55 = app(sK56,sK56),
    inference(cnf_transformation,[],[f346]) ).

fof(f585,plain,
    sF58 = app(sK56,sK56),
    introduced(function_definition,[]) ).

fof(f1346,plain,
    ! [X0] :
      ( memberP(app(X0,sK54),sK57)
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f1345,f542]) ).

fof(f542,plain,
    ssItem(sK57),
    inference(cnf_transformation,[],[f346]) ).

fof(f1345,plain,
    ! [X0] :
      ( memberP(app(X0,sK54),sK57)
      | ~ ssList(X0)
      | ~ ssItem(sK57) ),
    inference(subsumption_resolution,[],[f1340,f597]) ).

fof(f1340,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ ssList(sK54)
      | memberP(app(X0,sK54),sK57)
      | ~ ssItem(sK57) ),
    inference(resolution,[],[f533,f544]) ).

fof(f544,plain,
    memberP(sK54,sK57),
    inference(cnf_transformation,[],[f346]) ).

fof(f533,plain,
    ! [X2,X0,X1] :
      ( ~ memberP(X2,X0)
      | ~ ssItem(X0)
      | memberP(app(X1,X2),X0)
      | ~ ssList(X2)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f340]) ).

fof(f340,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ! [X2] :
              ( ( ( memberP(X1,X0)
                  | memberP(X2,X0)
                  | ~ memberP(app(X1,X2),X0) )
                & ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X1,X0)
                    & ~ memberP(X2,X0) ) ) )
              | ~ ssList(X2) ) ) ),
    inference(flattening,[],[f339]) ).

fof(f339,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ! [X2] :
              ( ( ( memberP(X1,X0)
                  | memberP(X2,X0)
                  | ~ memberP(app(X1,X2),X0) )
                & ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X1,X0)
                    & ~ memberP(X2,X0) ) ) )
              | ~ ssList(X2) ) ) ),
    inference(nnf_transformation,[],[f174]) ).

fof(f174,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ! [X2] :
              ( ( ( memberP(X1,X0)
                  | memberP(X2,X0) )
              <=> memberP(app(X1,X2),X0) )
              | ~ ssList(X2) ) ) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( ( memberP(X1,X0)
                  | memberP(X2,X0) )
              <=> memberP(app(X1,X2),X0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC408+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n009.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 18:51:35 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.46  % (32722)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)
% 0.20/0.46  % (32707)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.47  % (32714)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)
% 0.20/0.47  % (32715)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)
% 0.20/0.48  % (32706)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)
% 0.20/0.49  % (32707)Instruction limit reached!
% 0.20/0.49  % (32707)------------------------------
% 0.20/0.49  % (32707)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (32707)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (32707)Termination reason: Unknown
% 0.20/0.49  % (32707)Termination phase: Property scanning
% 0.20/0.49  
% 0.20/0.49  % (32707)Memory used [KB]: 1279
% 0.20/0.49  % (32707)Time elapsed: 0.006 s
% 0.20/0.49  % (32707)Instructions burned: 7 (million)
% 0.20/0.49  % (32707)------------------------------
% 0.20/0.49  % (32707)------------------------------
% 0.20/0.50  % (32723)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)
% 0.20/0.51  % (32712)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.51  % (32710)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52  % (32708)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52  % (32708)Instruction limit reached!
% 0.20/0.52  % (32708)------------------------------
% 0.20/0.52  % (32708)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (32708)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (32708)Termination reason: Unknown
% 0.20/0.52  % (32708)Termination phase: Preprocessing 2
% 0.20/0.52  
% 0.20/0.52  % (32708)Memory used [KB]: 1023
% 0.20/0.52  % (32708)Time elapsed: 0.002 s
% 0.20/0.52  % (32708)Instructions burned: 2 (million)
% 0.20/0.52  % (32708)------------------------------
% 0.20/0.52  % (32708)------------------------------
% 0.20/0.53  % (32702)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)
% 0.20/0.53  % (32704)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (32701)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)
% 0.20/0.53  % (32703)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)
% 0.20/0.53  % (32705)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)
% 0.20/0.53  % (32709)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (32711)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53  % (32713)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53  % (32726)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)
% 0.20/0.54  TRYING [1]
% 1.44/0.54  TRYING [2]
% 1.44/0.54  % (32728)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.44/0.54  % (32715)First to succeed.
% 1.44/0.54  % (32717)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.44/0.54  % (32727)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)
% 1.44/0.54  % (32729)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.44/0.54  % (32718)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.44/0.55  % (32700)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)
% 1.44/0.55  % (32715)Refutation found. Thanks to Tanya!
% 1.44/0.55  % SZS status Theorem for theBenchmark
% 1.44/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 1.44/0.55  % (32715)------------------------------
% 1.44/0.55  % (32715)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.44/0.55  % (32715)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.44/0.55  % (32715)Termination reason: Refutation
% 1.44/0.55  
% 1.44/0.55  % (32715)Memory used [KB]: 2174
% 1.44/0.55  % (32715)Time elapsed: 0.132 s
% 1.44/0.55  % (32715)Instructions burned: 59 (million)
% 1.44/0.55  % (32715)------------------------------
% 1.44/0.55  % (32715)------------------------------
% 1.44/0.55  % (32699)Success in time 0.195 s
%------------------------------------------------------------------------------