TSTP Solution File: SWC105+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC105+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 : n004.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 18:41:46 EDT 2022

% Result   : Theorem 0.23s 0.57s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   42 (   9 unt;   0 def)
%            Number of atoms       :  259 ( 107 equ)
%            Maximal formula atoms :   30 (   6 avg)
%            Number of connectives :  301 (  84   ~;  81   |; 117   &)
%                                         (   4 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   46 (  22   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f676,plain,
    $false,
    inference(subsumption_resolution,[],[f675,f496]) ).

fof(f496,plain,
    ssList(sK41),
    inference(cnf_transformation,[],[f317]) ).

fof(f317,plain,
    ( ssList(sK41)
    & ( ( nil = sK42
        & nil != sK41 )
      | ( neq(sK42,nil)
        & ( ~ neq(sK41,nil)
          | ~ rearsegP(sK42,sK41) ) ) )
    & sK43 = sK41
    & ( ( neq(sK43,nil)
        & rearsegP(sK44,sK43) )
      | ( nil = sK43
        & nil = sK44 ) )
    & ssList(sK44)
    & sK44 = sK42
    & ssList(sK43)
    & ssList(sK42) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43,sK44])],[f139,f316,f315,f314,f313]) ).

fof(f313,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X1
                        & nil != X0 )
                      | ( neq(X1,nil)
                        & ( ~ neq(X0,nil)
                          | ~ rearsegP(X1,X0) ) ) )
                    & X0 = X2
                    & ( ( neq(X2,nil)
                        & rearsegP(X3,X2) )
                      | ( nil = X2
                        & nil = X3 ) )
                    & ssList(X3)
                    & X1 = X3 )
                & ssList(X2) )
            & ssList(X1) ) )
   => ( ssList(sK41)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X1
                      & nil != sK41 )
                    | ( neq(X1,nil)
                      & ( ~ neq(sK41,nil)
                        | ~ rearsegP(X1,sK41) ) ) )
                  & sK41 = X2
                  & ( ( neq(X2,nil)
                      & rearsegP(X3,X2) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ssList(X3)
                  & X1 = X3 )
              & ssList(X2) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f314,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X1
                    & nil != sK41 )
                  | ( neq(X1,nil)
                    & ( ~ neq(sK41,nil)
                      | ~ rearsegP(X1,sK41) ) ) )
                & sK41 = X2
                & ( ( neq(X2,nil)
                    & rearsegP(X3,X2) )
                  | ( nil = X2
                    & nil = X3 ) )
                & ssList(X3)
                & X1 = X3 )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil = sK42
                  & nil != sK41 )
                | ( neq(sK42,nil)
                  & ( ~ neq(sK41,nil)
                    | ~ rearsegP(sK42,sK41) ) ) )
              & sK41 = X2
              & ( ( neq(X2,nil)
                  & rearsegP(X3,X2) )
                | ( nil = X2
                  & nil = X3 ) )
              & ssList(X3)
              & sK42 = X3 )
          & ssList(X2) )
      & ssList(sK42) ) ),
    introduced(choice_axiom,[]) ).

fof(f315,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = sK42
                & nil != sK41 )
              | ( neq(sK42,nil)
                & ( ~ neq(sK41,nil)
                  | ~ rearsegP(sK42,sK41) ) ) )
            & sK41 = X2
            & ( ( neq(X2,nil)
                & rearsegP(X3,X2) )
              | ( nil = X2
                & nil = X3 ) )
            & ssList(X3)
            & sK42 = X3 )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK42
              & nil != sK41 )
            | ( neq(sK42,nil)
              & ( ~ neq(sK41,nil)
                | ~ rearsegP(sK42,sK41) ) ) )
          & sK43 = sK41
          & ( ( neq(sK43,nil)
              & rearsegP(X3,sK43) )
            | ( nil = sK43
              & nil = X3 ) )
          & ssList(X3)
          & sK42 = X3 )
      & ssList(sK43) ) ),
    introduced(choice_axiom,[]) ).

fof(f316,plain,
    ( ? [X3] :
        ( ( ( nil = sK42
            & nil != sK41 )
          | ( neq(sK42,nil)
            & ( ~ neq(sK41,nil)
              | ~ rearsegP(sK42,sK41) ) ) )
        & sK43 = sK41
        & ( ( neq(sK43,nil)
            & rearsegP(X3,sK43) )
          | ( nil = sK43
            & nil = X3 ) )
        & ssList(X3)
        & sK42 = X3 )
   => ( ( ( nil = sK42
          & nil != sK41 )
        | ( neq(sK42,nil)
          & ( ~ neq(sK41,nil)
            | ~ rearsegP(sK42,sK41) ) ) )
      & sK43 = sK41
      & ( ( neq(sK43,nil)
          & rearsegP(sK44,sK43) )
        | ( nil = sK43
          & nil = sK44 ) )
      & ssList(sK44)
      & sK44 = sK42 ) ),
    introduced(choice_axiom,[]) ).

fof(f139,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X1
                      & nil != X0 )
                    | ( neq(X1,nil)
                      & ( ~ neq(X0,nil)
                        | ~ rearsegP(X1,X0) ) ) )
                  & X0 = X2
                  & ( ( neq(X2,nil)
                      & rearsegP(X3,X2) )
                    | ( nil = X2
                      & nil = X3 ) )
                  & ssList(X3)
                  & X1 = X3 )
              & ssList(X2) )
          & ssList(X1) ) ),
    inference(flattening,[],[f138]) ).

fof(f138,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & ( ( nil = X1
                      & nil != X0 )
                    | ( neq(X1,nil)
                      & ( ~ neq(X0,nil)
                        | ~ rearsegP(X1,X0) ) ) )
                  & X0 = X2
                  & ( ( neq(X2,nil)
                      & rearsegP(X3,X2) )
                    | ( 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)
                   => ( X1 != X3
                      | ( ( nil = X0
                          | nil != X1 )
                        & ( ~ neq(X1,nil)
                          | ( neq(X0,nil)
                            & rearsegP(X1,X0) ) ) )
                      | X0 != X2
                      | ( ( ~ rearsegP(X3,X2)
                          | ~ neq(X2,nil) )
                        & ( nil != X3
                          | nil != X2 ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f675,plain,
    ~ ssList(sK41),
    inference(subsumption_resolution,[],[f672,f621]) ).

fof(f621,plain,
    nil != sK41,
    inference(subsumption_resolution,[],[f620,f612]) ).

fof(f612,plain,
    ssList(nil),
    inference(backward_demodulation,[],[f483,f611]) ).

fof(f611,plain,
    nil = sK42,
    inference(subsumption_resolution,[],[f610,f564]) ).

fof(f564,plain,
    ( rearsegP(sK42,sK41)
    | nil = sK42 ),
    inference(definition_unfolding,[],[f487,f485,f491,f485]) ).

fof(f491,plain,
    sK43 = sK41,
    inference(cnf_transformation,[],[f317]) ).

fof(f485,plain,
    sK44 = sK42,
    inference(cnf_transformation,[],[f317]) ).

fof(f487,plain,
    ( rearsegP(sK44,sK43)
    | nil = sK44 ),
    inference(cnf_transformation,[],[f317]) ).

fof(f610,plain,
    ( nil = sK42
    | ~ rearsegP(sK42,sK41) ),
    inference(subsumption_resolution,[],[f494,f562]) ).

fof(f562,plain,
    ( neq(sK41,nil)
    | nil = sK42 ),
    inference(definition_unfolding,[],[f489,f491,f485]) ).

fof(f489,plain,
    ( neq(sK43,nil)
    | nil = sK44 ),
    inference(cnf_transformation,[],[f317]) ).

fof(f494,plain,
    ( nil = sK42
    | ~ rearsegP(sK42,sK41)
    | ~ neq(sK41,nil) ),
    inference(cnf_transformation,[],[f317]) ).

fof(f483,plain,
    ssList(sK42),
    inference(cnf_transformation,[],[f317]) ).

fof(f620,plain,
    ( ~ ssList(nil)
    | nil != sK41 ),
    inference(resolution,[],[f599,f614]) ).

fof(f614,plain,
    ( neq(nil,nil)
    | nil != sK41 ),
    inference(backward_demodulation,[],[f493,f611]) ).

fof(f493,plain,
    ( neq(sK42,nil)
    | nil != sK41 ),
    inference(cnf_transformation,[],[f317]) ).

fof(f599,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f573]) ).

fof(f573,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f401]) ).

fof(f401,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f255]) ).

fof(f255,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f185]) ).

fof(f185,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( X0 != X1
          <=> neq(X0,X1) )
          | ~ ssList(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(f672,plain,
    ( nil = sK41
    | ~ ssList(sK41) ),
    inference(duplicate_literal_removal,[],[f669]) ).

fof(f669,plain,
    ( nil = sK41
    | nil = sK41
    | ~ ssList(sK41) ),
    inference(resolution,[],[f441,f616]) ).

fof(f616,plain,
    ( rearsegP(nil,sK41)
    | nil = sK41 ),
    inference(backward_demodulation,[],[f563,f611]) ).

fof(f563,plain,
    ( rearsegP(sK42,sK41)
    | nil = sK41 ),
    inference(definition_unfolding,[],[f488,f485,f491,f491]) ).

fof(f488,plain,
    ( rearsegP(sK44,sK43)
    | nil = sK43 ),
    inference(cnf_transformation,[],[f317]) ).

fof(f441,plain,
    ! [X0] :
      ( ~ rearsegP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f282]) ).

fof(f282,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( ( nil = X0
          | ~ rearsegP(nil,X0) )
        & ( rearsegP(nil,X0)
          | nil != X0 ) ) ),
    inference(nnf_transformation,[],[f141]) ).

fof(f141,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ( nil = X0
      <=> rearsegP(nil,X0) ) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil = X0
      <=> rearsegP(nil,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14  % Problem    : SWC105+1 : TPTP v8.1.0. Released v2.4.0.
% 0.09/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.37  % Computer : n004.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38  % CPULimit   : 300
% 0.15/0.38  % WCLimit    : 300
% 0.15/0.38  % DateTime   : Tue Aug 30 18:15:19 EDT 2022
% 0.15/0.38  % CPUTime    : 
% 0.23/0.54  % (12603)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)
% 0.23/0.54  % (12595)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)
% 0.23/0.55  % (12587)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)
% 0.23/0.55  % (12589)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.23/0.55  % (12589)Instruction limit reached!
% 0.23/0.55  % (12589)------------------------------
% 0.23/0.55  % (12589)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.23/0.55  % (12589)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.23/0.55  % (12589)Termination reason: Unknown
% 0.23/0.55  % (12589)Termination phase: Preprocessing 2
% 0.23/0.55  
% 0.23/0.55  % (12589)Memory used [KB]: 1023
% 0.23/0.55  % (12589)Time elapsed: 0.002 s
% 0.23/0.55  % (12589)Instructions burned: 2 (million)
% 0.23/0.55  % (12589)------------------------------
% 0.23/0.55  % (12589)------------------------------
% 0.23/0.55  % (12588)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.23/0.55  % (12581)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)
% 0.23/0.55  % (12588)Instruction limit reached!
% 0.23/0.55  % (12588)------------------------------
% 0.23/0.55  % (12588)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.23/0.56  % (12609)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.23/0.56  % (12591)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.23/0.56  % (12586)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)
% 0.23/0.56  % (12610)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)
% 0.23/0.56  % (12588)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.23/0.56  % (12588)Termination reason: Unknown
% 0.23/0.56  % (12588)Termination phase: Property scanning
% 0.23/0.56  
% 0.23/0.56  % (12588)Memory used [KB]: 1279
% 0.23/0.56  % (12588)Time elapsed: 0.005 s
% 0.23/0.56  % (12588)Instructions burned: 7 (million)
% 0.23/0.56  % (12588)------------------------------
% 0.23/0.56  % (12588)------------------------------
% 0.23/0.56  % (12603)First to succeed.
% 0.23/0.56  % (12604)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)
% 0.23/0.57  % (12602)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.23/0.57  % (12583)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)
% 0.23/0.57  % (12603)Refutation found. Thanks to Tanya!
% 0.23/0.57  % SZS status Theorem for theBenchmark
% 0.23/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.57  % (12603)------------------------------
% 0.23/0.57  % (12603)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.23/0.57  % (12603)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.23/0.57  % (12603)Termination reason: Refutation
% 0.23/0.57  
% 0.23/0.57  % (12603)Memory used [KB]: 1407
% 0.23/0.57  % (12603)Time elapsed: 0.073 s
% 0.23/0.57  % (12603)Instructions burned: 16 (million)
% 0.23/0.57  % (12603)------------------------------
% 0.23/0.57  % (12603)------------------------------
% 0.23/0.57  % (12580)Success in time 0.182 s
%------------------------------------------------------------------------------