TSTP Solution File: SWC007+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC007+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 : n017.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 18:41:10 EDT 2022

% Result   : Theorem 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   41 (  11 unt;   0 def)
%            Number of atoms       :  233 ( 114 equ)
%            Maximal formula atoms :   24 (   5 avg)
%            Number of connectives :  307 ( 115   ~;  95   |;  79   &)
%                                         (   2 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   98 (  68   !;  30   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f658,plain,
    $false,
    inference(subsumption_resolution,[],[f657,f628]) ).

fof(f628,plain,
    sK49 = app(sK49,nil),
    inference(resolution,[],[f497,f515]) ).

fof(f515,plain,
    ssList(sK49),
    inference(cnf_transformation,[],[f336]) ).

fof(f336,plain,
    ( ssList(sK48)
    & ssList(sK50)
    & ! [X4] :
        ( ~ ssList(X4)
        | ! [X5] :
            ( ~ ssList(X5)
            | ! [X6] :
                ( ~ ssList(X6)
                | app(app(X4,X5),X6) != sK49
                | app(X4,X6) != sK48 ) ) )
    & nil = sK50
    & ssList(sK51)
    & sK48 = sK50
    & sK49 = sK51
    & ssList(sK49) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50,sK51])],[f105,f335,f334,f333,f332]) ).

fof(f332,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( ! [X4] :
                        ( ~ ssList(X4)
                        | ! [X5] :
                            ( ~ ssList(X5)
                            | ! [X6] :
                                ( ~ ssList(X6)
                                | app(app(X4,X5),X6) != X1
                                | app(X4,X6) != X0 ) ) )
                    & nil = X2
                    & ssList(X3)
                    & X0 = X2
                    & X1 = X3 ) )
            & ssList(X1) ) )
   => ( ssList(sK48)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ! [X4] :
                      ( ~ ssList(X4)
                      | ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | app(app(X4,X5),X6) != X1
                              | app(X4,X6) != sK48 ) ) )
                  & nil = X2
                  & ssList(X3)
                  & sK48 = X2
                  & X1 = X3 ) )
          & ssList(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f333,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ! [X4] :
                    ( ~ ssList(X4)
                    | ! [X5] :
                        ( ~ ssList(X5)
                        | ! [X6] :
                            ( ~ ssList(X6)
                            | app(app(X4,X5),X6) != X1
                            | app(X4,X6) != sK48 ) ) )
                & nil = X2
                & ssList(X3)
                & sK48 = X2
                & X1 = X3 ) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ! [X4] :
                  ( ~ ssList(X4)
                  | ! [X5] :
                      ( ~ ssList(X5)
                      | ! [X6] :
                          ( ~ ssList(X6)
                          | app(app(X4,X5),X6) != sK49
                          | app(X4,X6) != sK48 ) ) )
              & nil = X2
              & ssList(X3)
              & sK48 = X2
              & sK49 = X3 ) )
      & ssList(sK49) ) ),
    introduced(choice_axiom,[]) ).

fof(f334,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( ! [X4] :
                ( ~ ssList(X4)
                | ! [X5] :
                    ( ~ ssList(X5)
                    | ! [X6] :
                        ( ~ ssList(X6)
                        | app(app(X4,X5),X6) != sK49
                        | app(X4,X6) != sK48 ) ) )
            & nil = X2
            & ssList(X3)
            & sK48 = X2
            & sK49 = X3 ) )
   => ( ssList(sK50)
      & ? [X3] :
          ( ! [X4] :
              ( ~ ssList(X4)
              | ! [X5] :
                  ( ~ ssList(X5)
                  | ! [X6] :
                      ( ~ ssList(X6)
                      | app(app(X4,X5),X6) != sK49
                      | app(X4,X6) != sK48 ) ) )
          & nil = sK50
          & ssList(X3)
          & sK48 = sK50
          & sK49 = X3 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f335,plain,
    ( ? [X3] :
        ( ! [X4] :
            ( ~ ssList(X4)
            | ! [X5] :
                ( ~ ssList(X5)
                | ! [X6] :
                    ( ~ ssList(X6)
                    | app(app(X4,X5),X6) != sK49
                    | app(X4,X6) != sK48 ) ) )
        & nil = sK50
        & ssList(X3)
        & sK48 = sK50
        & sK49 = X3 )
   => ( ! [X4] :
          ( ~ ssList(X4)
          | ! [X5] :
              ( ~ ssList(X5)
              | ! [X6] :
                  ( ~ ssList(X6)
                  | app(app(X4,X5),X6) != sK49
                  | app(X4,X6) != sK48 ) ) )
      & nil = sK50
      & ssList(sK51)
      & sK48 = sK50
      & sK49 = sK51 ) ),
    introduced(choice_axiom,[]) ).

fof(f105,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( ! [X4] :
                      ( ~ ssList(X4)
                      | ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | app(app(X4,X5),X6) != X1
                              | app(X4,X6) != X0 ) ) )
                  & nil = X2
                  & ssList(X3)
                  & X0 = X2
                  & X1 = X3 ) )
          & ssList(X1) ) ),
    inference(flattening,[],[f104]) ).

fof(f104,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( nil = X2
                  & X1 = X3
                  & ! [X4] :
                      ( ~ ssList(X4)
                      | ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | app(app(X4,X5),X6) != X1
                              | app(X4,X6) != X0 ) ) )
                  & 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)
                   => ( nil != X2
                      | X1 != X3
                      | ? [X4] :
                          ( ? [X5] :
                              ( ssList(X5)
                              & ? [X6] :
                                  ( ssList(X6)
                                  & app(app(X4,X5),X6) = X1
                                  & app(X4,X6) = X0 ) )
                          & ssList(X4) )
                      | X0 != X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( nil != X2
                    | X1 != X3
                    | ? [X4] :
                        ( ? [X5] :
                            ( ssList(X5)
                            & ? [X6] :
                                ( ssList(X6)
                                & app(app(X4,X5),X6) = X1
                                & app(X4,X6) = X0 ) )
                        & ssList(X4) )
                    | X0 != X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f497,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f222]) ).

fof(f222,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).

fof(f657,plain,
    sK49 != app(sK49,nil),
    inference(subsumption_resolution,[],[f655,f515]) ).

fof(f655,plain,
    ( ~ ssList(sK49)
    | sK49 != app(sK49,nil) ),
    inference(superposition,[],[f600,f651]) ).

fof(f651,plain,
    sK49 = app(nil,sK49),
    inference(resolution,[],[f551,f515]) ).

fof(f551,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f600,plain,
    ! [X0] :
      ( sK49 != app(app(nil,X0),nil)
      | ~ ssList(X0) ),
    inference(subsumption_resolution,[],[f599,f385]) ).

fof(f385,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f599,plain,
    ! [X0] :
      ( ~ ssList(nil)
      | ~ ssList(X0)
      | sK49 != app(app(nil,X0),nil) ),
    inference(trivial_inequality_removal,[],[f598]) ).

fof(f598,plain,
    ! [X0] :
      ( nil != nil
      | ~ ssList(X0)
      | sK49 != app(app(nil,X0),nil)
      | ~ ssList(nil) ),
    inference(duplicate_literal_removal,[],[f597]) ).

fof(f597,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | sK49 != app(app(nil,X0),nil)
      | ~ ssList(nil)
      | ~ ssList(nil)
      | nil != nil ),
    inference(superposition,[],[f593,f590]) ).

fof(f590,plain,
    nil = app(nil,nil),
    inference(subsumption_resolution,[],[f585,f385]) ).

fof(f585,plain,
    ( ~ ssList(nil)
    | nil = app(nil,nil) ),
    inference(duplicate_literal_removal,[],[f563]) ).

fof(f563,plain,
    ( ~ ssList(nil)
    | ~ ssList(nil)
    | nil = app(nil,nil) ),
    inference(equality_resolution,[],[f562]) ).

fof(f562,plain,
    ! [X0] :
      ( ~ ssList(nil)
      | nil = app(X0,nil)
      | nil != X0
      | ~ ssList(X0) ),
    inference(equality_resolution,[],[f414]) ).

fof(f414,plain,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | nil = app(X0,X1)
      | nil != X1
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f274]) ).

fof(f274,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( nil = app(X0,X1)
              | nil != X1
              | nil != X0 )
            & ( ( nil = X1
                & nil = X0 )
              | nil != app(X0,X1) ) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f273]) ).

fof(f273,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( nil = app(X0,X1)
              | nil != X1
              | nil != X0 )
            & ( ( nil = X1
                & nil = X0 )
              | nil != app(X0,X1) ) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( nil = app(X0,X1)
          <=> ( nil = X1
              & nil = X0 ) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil = app(X0,X1)
          <=> ( nil = X1
              & nil = X0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).

fof(f593,plain,
    ! [X6,X4,X5] :
      ( nil != app(X4,X6)
      | app(app(X4,X5),X6) != sK49
      | ~ ssList(X6)
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(backward_demodulation,[],[f520,f592]) ).

fof(f592,plain,
    nil = sK48,
    inference(forward_demodulation,[],[f517,f519]) ).

fof(f519,plain,
    nil = sK50,
    inference(cnf_transformation,[],[f336]) ).

fof(f517,plain,
    sK48 = sK50,
    inference(cnf_transformation,[],[f336]) ).

fof(f520,plain,
    ! [X6,X4,X5] :
      ( app(X4,X6) != sK48
      | app(app(X4,X5),X6) != sK49
      | ~ ssList(X6)
      | ~ ssList(X4)
      | ~ ssList(X5) ),
    inference(cnf_transformation,[],[f336]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC007+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
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 17:17:50 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.20/0.50  % (14973)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)
% 0.20/0.51  % (14971)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51  % (14992)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  % (14977)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)
% 0.20/0.51  % (14983)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)
% 0.20/0.51  % (14991)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)
% 0.20/0.51  % (14974)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.51  % (14972)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)
% 0.20/0.52  % (14989)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.52  % (14978)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  % (14998)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)
% 0.20/0.52  % (14980)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.52  % (14982)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)
% 0.20/0.52  % (14997)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.52  % (14974)Instruction limit reached!
% 0.20/0.52  % (14974)------------------------------
% 0.20/0.52  % (14974)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (14974)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (14974)Termination reason: Unknown
% 0.20/0.52  % (14974)Termination phase: shuffling
% 0.20/0.52  
% 0.20/0.52  % (14974)Memory used [KB]: 1279
% 0.20/0.52  % (14974)Time elapsed: 0.011 s
% 0.20/0.52  % (14974)Instructions burned: 8 (million)
% 0.20/0.52  % (14974)------------------------------
% 0.20/0.52  % (14974)------------------------------
% 0.20/0.52  % (14968)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  % (14981)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  % (14967)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)
% 0.20/0.53  % (14983)First to succeed.
% 0.20/0.53  % (14990)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.53  % (14976)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.53  % (14969)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  % (14976)Instruction limit reached!
% 0.20/0.53  % (14976)------------------------------
% 0.20/0.53  % (14976)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (14976)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (14976)Termination reason: Unknown
% 0.20/0.53  % (14976)Termination phase: Naming
% 0.20/0.53  
% 0.20/0.53  % (14976)Memory used [KB]: 1023
% 0.20/0.53  % (14976)Time elapsed: 0.003 s
% 0.20/0.53  % (14976)Instructions burned: 3 (million)
% 0.20/0.53  % (14976)------------------------------
% 0.20/0.53  % (14976)------------------------------
% 0.20/0.54  % (14970)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)
% 0.20/0.54  % (14983)Refutation found. Thanks to Tanya!
% 0.20/0.54  % SZS status Theorem for theBenchmark
% 0.20/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54  % (14983)------------------------------
% 0.20/0.54  % (14983)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (14983)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (14983)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (14983)Memory used [KB]: 1535
% 0.20/0.54  % (14983)Time elapsed: 0.081 s
% 0.20/0.54  % (14983)Instructions burned: 18 (million)
% 0.20/0.54  % (14983)------------------------------
% 0.20/0.54  % (14983)------------------------------
% 0.20/0.54  % (14962)Success in time 0.186 s
%------------------------------------------------------------------------------