TSTP Solution File: SWC094+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC094+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 : n018.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 18:41:42 EDT 2022

% Result   : Theorem 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   31 (  13 unt;   0 def)
%            Number of atoms       :  186 (  83 equ)
%            Maximal formula atoms :   24 (   6 avg)
%            Number of connectives :  243 (  88   ~;  69   |;  73   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   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   :   82 (  52   !;  30   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f614,plain,
    $false,
    inference(resolution,[],[f613,f374]) ).

fof(f374,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f613,plain,
    ~ ssList(nil),
    inference(resolution,[],[f611,f558]) ).

fof(f558,plain,
    ssList(sK8),
    inference(definition_unfolding,[],[f392,f555]) ).

fof(f555,plain,
    sK11 = sK8,
    inference(definition_unfolding,[],[f389,f390]) ).

fof(f390,plain,
    sK10 = sK8,
    inference(cnf_transformation,[],[f249]) ).

fof(f249,plain,
    ( ssList(sK8)
    & ssList(sK9)
    & ssList(sK11)
    & sK9 = sK11
    & sK10 = sK8
    & sK11 = sK10
    & ! [X4] :
        ( ~ ssList(X4)
        | ! [X5] :
            ( ~ ssList(X5)
            | ! [X6] :
                ( ~ ssList(X6)
                | app(app(X4,X5),X6) != sK8
                | app(X4,X6) != sK9 ) ) )
    & ssList(sK10) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f142,f248,f247,f246,f245]) ).

fof(f245,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ? [X3] :
                    ( ssList(X3)
                    & X1 = X3
                    & X0 = X2
                    & X2 = X3
                    & ! [X4] :
                        ( ~ ssList(X4)
                        | ! [X5] :
                            ( ~ ssList(X5)
                            | ! [X6] :
                                ( ~ ssList(X6)
                                | app(app(X4,X5),X6) != X0
                                | app(X4,X6) != X1 ) ) ) )
                & ssList(X2) ) ) )
   => ( ssList(sK8)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & X1 = X3
                  & sK8 = X2
                  & X2 = X3
                  & ! [X4] :
                      ( ~ ssList(X4)
                      | ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | app(app(X4,X5),X6) != sK8
                              | app(X4,X6) != X1 ) ) ) )
              & ssList(X2) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f246,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ? [X3] :
                ( ssList(X3)
                & X1 = X3
                & sK8 = X2
                & X2 = X3
                & ! [X4] :
                    ( ~ ssList(X4)
                    | ! [X5] :
                        ( ~ ssList(X5)
                        | ! [X6] :
                            ( ~ ssList(X6)
                            | app(app(X4,X5),X6) != sK8
                            | app(X4,X6) != X1 ) ) ) )
            & ssList(X2) ) )
   => ( ssList(sK9)
      & ? [X2] :
          ( ? [X3] :
              ( ssList(X3)
              & sK9 = X3
              & sK8 = X2
              & X2 = X3
              & ! [X4] :
                  ( ~ ssList(X4)
                  | ! [X5] :
                      ( ~ ssList(X5)
                      | ! [X6] :
                          ( ~ ssList(X6)
                          | app(app(X4,X5),X6) != sK8
                          | app(X4,X6) != sK9 ) ) ) )
          & ssList(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f247,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ssList(X3)
            & sK9 = X3
            & sK8 = X2
            & X2 = X3
            & ! [X4] :
                ( ~ ssList(X4)
                | ! [X5] :
                    ( ~ ssList(X5)
                    | ! [X6] :
                        ( ~ ssList(X6)
                        | app(app(X4,X5),X6) != sK8
                        | app(X4,X6) != sK9 ) ) ) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ssList(X3)
          & sK9 = X3
          & sK10 = sK8
          & sK10 = X3
          & ! [X4] :
              ( ~ ssList(X4)
              | ! [X5] :
                  ( ~ ssList(X5)
                  | ! [X6] :
                      ( ~ ssList(X6)
                      | app(app(X4,X5),X6) != sK8
                      | app(X4,X6) != sK9 ) ) ) )
      & ssList(sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f248,plain,
    ( ? [X3] :
        ( ssList(X3)
        & sK9 = X3
        & sK10 = sK8
        & sK10 = X3
        & ! [X4] :
            ( ~ ssList(X4)
            | ! [X5] :
                ( ~ ssList(X5)
                | ! [X6] :
                    ( ~ ssList(X6)
                    | app(app(X4,X5),X6) != sK8
                    | app(X4,X6) != sK9 ) ) ) )
   => ( ssList(sK11)
      & sK9 = sK11
      & sK10 = sK8
      & sK11 = sK10
      & ! [X4] :
          ( ~ ssList(X4)
          | ! [X5] :
              ( ~ ssList(X5)
              | ! [X6] :
                  ( ~ ssList(X6)
                  | app(app(X4,X5),X6) != sK8
                  | app(X4,X6) != sK9 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f142,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & X1 = X3
                  & X0 = X2
                  & X2 = X3
                  & ! [X4] :
                      ( ~ ssList(X4)
                      | ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | app(app(X4,X5),X6) != X0
                              | app(X4,X6) != X1 ) ) ) )
              & ssList(X2) ) ) ),
    inference(flattening,[],[f141]) ).

fof(f141,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & X2 = X3
                  & X0 = X2
                  & ! [X4] :
                      ( ~ ssList(X4)
                      | ! [X5] :
                          ( ~ ssList(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | app(app(X4,X5),X6) != X0
                              | app(X4,X6) != X1 ) ) )
                  & 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
                      | X2 != X3
                      | X0 != X2
                      | ? [X4] :
                          ( ssList(X4)
                          & ? [X5] :
                              ( ssList(X5)
                              & ? [X6] :
                                  ( app(app(X4,X5),X6) = X0
                                  & app(X4,X6) = X1
                                  & ssList(X6) ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f389,plain,
    sK11 = sK10,
    inference(cnf_transformation,[],[f249]) ).

fof(f392,plain,
    ssList(sK11),
    inference(cnf_transformation,[],[f249]) ).

fof(f611,plain,
    ( ~ ssList(sK8)
    | ~ ssList(nil) ),
    inference(trivial_inequality_removal,[],[f609]) ).

fof(f609,plain,
    ( ~ ssList(sK8)
    | ~ ssList(nil)
    | sK8 != sK8 ),
    inference(superposition,[],[f608,f596]) ).

fof(f596,plain,
    app(nil,sK8) = sK8,
    inference(resolution,[],[f348,f558]) ).

fof(f348,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f176]) ).

fof(f176,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

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

fof(f608,plain,
    ! [X0] :
      ( app(nil,X0) != sK8
      | ~ ssList(X0)
      | ~ ssList(nil) ),
    inference(duplicate_literal_removal,[],[f607]) ).

fof(f607,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ ssList(nil)
      | app(nil,X0) != sK8
      | ~ ssList(nil)
      | app(nil,X0) != sK8 ),
    inference(superposition,[],[f559,f595]) ).

fof(f595,plain,
    nil = app(nil,nil),
    inference(resolution,[],[f348,f374]) ).

fof(f559,plain,
    ! [X6,X4,X5] :
      ( app(app(X4,X5),X6) != sK8
      | ~ ssList(X4)
      | ~ ssList(X5)
      | app(X4,X6) != sK8
      | ~ ssList(X6) ),
    inference(definition_unfolding,[],[f388,f556]) ).

fof(f556,plain,
    sK9 = sK8,
    inference(definition_unfolding,[],[f391,f555]) ).

fof(f391,plain,
    sK9 = sK11,
    inference(cnf_transformation,[],[f249]) ).

fof(f388,plain,
    ! [X6,X4,X5] :
      ( ~ ssList(X4)
      | ~ ssList(X5)
      | ~ ssList(X6)
      | app(app(X4,X5),X6) != sK8
      | app(X4,X6) != sK9 ),
    inference(cnf_transformation,[],[f249]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC094+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 18:17:55 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (26894)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)
% 0.20/0.50  % (26911)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51  % (26903)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51  % (26904)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  % (26895)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)
% 0.20/0.51  % (26906)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)
% 0.20/0.52  % (26905)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  % (26903)Instruction limit reached!
% 0.20/0.52  % (26903)------------------------------
% 0.20/0.52  % (26903)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (26912)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.53  % (26903)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (26903)Termination reason: Unknown
% 0.20/0.53  % (26903)Termination phase: Preprocessing 3
% 0.20/0.53  
% 0.20/0.53  % (26903)Memory used [KB]: 1023
% 0.20/0.53  % (26903)Time elapsed: 0.004 s
% 0.20/0.53  % (26903)Instructions burned: 3 (million)
% 0.20/0.53  % (26903)------------------------------
% 0.20/0.53  % (26903)------------------------------
% 0.20/0.53  % (26914)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53  % (26897)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  % (26902)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53  % (26901)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)
% 0.20/0.53  % (26895)Refutation not found, incomplete strategy% (26895)------------------------------
% 0.20/0.53  % (26895)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (26896)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  TRYING [1]
% 0.20/0.53  % (26910)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)
% 0.20/0.53  % (26904)First to succeed.
% 0.20/0.54  TRYING [2]
% 0.20/0.54  % (26907)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.54  % (26898)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (26919)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.54  % (26925)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)
% 0.20/0.54  % (26924)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54  % (26900)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)
% 0.20/0.55  % (26904)Refutation found. Thanks to Tanya!
% 0.20/0.55  % SZS status Theorem for theBenchmark
% 0.20/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55  % (26904)------------------------------
% 0.20/0.55  % (26904)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (26904)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (26904)Termination reason: Refutation
% 0.20/0.55  
% 0.20/0.55  % (26904)Memory used [KB]: 1407
% 0.20/0.55  % (26904)Time elapsed: 0.111 s
% 0.20/0.55  % (26904)Instructions burned: 17 (million)
% 0.20/0.55  % (26904)------------------------------
% 0.20/0.55  % (26904)------------------------------
% 0.20/0.55  % (26890)Success in time 0.19 s
%------------------------------------------------------------------------------