TSTP Solution File: SWC097+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC097+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 : n012.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 18:41:43 EDT 2022

% Result   : Theorem 0.18s 0.52s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   26 (   7 unt;   0 def)
%            Number of atoms       :  210 (  70 equ)
%            Maximal formula atoms :   26 (   8 avg)
%            Number of connectives :  248 (  64   ~;  48   |; 116   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   73 (  30   !;  43   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f611,plain,
    $false,
    inference(subsumption_resolution,[],[f610,f608]) ).

fof(f608,plain,
    app(sK24,cons(sK26,nil)) = sK25,
    inference(subsumption_resolution,[],[f437,f605]) ).

fof(f605,plain,
    neq(sK25,nil),
    inference(duplicate_literal_removal,[],[f565]) ).

fof(f565,plain,
    ( neq(sK25,nil)
    | neq(sK25,nil) ),
    inference(definition_unfolding,[],[f442,f444,f444]) ).

fof(f444,plain,
    sK23 = sK25,
    inference(cnf_transformation,[],[f282]) ).

fof(f282,plain,
    ( ssList(sK23)
    & ssList(sK24)
    & sK22 = sK24
    & sK23 = sK25
    & ssList(sK25)
    & ( ( neq(sK23,nil)
        & ! [X4] :
            ( ~ ssItem(X4)
            | sK23 != app(sK22,cons(X4,nil)) )
        & app(sK24,cons(sK26,nil)) = sK25
        & ssItem(sK26) )
      | ( neq(sK23,nil)
        & ~ neq(sK25,nil) ) )
    & ssList(sK22) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24,sK25,sK26])],[f276,f281,f280,f279,f278,f277]) ).

fof(f277,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( X0 = X2
                    & X1 = X3
                    & ssList(X3)
                    & ( ( neq(X1,nil)
                        & ! [X4] :
                            ( ~ ssItem(X4)
                            | app(X0,cons(X4,nil)) != X1 )
                        & ? [X5] :
                            ( app(X2,cons(X5,nil)) = X3
                            & ssItem(X5) ) )
                      | ( neq(X1,nil)
                        & ~ neq(X3,nil) ) ) ) ) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( sK22 = X2
                  & X1 = X3
                  & ssList(X3)
                  & ( ( neq(X1,nil)
                      & ! [X4] :
                          ( ~ ssItem(X4)
                          | app(sK22,cons(X4,nil)) != X1 )
                      & ? [X5] :
                          ( app(X2,cons(X5,nil)) = X3
                          & ssItem(X5) ) )
                    | ( neq(X1,nil)
                      & ~ neq(X3,nil) ) ) ) ) )
      & ssList(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f278,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( sK22 = X2
                & X1 = X3
                & ssList(X3)
                & ( ( neq(X1,nil)
                    & ! [X4] :
                        ( ~ ssItem(X4)
                        | app(sK22,cons(X4,nil)) != X1 )
                    & ? [X5] :
                        ( app(X2,cons(X5,nil)) = X3
                        & ssItem(X5) ) )
                  | ( neq(X1,nil)
                    & ~ neq(X3,nil) ) ) ) ) )
   => ( ssList(sK23)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( sK22 = X2
              & sK23 = X3
              & ssList(X3)
              & ( ( neq(sK23,nil)
                  & ! [X4] :
                      ( ~ ssItem(X4)
                      | sK23 != app(sK22,cons(X4,nil)) )
                  & ? [X5] :
                      ( app(X2,cons(X5,nil)) = X3
                      & ssItem(X5) ) )
                | ( neq(sK23,nil)
                  & ~ neq(X3,nil) ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f279,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( sK22 = X2
            & sK23 = X3
            & ssList(X3)
            & ( ( neq(sK23,nil)
                & ! [X4] :
                    ( ~ ssItem(X4)
                    | sK23 != app(sK22,cons(X4,nil)) )
                & ? [X5] :
                    ( app(X2,cons(X5,nil)) = X3
                    & ssItem(X5) ) )
              | ( neq(sK23,nil)
                & ~ neq(X3,nil) ) ) ) )
   => ( ssList(sK24)
      & ? [X3] :
          ( sK22 = sK24
          & sK23 = X3
          & ssList(X3)
          & ( ( neq(sK23,nil)
              & ! [X4] :
                  ( ~ ssItem(X4)
                  | sK23 != app(sK22,cons(X4,nil)) )
              & ? [X5] :
                  ( app(sK24,cons(X5,nil)) = X3
                  & ssItem(X5) ) )
            | ( neq(sK23,nil)
              & ~ neq(X3,nil) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f280,plain,
    ( ? [X3] :
        ( sK22 = sK24
        & sK23 = X3
        & ssList(X3)
        & ( ( neq(sK23,nil)
            & ! [X4] :
                ( ~ ssItem(X4)
                | sK23 != app(sK22,cons(X4,nil)) )
            & ? [X5] :
                ( app(sK24,cons(X5,nil)) = X3
                & ssItem(X5) ) )
          | ( neq(sK23,nil)
            & ~ neq(X3,nil) ) ) )
   => ( sK22 = sK24
      & sK23 = sK25
      & ssList(sK25)
      & ( ( neq(sK23,nil)
          & ! [X4] :
              ( ~ ssItem(X4)
              | sK23 != app(sK22,cons(X4,nil)) )
          & ? [X5] :
              ( sK25 = app(sK24,cons(X5,nil))
              & ssItem(X5) ) )
        | ( neq(sK23,nil)
          & ~ neq(sK25,nil) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f281,plain,
    ( ? [X5] :
        ( sK25 = app(sK24,cons(X5,nil))
        & ssItem(X5) )
   => ( app(sK24,cons(sK26,nil)) = sK25
      & ssItem(sK26) ) ),
    introduced(choice_axiom,[]) ).

fof(f276,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X0 = X2
                  & X1 = X3
                  & ssList(X3)
                  & ( ( neq(X1,nil)
                      & ! [X4] :
                          ( ~ ssItem(X4)
                          | app(X0,cons(X4,nil)) != X1 )
                      & ? [X5] :
                          ( app(X2,cons(X5,nil)) = X3
                          & ssItem(X5) ) )
                    | ( neq(X1,nil)
                      & ~ neq(X3,nil) ) ) ) ) )
      & ssList(X0) ),
    inference(rectify,[],[f180]) ).

fof(f180,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X0 = X2
                  & X1 = X3
                  & ssList(X3)
                  & ( ( neq(X1,nil)
                      & ! [X5] :
                          ( ~ ssItem(X5)
                          | app(X0,cons(X5,nil)) != X1 )
                      & ? [X4] :
                          ( app(X2,cons(X4,nil)) = X3
                          & ssItem(X4) ) )
                    | ( neq(X1,nil)
                      & ~ neq(X3,nil) ) ) ) ) )
      & ssList(X0) ),
    inference(flattening,[],[f179]) ).

fof(f179,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( neq(X1,nil)
                      & ! [X5] :
                          ( ~ ssItem(X5)
                          | app(X0,cons(X5,nil)) != X1 )
                      & ? [X4] :
                          ( app(X2,cons(X4,nil)) = X3
                          & ssItem(X4) ) )
                    | ( neq(X1,nil)
                      & ~ neq(X3,nil) ) )
                  & X1 = X3
                  & X0 = X2
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( ! [X4] :
                              ( ssItem(X4)
                             => app(X2,cons(X4,nil)) != X3 )
                          | ? [X5] :
                              ( ssItem(X5)
                              & app(X0,cons(X5,nil)) = X1 )
                          | ~ neq(X1,nil) )
                        & ( ~ neq(X1,nil)
                          | neq(X3,nil) ) )
                      | X1 != X3
                      | X0 != X2 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( X1 != X3
                      | X0 != X2
                      | ( ( ~ neq(X1,nil)
                          | ! [X5] :
                              ( ssItem(X5)
                             => app(X2,cons(X5,nil)) != X3 )
                          | ? [X4] :
                              ( app(X0,cons(X4,nil)) = X1
                              & ssItem(X4) ) )
                        & ( ~ neq(X1,nil)
                          | neq(X3,nil) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f442,plain,
    ( neq(sK23,nil)
    | neq(sK23,nil) ),
    inference(cnf_transformation,[],[f282]) ).

fof(f437,plain,
    ( ~ neq(sK25,nil)
    | app(sK24,cons(sK26,nil)) = sK25 ),
    inference(cnf_transformation,[],[f282]) ).

fof(f610,plain,
    app(sK24,cons(sK26,nil)) != sK25,
    inference(resolution,[],[f609,f607]) ).

fof(f607,plain,
    ssItem(sK26),
    inference(subsumption_resolution,[],[f435,f605]) ).

fof(f435,plain,
    ( ssItem(sK26)
    | ~ neq(sK25,nil) ),
    inference(cnf_transformation,[],[f282]) ).

fof(f609,plain,
    ! [X4] :
      ( ~ ssItem(X4)
      | app(sK24,cons(X4,nil)) != sK25 ),
    inference(subsumption_resolution,[],[f568,f605]) ).

fof(f568,plain,
    ! [X4] :
      ( ~ neq(sK25,nil)
      | app(sK24,cons(X4,nil)) != sK25
      | ~ ssItem(X4) ),
    inference(definition_unfolding,[],[f439,f444,f445]) ).

fof(f445,plain,
    sK22 = sK24,
    inference(cnf_transformation,[],[f282]) ).

fof(f439,plain,
    ! [X4] :
      ( ~ ssItem(X4)
      | sK23 != app(sK22,cons(X4,nil))
      | ~ neq(sK25,nil) ),
    inference(cnf_transformation,[],[f282]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SWC097+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n012.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 18:13:20 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.49  % (778)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.49  % (796)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)
% 0.18/0.49  % (776)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)
% 0.18/0.50  % (802)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.18/0.50  % (788)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)
% 0.18/0.50  % (780)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)
% 0.18/0.50  % (794)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)
% 0.18/0.50  % (786)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.18/0.50  % (790)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)
% 0.18/0.51  % (800)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)
% 0.18/0.51  % (783)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)
% 0.18/0.51  % (777)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)
% 0.18/0.51  % (774)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)
% 0.18/0.51  % (784)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.51  % (791)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.18/0.51  % (797)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)
% 0.18/0.51  % (792)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.51  % (801)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)
% 0.18/0.51  % (796)First to succeed.
% 0.18/0.51  % (779)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)
% 0.18/0.51  % (799)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.18/0.51  % (781)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.51  % (775)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)
% 0.18/0.52  % (803)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)
% 0.18/0.52  % (781)Instruction limit reached!
% 0.18/0.52  % (781)------------------------------
% 0.18/0.52  % (781)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (795)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.18/0.52  % (796)Refutation found. Thanks to Tanya!
% 0.18/0.52  % SZS status Theorem for theBenchmark
% 0.18/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52  % (796)------------------------------
% 0.18/0.52  % (796)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (796)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (796)Termination reason: Refutation
% 0.18/0.52  
% 0.18/0.52  % (796)Memory used [KB]: 1407
% 0.18/0.52  % (796)Time elapsed: 0.088 s
% 0.18/0.52  % (796)Instructions burned: 12 (million)
% 0.18/0.52  % (796)------------------------------
% 0.18/0.52  % (796)------------------------------
% 0.18/0.52  % (773)Success in time 0.187 s
%------------------------------------------------------------------------------