TSTP Solution File: SWC097+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC097+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 : Tue May 21 04:47:10 EDT 2024

% Result   : Theorem 0.20s 0.45s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   40 (   7 unt;   0 def)
%            Number of atoms       :  213 (  56 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  238 (  65   ~;  55   |;  98   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   99 (  62   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2062,plain,
    $false,
    inference(resolution,[],[f2061,f700]) ).

fof(f700,plain,
    neq(sK21,nil),
    inference(duplicate_literal_removal,[],[f698]) ).

fof(f698,plain,
    ( neq(sK21,nil)
    | neq(sK21,nil) ),
    inference(resolution,[],[f381,f649]) ).

fof(f649,plain,
    ( sP0(sK21,sK20,sK21,sK20)
    | neq(sK21,nil) ),
    inference(forward_demodulation,[],[f648,f389]) ).

fof(f389,plain,
    sK21 = sK23,
    inference(cnf_transformation,[],[f261]) ).

fof(f261,plain,
    ( ( ( ~ neq(sK23,nil)
        & neq(sK21,nil) )
      | sP0(sK23,sK22,sK21,sK20) )
    & sK20 = sK22
    & sK21 = sK23
    & ssList(sK23)
    & ssList(sK22)
    & ssList(sK21)
    & ssList(sK20) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23])],[f225,f260,f259,f258,f257]) ).

fof(f257,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | sP0(X3,X2,X1,X0) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | sP0(X3,X2,X1,sK20) )
                  & sK20 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f258,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | sP0(X3,X2,X1,sK20) )
                & sK20 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK21,nil) )
                | sP0(X3,X2,sK21,sK20) )
              & sK20 = X2
              & sK21 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f259,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK21,nil) )
              | sP0(X3,X2,sK21,sK20) )
            & sK20 = X2
            & sK21 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK21,nil) )
            | sP0(X3,sK22,sK21,sK20) )
          & sK20 = sK22
          & sK21 = X3
          & ssList(X3) )
      & ssList(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f260,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK21,nil) )
          | sP0(X3,sK22,sK21,sK20) )
        & sK20 = sK22
        & sK21 = X3
        & ssList(X3) )
   => ( ( ( ~ neq(sK23,nil)
          & neq(sK21,nil) )
        | sP0(sK23,sK22,sK21,sK20) )
      & sK20 = sK22
      & sK21 = sK23
      & ssList(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f225,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | sP0(X3,X2,X1,X0) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f100,f224]) ).

fof(f224,plain,
    ! [X3,X2,X1,X0] :
      ( ( ? [X4] :
            ( app(X2,cons(X4,nil)) = X3
            & ssItem(X4) )
        & ! [X5] :
            ( app(X0,cons(X5,nil)) != X1
            | ~ ssItem(X5) )
        & neq(X1,nil) )
      | ~ sP0(X3,X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( app(X2,cons(X4,nil)) = X3
                          & ssItem(X4) )
                      & ! [X5] :
                          ( app(X0,cons(X5,nil)) != X1
                          | ~ ssItem(X5) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( app(X2,cons(X4,nil)) = X3
                          & ssItem(X4) )
                      & ! [X5] :
                          ( app(X0,cons(X5,nil)) != X1
                          | ~ ssItem(X5) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & 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)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ! [X4] :
                              ( ssItem(X4)
                             => app(X2,cons(X4,nil)) != X3 )
                          | ? [X5] :
                              ( app(X0,cons(X5,nil)) = X1
                              & ssItem(X5) )
                          | ~ neq(X1,nil) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

fof(f648,plain,
    ( sP0(sK23,sK20,sK21,sK20)
    | neq(sK21,nil) ),
    inference(forward_demodulation,[],[f391,f390]) ).

fof(f390,plain,
    sK20 = sK22,
    inference(cnf_transformation,[],[f261]) ).

fof(f391,plain,
    ( neq(sK21,nil)
    | sP0(sK23,sK22,sK21,sK20) ),
    inference(cnf_transformation,[],[f261]) ).

fof(f381,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0,X1,X2,X3)
      | neq(X2,nil) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f256,plain,
    ! [X0,X1,X2,X3] :
      ( ( app(X1,cons(sK19(X0,X1),nil)) = X0
        & ssItem(sK19(X0,X1))
        & ! [X5] :
            ( app(X3,cons(X5,nil)) != X2
            | ~ ssItem(X5) )
        & neq(X2,nil) )
      | ~ sP0(X0,X1,X2,X3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f254,f255]) ).

fof(f255,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( app(X1,cons(X4,nil)) = X0
          & ssItem(X4) )
     => ( app(X1,cons(sK19(X0,X1),nil)) = X0
        & ssItem(sK19(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f254,plain,
    ! [X0,X1,X2,X3] :
      ( ( ? [X4] :
            ( app(X1,cons(X4,nil)) = X0
            & ssItem(X4) )
        & ! [X5] :
            ( app(X3,cons(X5,nil)) != X2
            | ~ ssItem(X5) )
        & neq(X2,nil) )
      | ~ sP0(X0,X1,X2,X3) ),
    inference(rectify,[],[f253]) ).

fof(f253,plain,
    ! [X3,X2,X1,X0] :
      ( ( ? [X4] :
            ( app(X2,cons(X4,nil)) = X3
            & ssItem(X4) )
        & ! [X5] :
            ( app(X0,cons(X5,nil)) != X1
            | ~ ssItem(X5) )
        & neq(X1,nil) )
      | ~ sP0(X3,X2,X1,X0) ),
    inference(nnf_transformation,[],[f224]) ).

fof(f2061,plain,
    ~ neq(sK21,nil),
    inference(resolution,[],[f2058,f731]) ).

fof(f731,plain,
    ( ssItem(sK19(sK21,sK20))
    | ~ neq(sK21,nil) ),
    inference(resolution,[],[f383,f647]) ).

fof(f647,plain,
    ( sP0(sK21,sK20,sK21,sK20)
    | ~ neq(sK21,nil) ),
    inference(forward_demodulation,[],[f646,f389]) ).

fof(f646,plain,
    ( sP0(sK23,sK20,sK21,sK20)
    | ~ neq(sK21,nil) ),
    inference(forward_demodulation,[],[f645,f390]) ).

fof(f645,plain,
    ( ~ neq(sK21,nil)
    | sP0(sK23,sK22,sK21,sK20) ),
    inference(forward_demodulation,[],[f392,f389]) ).

fof(f392,plain,
    ( ~ neq(sK23,nil)
    | sP0(sK23,sK22,sK21,sK20) ),
    inference(cnf_transformation,[],[f261]) ).

fof(f383,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0,X1,X2,X3)
      | ssItem(sK19(X0,X1)) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f2058,plain,
    ~ ssItem(sK19(sK21,sK20)),
    inference(resolution,[],[f2057,f700]) ).

fof(f2057,plain,
    ( ~ neq(sK21,nil)
    | ~ ssItem(sK19(sK21,sK20)) ),
    inference(resolution,[],[f2049,f647]) ).

fof(f2049,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1,sK21,sK20)
      | ~ ssItem(sK19(sK21,sK20)) ),
    inference(superposition,[],[f610,f2046]) ).

fof(f2046,plain,
    sK21 = app(sK20,cons(sK19(sK21,sK20),nil)),
    inference(resolution,[],[f2045,f700]) ).

fof(f2045,plain,
    ( ~ neq(sK21,nil)
    | sK21 = app(sK20,cons(sK19(sK21,sK20),nil)) ),
    inference(resolution,[],[f384,f647]) ).

fof(f384,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0,X1,X2,X3)
      | app(X1,cons(sK19(X0,X1),nil)) = X0 ),
    inference(cnf_transformation,[],[f256]) ).

fof(f610,plain,
    ! [X3,X0,X1,X5] :
      ( ~ sP0(X0,X1,app(X3,cons(X5,nil)),X3)
      | ~ ssItem(X5) ),
    inference(equality_resolution,[],[f382]) ).

fof(f382,plain,
    ! [X2,X3,X0,X1,X5] :
      ( app(X3,cons(X5,nil)) != X2
      | ~ ssItem(X5)
      | ~ sP0(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f256]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SWC097+1 : TPTP v8.2.0. Released v2.4.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n018.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 19 03:53:37 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (2417)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (2418)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (2424)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38  % (2423)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38  % (2420)WARNING: value z3 for option sas not known
% 0.14/0.38  % (2419)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (2420)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (2422)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  % (2421)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40  TRYING [1]
% 0.14/0.40  TRYING [2]
% 0.14/0.41  TRYING [3]
% 0.14/0.41  TRYING [1]
% 0.14/0.42  TRYING [2]
% 0.14/0.42  TRYING [4]
% 0.14/0.43  TRYING [3]
% 0.20/0.45  % (2423)First to succeed.
% 0.20/0.45  % (2423)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2417"
% 0.20/0.45  % (2423)Refutation found. Thanks to Tanya!
% 0.20/0.45  % SZS status Theorem for theBenchmark
% 0.20/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.45  % (2423)------------------------------
% 0.20/0.45  % (2423)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.45  % (2423)Termination reason: Refutation
% 0.20/0.45  
% 0.20/0.45  % (2423)Memory used [KB]: 2807
% 0.20/0.45  % (2423)Time elapsed: 0.076 s
% 0.20/0.45  % (2423)Instructions burned: 148 (million)
% 0.20/0.45  % (2417)Success in time 0.09 s
%------------------------------------------------------------------------------