TSTP Solution File: SWC037+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC037+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 : n014.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 04:41:01 EDT 2024

% Result   : Theorem 0.13s 0.39s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   47 (  14 unt;   0 def)
%            Number of atoms       :  250 ( 104 equ)
%            Maximal formula atoms :   22 (   5 avg)
%            Number of connectives :  268 (  65   ~;  57   |; 124   &)
%                                         (   4 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   76 (  42   !;  34   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f772,plain,
    $false,
    inference(subsumption_resolution,[],[f771,f402]) ).

fof(f402,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f771,plain,
    ~ ssList(nil),
    inference(resolution,[],[f769,f639]) ).

fof(f639,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f632]) ).

fof(f632,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f581]) ).

fof(f581,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f361]) ).

fof(f361,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f198]) ).

fof(f198,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f769,plain,
    neq(nil,nil),
    inference(subsumption_resolution,[],[f766,f656]) ).

fof(f656,plain,
    sP0(sK20,nil),
    inference(forward_demodulation,[],[f655,f390]) ).

fof(f390,plain,
    sK20 = sK22,
    inference(cnf_transformation,[],[f260]) ).

fof(f260,plain,
    ( ( ( nil = sK22
        & nil = sK23 )
      | sP0(sK22,sK23) )
    & nil != sK20
    & sK20 = sK22
    & sK21 = sK23
    & nil = sK21
    & ssList(sK23)
    & ssList(sK22)
    & ssList(sK21)
    & ssList(sK20) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23])],[f224,f259,f258,f257,f256]) ).

fof(f256,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X2
                        & nil = X3 )
                      | sP0(X2,X3) )
                    & nil != X0
                    & X0 = X2
                    & X1 = X3
                    & nil = X1
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | sP0(X2,X3) )
                  & nil != sK20
                  & sK20 = X2
                  & X1 = X3
                  & nil = X1
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f257,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X2
                    & nil = X3 )
                  | sP0(X2,X3) )
                & nil != sK20
                & sK20 = X2
                & X1 = X3
                & nil = X1
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil = X2
                  & nil = X3 )
                | sP0(X2,X3) )
              & nil != sK20
              & sK20 = X2
              & sK21 = X3
              & nil = sK21
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f258,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = X2
                & nil = X3 )
              | sP0(X2,X3) )
            & nil != sK20
            & sK20 = X2
            & sK21 = X3
            & nil = sK21
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK22
              & nil = X3 )
            | sP0(sK22,X3) )
          & nil != sK20
          & sK20 = sK22
          & sK21 = X3
          & nil = sK21
          & ssList(X3) )
      & ssList(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f259,plain,
    ( ? [X3] :
        ( ( ( nil = sK22
            & nil = X3 )
          | sP0(sK22,X3) )
        & nil != sK20
        & sK20 = sK22
        & sK21 = X3
        & nil = sK21
        & ssList(X3) )
   => ( ( ( nil = sK22
          & nil = sK23 )
        | sP0(sK22,sK23) )
      & nil != sK20
      & sK20 = sK22
      & sK21 = sK23
      & nil = sK21
      & ssList(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f224,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | sP0(X2,X3) )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & nil = X1
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f99,f223]) ).

fof(f223,plain,
    ! [X2,X3] :
      ( ? [X4] :
          ( segmentP(X2,X4)
          & segmentP(X3,X4)
          & neq(X4,nil)
          & ssList(X4) )
      | ~ sP0(X2,X3) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( segmentP(X2,X4)
                        & segmentP(X3,X4)
                        & neq(X4,nil)
                        & ssList(X4) ) )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & nil = X1
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( segmentP(X2,X4)
                        & segmentP(X3,X4)
                        & neq(X4,nil)
                        & ssList(X4) ) )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & nil = 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)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X4] :
                            ( ssList(X4)
                           => ( ~ segmentP(X2,X4)
                              | ~ segmentP(X3,X4)
                              | ~ neq(X4,nil) ) ) )
                      | nil = X0
                      | X0 != X2
                      | X1 != X3
                      | nil != X1 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f655,plain,
    sP0(sK22,nil),
    inference(forward_demodulation,[],[f654,f650]) ).

fof(f650,plain,
    nil = sK23,
    inference(forward_demodulation,[],[f389,f388]) ).

fof(f388,plain,
    nil = sK21,
    inference(cnf_transformation,[],[f260]) ).

fof(f389,plain,
    sK21 = sK23,
    inference(cnf_transformation,[],[f260]) ).

fof(f654,plain,
    sP0(sK22,sK23),
    inference(subsumption_resolution,[],[f653,f391]) ).

fof(f391,plain,
    nil != sK20,
    inference(cnf_transformation,[],[f260]) ).

fof(f653,plain,
    ( nil = sK20
    | sP0(sK22,sK23) ),
    inference(forward_demodulation,[],[f393,f390]) ).

fof(f393,plain,
    ( nil = sK22
    | sP0(sK22,sK23) ),
    inference(cnf_transformation,[],[f260]) ).

fof(f766,plain,
    ( neq(nil,nil)
    | ~ sP0(sK20,nil) ),
    inference(superposition,[],[f381,f763]) ).

fof(f763,plain,
    nil = sK19(sK20,nil),
    inference(resolution,[],[f753,f656]) ).

fof(f753,plain,
    ! [X0] :
      ( ~ sP0(X0,nil)
      | nil = sK19(X0,nil) ),
    inference(subsumption_resolution,[],[f749,f380]) ).

fof(f380,plain,
    ! [X0,X1] :
      ( ssList(sK19(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f255]) ).

fof(f255,plain,
    ! [X0,X1] :
      ( ( segmentP(X0,sK19(X0,X1))
        & segmentP(X1,sK19(X0,X1))
        & neq(sK19(X0,X1),nil)
        & ssList(sK19(X0,X1)) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f253,f254]) ).

fof(f254,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( segmentP(X0,X2)
          & segmentP(X1,X2)
          & neq(X2,nil)
          & ssList(X2) )
     => ( segmentP(X0,sK19(X0,X1))
        & segmentP(X1,sK19(X0,X1))
        & neq(sK19(X0,X1),nil)
        & ssList(sK19(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( segmentP(X0,X2)
          & segmentP(X1,X2)
          & neq(X2,nil)
          & ssList(X2) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f252]) ).

fof(f252,plain,
    ! [X2,X3] :
      ( ? [X4] :
          ( segmentP(X2,X4)
          & segmentP(X3,X4)
          & neq(X4,nil)
          & ssList(X4) )
      | ~ sP0(X2,X3) ),
    inference(nnf_transformation,[],[f223]) ).

fof(f749,plain,
    ! [X0] :
      ( nil = sK19(X0,nil)
      | ~ ssList(sK19(X0,nil))
      | ~ sP0(X0,nil) ),
    inference(resolution,[],[f562,f382]) ).

fof(f382,plain,
    ! [X0,X1] :
      ( segmentP(X1,sK19(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f255]) ).

fof(f562,plain,
    ! [X0] :
      ( ~ segmentP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f355]) ).

fof(f355,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f177]) ).

fof(f177,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

fof(f381,plain,
    ! [X0,X1] :
      ( neq(sK19(X0,X1),nil)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f255]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWC037+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
% 0.13/0.35  % Computer : n014.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   : Sun May 19 02:40:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (2472)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (2475)WARNING: value z3 for option sas not known
% 0.13/0.37  % (2473)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (2474)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (2476)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (2475)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)
% 0.13/0.37  % (2477)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)
% 0.13/0.37  % (2478)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)
% 0.13/0.37  % (2479)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)
% 0.13/0.39  TRYING [1]
% 0.13/0.39  TRYING [1]
% 0.13/0.39  % (2475)First to succeed.
% 0.13/0.39  % (2475)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2472"
% 0.13/0.39  TRYING [2]
% 0.13/0.39  TRYING [2]
% 0.13/0.39  % (2475)Refutation found. Thanks to Tanya!
% 0.13/0.39  % SZS status Theorem for theBenchmark
% 0.13/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.39  % (2475)------------------------------
% 0.13/0.39  % (2475)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.39  % (2475)Termination reason: Refutation
% 0.13/0.39  
% 0.13/0.39  % (2475)Memory used [KB]: 1391
% 0.13/0.39  % (2475)Time elapsed: 0.019 s
% 0.13/0.39  % (2475)Instructions burned: 29 (million)
% 0.13/0.39  % (2472)Success in time 0.038 s
%------------------------------------------------------------------------------