TSTP Solution File: SWC068+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC068+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n029.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 Apr 30 15:49:44 EDT 2024

% Result   : Theorem 1.85s 0.62s
% Output   : Refutation 1.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   57 (  19 unt;   0 def)
%            Number of atoms       :  294 (  98 equ)
%            Maximal formula atoms :   26 (   5 avg)
%            Number of connectives :  393 ( 156   ~; 129   |;  85   &)
%                                         (   2 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   83 (  57   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7132,plain,
    $false,
    inference(trivial_inequality_removal,[],[f7131]) ).

fof(f7131,plain,
    nil != nil,
    inference(superposition,[],[f5641,f4480]) ).

fof(f4480,plain,
    nil = sK19,
    inference(resolution,[],[f4422,f391]) ).

fof(f391,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f4422,plain,
    ( ~ ssList(nil)
    | nil = sK19 ),
    inference(resolution,[],[f4421,f636]) ).

fof(f636,plain,
    ssList(sK19),
    inference(forward_demodulation,[],[f377,f379]) ).

fof(f379,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ( ( nil != sK18
      | nil != sK19 )
    & ! [X4] :
        ( ~ segmentP(sK18,X4)
        | ~ segmentP(sK19,X4)
        | ~ neq(X4,nil)
        | ~ ssList(X4) )
    & sK18 = sK20
    & sK19 = sK21
    & sK20 = app(sK21,sK21)
    & ssList(sK21)
    & ssList(sK20)
    & ssList(sK19)
    & ssList(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f99,f253,f252,f251,f250]) ).

fof(f250,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( nil != X0
                      | nil != X1 )
                    & ! [X4] :
                        ( ~ segmentP(X0,X4)
                        | ~ segmentP(X1,X4)
                        | ~ neq(X4,nil)
                        | ~ ssList(X4) )
                    & X0 = X2
                    & X1 = X3
                    & app(X3,X3) = X2
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( nil != sK18
                    | nil != X1 )
                  & ! [X4] :
                      ( ~ segmentP(sK18,X4)
                      | ~ segmentP(X1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & sK18 = X2
                  & X1 = X3
                  & app(X3,X3) = X2
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f251,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( nil != sK18
                  | nil != X1 )
                & ! [X4] :
                    ( ~ segmentP(sK18,X4)
                    | ~ segmentP(X1,X4)
                    | ~ neq(X4,nil)
                    | ~ ssList(X4) )
                & sK18 = X2
                & X1 = X3
                & app(X3,X3) = X2
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( nil != sK18
                | nil != sK19 )
              & ! [X4] :
                  ( ~ segmentP(sK18,X4)
                  | ~ segmentP(sK19,X4)
                  | ~ neq(X4,nil)
                  | ~ ssList(X4) )
              & sK18 = X2
              & sK19 = X3
              & app(X3,X3) = X2
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( nil != sK18
              | nil != sK19 )
            & ! [X4] :
                ( ~ segmentP(sK18,X4)
                | ~ segmentP(sK19,X4)
                | ~ neq(X4,nil)
                | ~ ssList(X4) )
            & sK18 = X2
            & sK19 = X3
            & app(X3,X3) = X2
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( nil != sK18
            | nil != sK19 )
          & ! [X4] :
              ( ~ segmentP(sK18,X4)
              | ~ segmentP(sK19,X4)
              | ~ neq(X4,nil)
              | ~ ssList(X4) )
          & sK18 = sK20
          & sK19 = X3
          & app(X3,X3) = sK20
          & ssList(X3) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X3] :
        ( ( nil != sK18
          | nil != sK19 )
        & ! [X4] :
            ( ~ segmentP(sK18,X4)
            | ~ segmentP(sK19,X4)
            | ~ neq(X4,nil)
            | ~ ssList(X4) )
        & sK18 = sK20
        & sK19 = X3
        & app(X3,X3) = sK20
        & ssList(X3) )
   => ( ( nil != sK18
        | nil != sK19 )
      & ! [X4] :
          ( ~ segmentP(sK18,X4)
          | ~ segmentP(sK19,X4)
          | ~ neq(X4,nil)
          | ~ ssList(X4) )
      & sK18 = sK20
      & sK19 = sK21
      & sK20 = app(sK21,sK21)
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

fof(f377,plain,
    ssList(sK21),
    inference(cnf_transformation,[],[f254]) ).

fof(f4421,plain,
    ( ~ ssList(sK19)
    | ~ ssList(nil)
    | nil = sK19 ),
    inference(duplicate_literal_removal,[],[f4418]) ).

fof(f4418,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK19)
    | nil = sK19
    | ~ ssList(sK19) ),
    inference(resolution,[],[f4417,f450]) ).

fof(f450,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).

fof(f4417,plain,
    ( ~ segmentP(sK19,sK19)
    | ~ ssList(nil)
    | ~ ssList(sK19)
    | nil = sK19 ),
    inference(duplicate_literal_removal,[],[f4408]) ).

fof(f4408,plain,
    ( ~ segmentP(sK19,sK19)
    | ~ ssList(nil)
    | ~ ssList(sK19)
    | ~ ssList(sK19)
    | ~ ssList(sK19)
    | nil = sK19
    | ~ ssList(nil) ),
    inference(resolution,[],[f4404,f958]) ).

fof(f958,plain,
    ( ~ segmentP(sK18,sK19)
    | ~ ssList(sK19)
    | nil = sK19
    | ~ ssList(nil) ),
    inference(duplicate_literal_removal,[],[f955]) ).

fof(f955,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK19)
    | nil = sK19
    | ~ segmentP(sK18,sK19)
    | ~ ssList(sK19) ),
    inference(resolution,[],[f949,f450]) ).

fof(f949,plain,
    ! [X0] :
      ( ~ segmentP(sK19,X0)
      | ~ ssList(nil)
      | ~ ssList(X0)
      | nil = X0
      | ~ segmentP(sK18,X0) ),
    inference(duplicate_literal_removal,[],[f948]) ).

fof(f948,plain,
    ! [X0] :
      ( nil = X0
      | ~ ssList(nil)
      | ~ ssList(X0)
      | ~ segmentP(sK19,X0)
      | ~ segmentP(sK18,X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f571,f381]) ).

fof(f381,plain,
    ! [X4] :
      ( ~ neq(X4,nil)
      | ~ segmentP(sK19,X4)
      | ~ segmentP(sK18,X4)
      | ~ ssList(X4) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f571,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f355]) ).

fof(f355,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(f4404,plain,
    ! [X0] :
      ( segmentP(sK18,X0)
      | ~ segmentP(sK19,X0)
      | ~ ssList(nil)
      | ~ ssList(sK19)
      | ~ ssList(X0) ),
    inference(superposition,[],[f4384,f639]) ).

fof(f639,plain,
    sK18 = app(sK18,nil),
    inference(resolution,[],[f453,f637]) ).

fof(f637,plain,
    ssList(sK18),
    inference(forward_demodulation,[],[f376,f380]) ).

fof(f380,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f254]) ).

fof(f376,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f254]) ).

fof(f453,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

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

fof(f4384,plain,
    ! [X0,X1] :
      ( segmentP(app(sK18,X0),X1)
      | ~ segmentP(sK19,X1)
      | ~ ssList(X0)
      | ~ ssList(sK19)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f4375]) ).

fof(f4375,plain,
    ! [X0,X1] :
      ( segmentP(app(sK18,X0),X1)
      | ~ segmentP(sK19,X1)
      | ~ ssList(X0)
      | ~ ssList(sK19)
      | ~ ssList(X1)
      | ~ ssList(sK19) ),
    inference(superposition,[],[f596,f635]) ).

fof(f635,plain,
    sK18 = app(sK19,sK19),
    inference(forward_demodulation,[],[f634,f380]) ).

fof(f634,plain,
    sK20 = app(sK19,sK19),
    inference(forward_demodulation,[],[f378,f379]) ).

fof(f378,plain,
    sK20 = app(sK21,sK21),
    inference(cnf_transformation,[],[f254]) ).

fof(f596,plain,
    ! [X2,X3,X0,X1] :
      ( segmentP(app(app(X2,X0),X3),X1)
      | ~ segmentP(X0,X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f222]) ).

fof(f222,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( segmentP(app(app(X2,X0),X3),X1)
                  | ~ segmentP(X0,X1)
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f221]) ).

fof(f221,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( segmentP(app(app(X2,X0),X3),X1)
                  | ~ segmentP(X0,X1)
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f56,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( segmentP(X0,X1)
                   => segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).

fof(f5641,plain,
    nil != sK19,
    inference(trivial_inequality_removal,[],[f5226]) ).

fof(f5226,plain,
    ( nil != nil
    | nil != sK19 ),
    inference(backward_demodulation,[],[f382,f5224]) ).

fof(f5224,plain,
    nil = sK18,
    inference(forward_demodulation,[],[f4483,f638]) ).

fof(f638,plain,
    nil = app(nil,nil),
    inference(resolution,[],[f453,f391]) ).

fof(f4483,plain,
    sK18 = app(nil,nil),
    inference(backward_demodulation,[],[f635,f4480]) ).

fof(f382,plain,
    ( nil != sK19
    | nil != sK18 ),
    inference(cnf_transformation,[],[f254]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SWC068+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n029.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 04:32:50 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (29622)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (29625)WARNING: value z3 for option sas not known
% 0.15/0.38  % (29626)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (29624)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (29623)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (29628)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)
% 0.15/0.38  % (29627)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)
% 0.15/0.38  % (29625)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)
% 0.15/0.38  % (29629)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)
% 0.15/0.40  TRYING [1]
% 0.15/0.40  TRYING [1]
% 0.15/0.40  TRYING [2]
% 0.15/0.40  TRYING [2]
% 0.21/0.41  TRYING [3]
% 0.21/0.41  TRYING [3]
% 0.21/0.46  TRYING [4]
% 0.21/0.47  TRYING [4]
% 0.21/0.50  TRYING [1]
% 0.21/0.51  TRYING [2]
% 0.21/0.51  TRYING [3]
% 0.21/0.55  TRYING [4]
% 0.21/0.57  TRYING [5]
% 0.21/0.57  TRYING [5]
% 1.85/0.62  % (29628)First to succeed.
% 1.85/0.62  % (29628)Refutation found. Thanks to Tanya!
% 1.85/0.62  % SZS status Theorem for theBenchmark
% 1.85/0.62  % SZS output start Proof for theBenchmark
% See solution above
% 1.85/0.62  % (29628)------------------------------
% 1.85/0.62  % (29628)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.85/0.62  % (29628)Termination reason: Refutation
% 1.85/0.62  
% 1.85/0.62  % (29628)Memory used [KB]: 4785
% 1.85/0.62  % (29628)Time elapsed: 0.237 s
% 1.85/0.62  % (29628)Instructions burned: 601 (million)
% 1.85/0.62  % (29628)------------------------------
% 1.85/0.62  % (29628)------------------------------
% 1.85/0.62  % (29622)Success in time 0.246 s
%------------------------------------------------------------------------------