TSTP Solution File: SWC179+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC179+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 : n005.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 : Sun May  5 10:10:03 EDT 2024

% Result   : Theorem 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   43 (   8 unt;   0 def)
%            Number of atoms       :  307 (  94 equ)
%            Maximal formula atoms :   20 (   7 avg)
%            Number of connectives :  364 ( 100   ~;  86   |; 149   &)
%                                         (   0 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-4 aty)
%            Number of variables   :  136 (  82   !;  54   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1473,plain,
    $false,
    inference(resolution,[],[f1328,f411]) ).

fof(f411,plain,
    duplicatefreeP(nil),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,axiom,
    duplicatefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).

fof(f1328,plain,
    ~ duplicatefreeP(nil),
    inference(backward_demodulation,[],[f655,f1324]) ).

fof(f1324,plain,
    nil = sK25,
    inference(duplicate_literal_removal,[],[f1322]) ).

fof(f1322,plain,
    ( nil = sK25
    | nil = sK25 ),
    inference(resolution,[],[f1321,f403]) ).

fof(f403,plain,
    ( sP1(sK25,sK26)
    | nil = sK25 ),
    inference(cnf_transformation,[],[f267]) ).

fof(f267,plain,
    ( ( ( nil = sK25
        & nil = sK26 )
      | sP1(sK25,sK26) )
    & ~ duplicatefreeP(sK23)
    & sK23 = sK25
    & sK24 = sK26
    & ssList(sK26)
    & ssList(sK25)
    & ssList(sK24)
    & ssList(sK23) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24,sK25,sK26])],[f226,f266,f265,f264,f263]) ).

fof(f263,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X2
                        & nil = X3 )
                      | sP1(X2,X3) )
                    & ~ duplicatefreeP(X0)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | sP1(X2,X3) )
                  & ~ duplicatefreeP(sK23)
                  & sK23 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f264,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X2
                    & nil = X3 )
                  | sP1(X2,X3) )
                & ~ duplicatefreeP(sK23)
                & sK23 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil = X2
                  & nil = X3 )
                | sP1(X2,X3) )
              & ~ duplicatefreeP(sK23)
              & sK23 = X2
              & sK24 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK24) ) ),
    introduced(choice_axiom,[]) ).

fof(f265,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = X2
                & nil = X3 )
              | sP1(X2,X3) )
            & ~ duplicatefreeP(sK23)
            & sK23 = X2
            & sK24 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK25
              & nil = X3 )
            | sP1(sK25,X3) )
          & ~ duplicatefreeP(sK23)
          & sK23 = sK25
          & sK24 = X3
          & ssList(X3) )
      & ssList(sK25) ) ),
    introduced(choice_axiom,[]) ).

fof(f266,plain,
    ( ? [X3] :
        ( ( ( nil = sK25
            & nil = X3 )
          | sP1(sK25,X3) )
        & ~ duplicatefreeP(sK23)
        & sK23 = sK25
        & sK24 = X3
        & ssList(X3) )
   => ( ( ( nil = sK25
          & nil = sK26 )
        | sP1(sK25,sK26) )
      & ~ duplicatefreeP(sK23)
      & sK23 = sK25
      & sK24 = sK26
      & ssList(sK26) ) ),
    introduced(choice_axiom,[]) ).

fof(f226,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | sP1(X2,X3) )
                  & ~ duplicatefreeP(X0)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f100,f225,f224]) ).

fof(f224,plain,
    ! [X4,X5,X3,X2] :
      ( ? [X6] :
          ( ! [X7] :
              ( ~ lt(X7,X4)
              | ~ memberP(X6,X7)
              | ~ ssItem(X7) )
          & ! [X8] :
              ( ~ lt(X4,X8)
              | ~ memberP(X5,X8)
              | ~ ssItem(X8) )
          & app(app(X5,X2),X6) = X3
          & cons(X4,nil) = X2
          & ssList(X6) )
      | ~ sP0(X4,X5,X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f225,plain,
    ! [X2,X3] :
      ( ? [X4] :
          ( ? [X5] :
              ( sP0(X4,X5,X3,X2)
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP1(X2,X3) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ! [X7] :
                                    ( ~ lt(X7,X4)
                                    | ~ memberP(X6,X7)
                                    | ~ ssItem(X7) )
                                & ! [X8] :
                                    ( ~ lt(X4,X8)
                                    | ~ memberP(X5,X8)
                                    | ~ ssItem(X8) )
                                & app(app(X5,X2),X6) = X3
                                & cons(X4,nil) = X2
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & ~ duplicatefreeP(X0)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ! [X7] :
                                    ( ~ lt(X7,X4)
                                    | ~ memberP(X6,X7)
                                    | ~ ssItem(X7) )
                                & ! [X8] :
                                    ( ~ lt(X4,X8)
                                    | ~ memberP(X5,X8)
                                    | ~ ssItem(X8) )
                                & app(app(X5,X2),X6) = X3
                                & cons(X4,nil) = X2
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) ) )
                  & ~ duplicatefreeP(X0)
                  & 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)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X4] :
                            ( ssItem(X4)
                           => ! [X5] :
                                ( ssList(X5)
                               => ! [X6] :
                                    ( ssList(X6)
                                   => ( ? [X7] :
                                          ( lt(X7,X4)
                                          & memberP(X6,X7)
                                          & ssItem(X7) )
                                      | ? [X8] :
                                          ( lt(X4,X8)
                                          & memberP(X5,X8)
                                          & ssItem(X8) )
                                      | app(app(X5,X2),X6) != X3
                                      | cons(X4,nil) != X2 ) ) ) ) )
                      | duplicatefreeP(X0)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X4] :
                            ( ssItem(X4)
                           => ! [X5] :
                                ( ssList(X5)
                               => ! [X6] :
                                    ( ssList(X6)
                                   => ( ? [X8] :
                                          ( lt(X8,X4)
                                          & memberP(X6,X8)
                                          & ssItem(X8) )
                                      | ? [X7] :
                                          ( lt(X4,X7)
                                          & memberP(X5,X7)
                                          & ssItem(X7) )
                                      | app(app(X5,X2),X6) != X3
                                      | cons(X4,nil) != X2 ) ) ) ) )
                      | duplicatefreeP(X0)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( nil != X2
                        | nil != X3 )
                      & ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ! [X6] :
                                  ( ssList(X6)
                                 => ( ? [X8] :
                                        ( lt(X8,X4)
                                        & memberP(X6,X8)
                                        & ssItem(X8) )
                                    | ? [X7] :
                                        ( lt(X4,X7)
                                        & memberP(X5,X7)
                                        & ssItem(X7) )
                                    | app(app(X5,X2),X6) != X3
                                    | cons(X4,nil) != X2 ) ) ) ) )
                    | duplicatefreeP(X0)
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f1321,plain,
    ( ~ sP1(sK25,sK26)
    | nil = sK25 ),
    inference(resolution,[],[f1320,f387]) ).

fof(f387,plain,
    ! [X0,X1] :
      ( ssItem(sK20(X0,X1))
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f258]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( ( sP0(sK20(X0,X1),sK21(X0,X1),X1,X0)
        & ssList(sK21(X0,X1))
        & ssItem(sK20(X0,X1)) )
      | ~ sP1(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f255,f257,f256]) ).

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

fof(f257,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sP0(sK20(X0,X1),X3,X1,X0)
          & ssList(X3) )
     => ( sP0(sK20(X0,X1),sK21(X0,X1),X1,X0)
        & ssList(sK21(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f255,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( sP0(X2,X3,X1,X0)
              & ssList(X3) )
          & ssItem(X2) )
      | ~ sP1(X0,X1) ),
    inference(rectify,[],[f254]) ).

fof(f254,plain,
    ! [X2,X3] :
      ( ? [X4] :
          ( ? [X5] :
              ( sP0(X4,X5,X3,X2)
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP1(X2,X3) ),
    inference(nnf_transformation,[],[f225]) ).

fof(f1320,plain,
    ( ~ ssItem(sK20(sK25,sK26))
    | nil = sK25 ),
    inference(resolution,[],[f1276,f655]) ).

fof(f1276,plain,
    ( duplicatefreeP(sK25)
    | ~ ssItem(sK20(sK25,sK26))
    | nil = sK25 ),
    inference(superposition,[],[f423,f1268]) ).

fof(f1268,plain,
    ( sK25 = cons(sK20(sK25,sK26),nil)
    | nil = sK25 ),
    inference(resolution,[],[f1139,f403]) ).

fof(f1139,plain,
    ! [X0,X1] :
      ( ~ sP1(X0,X1)
      | cons(sK20(X0,X1),nil) = X0 ),
    inference(resolution,[],[f389,f391]) ).

fof(f391,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0,X1,X2,X3)
      | cons(X0,nil) = X3 ),
    inference(cnf_transformation,[],[f262]) ).

fof(f262,plain,
    ! [X0,X1,X2,X3] :
      ( ( ! [X5] :
            ( ~ lt(X5,X0)
            | ~ memberP(sK22(X0,X1,X2,X3),X5)
            | ~ ssItem(X5) )
        & ! [X6] :
            ( ~ lt(X0,X6)
            | ~ memberP(X1,X6)
            | ~ ssItem(X6) )
        & app(app(X1,X3),sK22(X0,X1,X2,X3)) = X2
        & cons(X0,nil) = X3
        & ssList(sK22(X0,X1,X2,X3)) )
      | ~ sP0(X0,X1,X2,X3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f260,f261]) ).

fof(f261,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4] :
          ( ! [X5] :
              ( ~ lt(X5,X0)
              | ~ memberP(X4,X5)
              | ~ ssItem(X5) )
          & ! [X6] :
              ( ~ lt(X0,X6)
              | ~ memberP(X1,X6)
              | ~ ssItem(X6) )
          & app(app(X1,X3),X4) = X2
          & cons(X0,nil) = X3
          & ssList(X4) )
     => ( ! [X5] :
            ( ~ lt(X5,X0)
            | ~ memberP(sK22(X0,X1,X2,X3),X5)
            | ~ ssItem(X5) )
        & ! [X6] :
            ( ~ lt(X0,X6)
            | ~ memberP(X1,X6)
            | ~ ssItem(X6) )
        & app(app(X1,X3),sK22(X0,X1,X2,X3)) = X2
        & cons(X0,nil) = X3
        & ssList(sK22(X0,X1,X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f260,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4] :
          ( ! [X5] :
              ( ~ lt(X5,X0)
              | ~ memberP(X4,X5)
              | ~ ssItem(X5) )
          & ! [X6] :
              ( ~ lt(X0,X6)
              | ~ memberP(X1,X6)
              | ~ ssItem(X6) )
          & app(app(X1,X3),X4) = X2
          & cons(X0,nil) = X3
          & ssList(X4) )
      | ~ sP0(X0,X1,X2,X3) ),
    inference(rectify,[],[f259]) ).

fof(f259,plain,
    ! [X4,X5,X3,X2] :
      ( ? [X6] :
          ( ! [X7] :
              ( ~ lt(X7,X4)
              | ~ memberP(X6,X7)
              | ~ ssItem(X7) )
          & ! [X8] :
              ( ~ lt(X4,X8)
              | ~ memberP(X5,X8)
              | ~ ssItem(X8) )
          & app(app(X5,X2),X6) = X3
          & cons(X4,nil) = X2
          & ssList(X6) )
      | ~ sP0(X4,X5,X3,X2) ),
    inference(nnf_transformation,[],[f224]) ).

fof(f389,plain,
    ! [X0,X1] :
      ( sP0(sK20(X0,X1),sK21(X0,X1),X1,X0)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f258]) ).

fof(f423,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f71]) ).

fof(f71,axiom,
    ! [X0] :
      ( ssItem(X0)
     => duplicatefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).

fof(f655,plain,
    ~ duplicatefreeP(sK25),
    inference(forward_demodulation,[],[f401,f400]) ).

fof(f400,plain,
    sK23 = sK25,
    inference(cnf_transformation,[],[f267]) ).

fof(f401,plain,
    ~ duplicatefreeP(sK23),
    inference(cnf_transformation,[],[f267]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC179+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 20:30:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (32127)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (32130)WARNING: value z3 for option sas not known
% 0.20/0.37  % (32133)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)
% 0.20/0.37  % (32132)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)
% 0.20/0.37  % (32130)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)
% 0.20/0.37  % (32134)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)
% 0.20/0.37  % (32129)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37  % (32131)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37  % (32128)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.39  TRYING [1]
% 0.20/0.39  TRYING [2]
% 0.20/0.39  TRYING [1]
% 0.20/0.39  TRYING [2]
% 0.20/0.39  TRYING [1]
% 0.20/0.40  TRYING [2]
% 0.20/0.40  TRYING [3]
% 0.20/0.40  TRYING [3]
% 0.20/0.40  TRYING [3]
% 0.20/0.41  % (32133)First to succeed.
% 0.20/0.41  % (32133)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-32127"
% 0.20/0.41  % (32133)Refutation found. Thanks to Tanya!
% 0.20/0.41  % SZS status Theorem for theBenchmark
% 0.20/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.41  % (32133)------------------------------
% 0.20/0.41  % (32133)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.41  % (32133)Termination reason: Refutation
% 0.20/0.41  
% 0.20/0.41  % (32133)Memory used [KB]: 1930
% 0.20/0.41  % (32133)Time elapsed: 0.038 s
% 0.20/0.41  % (32133)Instructions burned: 78 (million)
% 0.20/0.41  % (32127)Success in time 0.055 s
%------------------------------------------------------------------------------