TSTP Solution File: COM017+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : COM017+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n032.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 10:47:05 EDT 2024

% Result   : Theorem 0.15s 0.40s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   53 (   8 unt;   0 def)
%            Number of atoms       :  390 (  27 equ)
%            Maximal formula atoms :   30 (   7 avg)
%            Number of connectives :  471 ( 134   ~; 143   |; 185   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :  108 (  75   !;  33   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1985,plain,
    $false,
    inference(subsumption_resolution,[],[f1984,f167]) ).

fof(f167,plain,
    aElement0(xv),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ( sdtmndtasgtdt0(xv,xR,xc)
    & ( ( sdtmndtplgtdt0(xv,xR,xc)
        & ( ( sdtmndtplgtdt0(sK18,xR,xc)
            & aReductOfIn0(sK18,xv,xR)
            & aElement0(sK18) )
          | aReductOfIn0(xc,xv,xR) ) )
      | xc = xv )
    & aReductOfIn0(xv,xa,xR)
    & aElement0(xv) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f21,f85]) ).

fof(f85,plain,
    ( ? [X0] :
        ( sdtmndtplgtdt0(X0,xR,xc)
        & aReductOfIn0(X0,xv,xR)
        & aElement0(X0) )
   => ( sdtmndtplgtdt0(sK18,xR,xc)
      & aReductOfIn0(sK18,xv,xR)
      & aElement0(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,axiom,
    ( sdtmndtasgtdt0(xv,xR,xc)
    & ( ( sdtmndtplgtdt0(xv,xR,xc)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xc)
              & aReductOfIn0(X0,xv,xR)
              & aElement0(X0) )
          | aReductOfIn0(xc,xv,xR) ) )
      | xc = xv )
    & aReductOfIn0(xv,xa,xR)
    & aElement0(xv) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__779) ).

fof(f1984,plain,
    ~ aElement0(xv),
    inference(subsumption_resolution,[],[f1975,f1802]) ).

fof(f1802,plain,
    ~ sP4(xu,xv),
    inference(duplicate_literal_removal,[],[f1801]) ).

fof(f1801,plain,
    ( ~ sP4(xu,xv)
    | ~ sP4(xu,xv) ),
    inference(resolution,[],[f1800,f454]) ).

fof(f454,plain,
    ! [X0] :
      ( ~ sP0(sK22(xu,X0))
      | ~ sP4(xu,X0) ),
    inference(resolution,[],[f193,f161]) ).

fof(f161,plain,
    ! [X0] :
      ( ~ sdtmndtasgtdt0(xu,xR,X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xu,xR,X0)
        & ~ sdtmndtplgtdt0(xu,xR,X0)
        & ! [X1] :
            ( ~ sdtmndtplgtdt0(X1,xR,X0)
            | ~ aReductOfIn0(X1,xu,xR)
            | ~ aElement0(X1) )
        & ~ aReductOfIn0(X0,xu,xR)
        & xu != X0 )
      | ~ sP0(X0) ),
    inference(rectify,[],[f83]) ).

fof(f83,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xu,xR,X0)
        & ~ sdtmndtplgtdt0(xu,xR,X0)
        & ! [X2] :
            ( ~ sdtmndtplgtdt0(X2,xR,X0)
            | ~ aReductOfIn0(X2,xu,xR)
            | ~ aElement0(X2) )
        & ~ aReductOfIn0(X0,xu,xR)
        & xu != X0 )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xu,xR,X0)
        & ~ sdtmndtplgtdt0(xu,xR,X0)
        & ! [X2] :
            ( ~ sdtmndtplgtdt0(X2,xR,X0)
            | ~ aReductOfIn0(X2,xu,xR)
            | ~ aElement0(X2) )
        & ~ aReductOfIn0(X0,xu,xR)
        & xu != X0 )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f193,plain,
    ! [X0,X1] :
      ( sdtmndtasgtdt0(X0,xR,sK22(X0,X1))
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ( sdtmndtasgtdt0(X0,xR,sK22(X0,X1))
        & sP3(sK22(X0,X1),X0)
        & sdtmndtasgtdt0(X1,xR,sK22(X0,X1))
        & sP2(sK22(X0,X1),X1)
        & aElement0(sK22(X0,X1)) )
      | ~ sP4(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f93,f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtmndtasgtdt0(X0,xR,X2)
          & sP3(X2,X0)
          & sdtmndtasgtdt0(X1,xR,X2)
          & sP2(X2,X1)
          & aElement0(X2) )
     => ( sdtmndtasgtdt0(X0,xR,sK22(X0,X1))
        & sP3(sK22(X0,X1),X0)
        & sdtmndtasgtdt0(X1,xR,sK22(X0,X1))
        & sP2(sK22(X0,X1),X1)
        & aElement0(sK22(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtmndtasgtdt0(X0,xR,X2)
          & sP3(X2,X0)
          & sdtmndtasgtdt0(X1,xR,X2)
          & sP2(X2,X1)
          & aElement0(X2) )
      | ~ sP4(X0,X1) ),
    inference(rectify,[],[f92]) ).

fof(f92,plain,
    ! [X5,X4] :
      ( ? [X6] :
          ( sdtmndtasgtdt0(X5,xR,X6)
          & sP3(X6,X5)
          & sdtmndtasgtdt0(X4,xR,X6)
          & sP2(X6,X4)
          & aElement0(X6) )
      | ~ sP4(X5,X4) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X5,X4] :
      ( ? [X6] :
          ( sdtmndtasgtdt0(X5,xR,X6)
          & sP3(X6,X5)
          & sdtmndtasgtdt0(X4,xR,X6)
          & sP2(X6,X4)
          & aElement0(X6) )
      | ~ sP4(X5,X4) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f1800,plain,
    ! [X0] :
      ( sP0(sK22(X0,xv))
      | ~ sP4(X0,xv) ),
    inference(subsumption_resolution,[],[f1799,f189]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( aElement0(sK22(X0,X1))
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f1799,plain,
    ! [X0] :
      ( ~ sP4(X0,xv)
      | sP0(sK22(X0,xv))
      | ~ aElement0(sK22(X0,xv)) ),
    inference(resolution,[],[f443,f162]) ).

fof(f162,plain,
    ! [X0] :
      ( sP1(X0)
      | sP0(X0)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( sP1(X0)
      | sP0(X0)
      | ~ aElement0(X0) ),
    inference(definition_folding,[],[f32,f58,f57]) ).

fof(f58,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xv,xR,X0)
        & ~ sdtmndtplgtdt0(xv,xR,X0)
        & ! [X1] :
            ( ~ sdtmndtplgtdt0(X1,xR,X0)
            | ~ aReductOfIn0(X1,xv,xR)
            | ~ aElement0(X1) )
        & ~ aReductOfIn0(X0,xv,xR)
        & xv != X0 )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f32,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xv,xR,X0)
        & ~ sdtmndtplgtdt0(xv,xR,X0)
        & ! [X1] :
            ( ~ sdtmndtplgtdt0(X1,xR,X0)
            | ~ aReductOfIn0(X1,xv,xR)
            | ~ aElement0(X1) )
        & ~ aReductOfIn0(X0,xv,xR)
        & xv != X0 )
      | ( ~ sdtmndtasgtdt0(xu,xR,X0)
        & ~ sdtmndtplgtdt0(xu,xR,X0)
        & ! [X2] :
            ( ~ sdtmndtplgtdt0(X2,xR,X0)
            | ~ aReductOfIn0(X2,xu,xR)
            | ~ aElement0(X2) )
        & ~ aReductOfIn0(X0,xu,xR)
        & xu != X0 )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ~ ? [X0] :
        ( ( sdtmndtasgtdt0(xv,xR,X0)
          | sdtmndtplgtdt0(xv,xR,X0)
          | ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,X0)
              & aReductOfIn0(X1,xv,xR)
              & aElement0(X1) )
          | aReductOfIn0(X0,xv,xR)
          | xv = X0 )
        & ( sdtmndtasgtdt0(xu,xR,X0)
          | sdtmndtplgtdt0(xu,xR,X0)
          | ? [X2] :
              ( sdtmndtplgtdt0(X2,xR,X0)
              & aReductOfIn0(X2,xu,xR)
              & aElement0(X2) )
          | aReductOfIn0(X0,xu,xR)
          | xu = X0 )
        & aElement0(X0) ),
    inference(rectify,[],[f23]) ).

fof(f23,negated_conjecture,
    ~ ? [X0] :
        ( ( sdtmndtasgtdt0(xv,xR,X0)
          | sdtmndtplgtdt0(xv,xR,X0)
          | ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,X0)
              & aReductOfIn0(X1,xv,xR)
              & aElement0(X1) )
          | aReductOfIn0(X0,xv,xR)
          | xv = X0 )
        & ( sdtmndtasgtdt0(xu,xR,X0)
          | sdtmndtplgtdt0(xu,xR,X0)
          | ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,X0)
              & aReductOfIn0(X1,xu,xR)
              & aElement0(X1) )
          | aReductOfIn0(X0,xu,xR)
          | xu = X0 )
        & aElement0(X0) ),
    inference(negated_conjecture,[],[f22]) ).

fof(f22,conjecture,
    ? [X0] :
      ( ( sdtmndtasgtdt0(xv,xR,X0)
        | sdtmndtplgtdt0(xv,xR,X0)
        | ? [X1] :
            ( sdtmndtplgtdt0(X1,xR,X0)
            & aReductOfIn0(X1,xv,xR)
            & aElement0(X1) )
        | aReductOfIn0(X0,xv,xR)
        | xv = X0 )
      & ( sdtmndtasgtdt0(xu,xR,X0)
        | sdtmndtplgtdt0(xu,xR,X0)
        | ? [X1] :
            ( sdtmndtplgtdt0(X1,xR,X0)
            & aReductOfIn0(X1,xu,xR)
            & aElement0(X1) )
        | aReductOfIn0(X0,xu,xR)
        | xu = X0 )
      & aElement0(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f443,plain,
    ! [X0] :
      ( ~ sP1(sK22(X0,xv))
      | ~ sP4(X0,xv) ),
    inference(resolution,[],[f191,f156]) ).

fof(f156,plain,
    ! [X0] :
      ( ~ sdtmndtasgtdt0(xv,xR,X0)
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xv,xR,X0)
        & ~ sdtmndtplgtdt0(xv,xR,X0)
        & ! [X1] :
            ( ~ sdtmndtplgtdt0(X1,xR,X0)
            | ~ aReductOfIn0(X1,xv,xR)
            | ~ aElement0(X1) )
        & ~ aReductOfIn0(X0,xv,xR)
        & xv != X0 )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f58]) ).

fof(f191,plain,
    ! [X0,X1] :
      ( sdtmndtasgtdt0(X1,xR,sK22(X0,X1))
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f1975,plain,
    ( sP4(xu,xv)
    | ~ aElement0(xv) ),
    inference(resolution,[],[f1642,f168]) ).

fof(f168,plain,
    aReductOfIn0(xv,xa,xR),
    inference(cnf_transformation,[],[f86]) ).

fof(f1642,plain,
    ! [X0] :
      ( ~ aReductOfIn0(X0,xa,xR)
      | sP4(xu,X0)
      | ~ aElement0(X0) ),
    inference(subsumption_resolution,[],[f1641,f164]) ).

fof(f164,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ( aElement0(xc)
    & aElement0(xb)
    & aElement0(xa) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).

fof(f1641,plain,
    ! [X0] :
      ( sP4(xu,X0)
      | ~ aReductOfIn0(X0,xa,xR)
      | ~ aElement0(X0)
      | ~ aElement0(xa) ),
    inference(subsumption_resolution,[],[f1628,f174]) ).

fof(f174,plain,
    aElement0(xu),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ( sdtmndtasgtdt0(xu,xR,xb)
    & ( ( sdtmndtplgtdt0(xu,xR,xb)
        & ( ( sdtmndtplgtdt0(sK19,xR,xb)
            & aReductOfIn0(sK19,xu,xR)
            & aElement0(sK19) )
          | aReductOfIn0(xb,xu,xR) ) )
      | xb = xu )
    & aReductOfIn0(xu,xa,xR)
    & aElement0(xu) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f20,f87]) ).

fof(f87,plain,
    ( ? [X0] :
        ( sdtmndtplgtdt0(X0,xR,xb)
        & aReductOfIn0(X0,xu,xR)
        & aElement0(X0) )
   => ( sdtmndtplgtdt0(sK19,xR,xb)
      & aReductOfIn0(sK19,xu,xR)
      & aElement0(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,axiom,
    ( sdtmndtasgtdt0(xu,xR,xb)
    & ( ( sdtmndtplgtdt0(xu,xR,xb)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xb)
              & aReductOfIn0(X0,xu,xR)
              & aElement0(X0) )
          | aReductOfIn0(xb,xu,xR) ) )
      | xb = xu )
    & aReductOfIn0(xu,xa,xR)
    & aElement0(xu) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).

fof(f1628,plain,
    ! [X0] :
      ( sP4(xu,X0)
      | ~ aReductOfIn0(X0,xa,xR)
      | ~ aElement0(xu)
      | ~ aElement0(X0)
      | ~ aElement0(xa) ),
    inference(resolution,[],[f202,f175]) ).

fof(f175,plain,
    aReductOfIn0(xu,xa,xR),
    inference(cnf_transformation,[],[f88]) ).

fof(f202,plain,
    ! [X3,X4,X5] :
      ( ~ aReductOfIn0(X5,X3,xR)
      | sP4(X5,X4)
      | ~ aReductOfIn0(X4,X3,xR)
      | ~ aElement0(X5)
      | ~ aElement0(X4)
      | ~ aElement0(X3) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( sP4(X5,X4)
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(definition_folding,[],[f34,f62,f61,f60]) ).

fof(f60,plain,
    ! [X6,X4] :
      ( ( sdtmndtplgtdt0(X4,xR,X6)
        & ( ? [X8] :
              ( sdtmndtplgtdt0(X8,xR,X6)
              & aReductOfIn0(X8,X4,xR)
              & aElement0(X8) )
          | aReductOfIn0(X6,X4,xR) ) )
      | X4 = X6
      | ~ sP2(X6,X4) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f61,plain,
    ! [X6,X5] :
      ( ( sdtmndtplgtdt0(X5,xR,X6)
        & ( ? [X7] :
              ( sdtmndtplgtdt0(X7,xR,X6)
              & aReductOfIn0(X7,X5,xR)
              & aElement0(X7) )
          | aReductOfIn0(X6,X5,xR) ) )
      | X5 = X6
      | ~ sP3(X6,X5) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f34,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | X5 = X6 )
            & sdtmndtasgtdt0(X4,xR,X6)
            & ( ( sdtmndtplgtdt0(X4,xR,X6)
                & ( ? [X8] :
                      ( sdtmndtplgtdt0(X8,xR,X6)
                      & aReductOfIn0(X8,X4,xR)
                      & aElement0(X8) )
                  | aReductOfIn0(X6,X4,xR) ) )
              | X4 = X6 )
            & aElement0(X6) )
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(flattening,[],[f33]) ).

fof(f33,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | X5 = X6 )
            & sdtmndtasgtdt0(X4,xR,X6)
            & ( ( sdtmndtplgtdt0(X4,xR,X6)
                & ( ? [X8] :
                      ( sdtmndtplgtdt0(X8,xR,X6)
                      & aReductOfIn0(X8,X4,xR)
                      & aElement0(X8) )
                  | aReductOfIn0(X6,X4,xR) ) )
              | X4 = X6 )
            & aElement0(X6) )
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( ( aElement0(X1)
          & aElement0(X0) )
       => ( ( sdtmndtplgtdt0(X0,xR,X1)
            | ? [X2] :
                ( sdtmndtplgtdt0(X2,xR,X1)
                & aReductOfIn0(X2,X0,xR)
                & aElement0(X2) )
            | aReductOfIn0(X1,X0,xR) )
         => iLess0(X1,X0) ) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ( aReductOfIn0(X5,X3,xR)
          & aReductOfIn0(X4,X3,xR)
          & aElement0(X5)
          & aElement0(X4)
          & aElement0(X3) )
       => ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | X5 = X6 )
            & sdtmndtasgtdt0(X4,xR,X6)
            & ( ( sdtmndtplgtdt0(X4,xR,X6)
                & ( ? [X8] :
                      ( sdtmndtplgtdt0(X8,xR,X6)
                      & aReductOfIn0(X8,X4,xR)
                      & aElement0(X8) )
                  | aReductOfIn0(X6,X4,xR) ) )
              | X4 = X6 )
            & aElement0(X6) ) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( ( aElement0(X1)
          & aElement0(X0) )
       => ( ( sdtmndtplgtdt0(X0,xR,X1)
            | ? [X2] :
                ( sdtmndtplgtdt0(X2,xR,X1)
                & aReductOfIn0(X2,X0,xR)
                & aElement0(X2) )
            | aReductOfIn0(X1,X0,xR) )
         => iLess0(X1,X0) ) )
    & isLocallyConfluent0(xR)
    & ! [X0,X1,X2] :
        ( ( aReductOfIn0(X2,X0,xR)
          & aReductOfIn0(X1,X0,xR)
          & aElement0(X2)
          & aElement0(X1)
          & aElement0(X0) )
       => ? [X3] :
            ( sdtmndtasgtdt0(X2,xR,X3)
            & ( ( sdtmndtplgtdt0(X2,xR,X3)
                & ( ? [X4] :
                      ( sdtmndtplgtdt0(X4,xR,X3)
                      & aReductOfIn0(X4,X2,xR)
                      & aElement0(X4) )
                  | aReductOfIn0(X3,X2,xR) ) )
              | X2 = X3 )
            & sdtmndtasgtdt0(X1,xR,X3)
            & ( ( sdtmndtplgtdt0(X1,xR,X3)
                & ( ? [X4] :
                      ( sdtmndtplgtdt0(X4,xR,X3)
                      & aReductOfIn0(X4,X1,xR)
                      & aElement0(X4) )
                  | aReductOfIn0(X3,X1,xR) ) )
              | X1 = X3 )
            & aElement0(X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : COM017+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n032.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Tue Apr 30 05:14:21 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.10/0.31  % (3206)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32  % (3210)WARNING: value z3 for option sas not known
% 0.15/0.33  % (3208)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33  % (3211)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33  % (3209)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33  % (3212)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)
% 0.15/0.33  % (3213)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)
% 0.15/0.33  % (3214)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)
% 0.15/0.33  % (3210)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)
% 0.15/0.34  TRYING [1]
% 0.15/0.34  TRYING [2]
% 0.15/0.35  TRYING [3]
% 0.15/0.37  TRYING [4]
% 0.15/0.39  % (3210)First to succeed.
% 0.15/0.40  % (3210)Refutation found. Thanks to Tanya!
% 0.15/0.40  % SZS status Theorem for theBenchmark
% 0.15/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40  % (3210)------------------------------
% 0.15/0.40  % (3210)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40  % (3210)Termination reason: Refutation
% 0.15/0.40  
% 0.15/0.40  % (3210)Memory used [KB]: 1839
% 0.15/0.40  % (3210)Time elapsed: 0.069 s
% 0.15/0.40  % (3210)Instructions burned: 134 (million)
% 0.15/0.40  % (3210)------------------------------
% 0.15/0.40  % (3210)------------------------------
% 0.15/0.40  % (3206)Success in time 0.085 s
%------------------------------------------------------------------------------