TSTP Solution File: RNG118+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : RNG118+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 : Fri May  3 02:57:44 EDT 2024

% Result   : Theorem 57.79s 8.20s
% Output   : CNFRefutation 57.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  104 (  17 unt;   0 def)
%            Number of atoms       :  404 ( 142 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  496 ( 196   ~; 200   |;  79   &)
%                                         (   3 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   5 con; 0-2 aty)
%            Number of variables   :  159 (   0 sgn  77   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aElement0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

fof(f16,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aElement0(X0) )
     => ( sz00 = sdtasdt0(X0,X1)
       => ( sz00 = X1
          | sz00 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).

fof(f20,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aElementOf0(X1,X0)
         => aElement0(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

fof(f24,axiom,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElement0(X2)
                 => aElementOf0(sdtasdt0(X2,X1),X0) )
              & ! [X2] :
                  ( aElementOf0(X2,X0)
                 => aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
        & aSet0(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( ( sz00 != X1
        & aElement0(X1)
        & aElement0(X0) )
     => ? [X2,X3] :
          ( ( sz00 != X3
           => iLess0(sbrdtbr0(X3),sbrdtbr0(X1)) )
          & sdtpldt0(sdtasdt0(X2,X1),X3) = X0
          & aElement0(X3)
          & aElement0(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivision) ).

fof(f39,axiom,
    ( aElement0(xb)
    & aElement0(xa) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).

fof(f42,axiom,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & aIdeal0(xI) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).

fof(f45,axiom,
    ( ! [X0] :
        ( ( sz00 != X0
          & aElementOf0(X0,xI) )
       => ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
    & sz00 != xu
    & aElementOf0(xu,xI) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).

fof(f50,conjecture,
    ? [X0,X1] :
      ( ( iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
        | sz00 = X1 )
      & xb = sdtpldt0(sdtasdt0(X0,xu),X1)
      & aElement0(X1)
      & aElement0(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f51,negated_conjecture,
    ~ ? [X0,X1] :
        ( ( iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
          | sz00 = X1 )
        & xb = sdtpldt0(sdtasdt0(X0,xu),X1)
        & aElement0(X1)
        & aElement0(X0) ),
    inference(negated_conjecture,[],[f50]) ).

fof(f55,plain,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElement0(X2)
                 => aElementOf0(sdtasdt0(X2,X1),X0) )
              & ! [X3] :
                  ( aElementOf0(X3,X0)
                 => aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
        & aSet0(X0) ) ),
    inference(rectify,[],[f24]) ).

fof(f79,plain,
    ! [X0] :
      ( ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f80]) ).

fof(f82,plain,
    ! [X0] :
      ( ! [X1] :
          ( aElement0(X1)
          | ~ aElementOf0(X1,X0) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f89,plain,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( ( ! [X2] :
                  ( aElementOf0(sdtasdt0(X2,X1),X0)
                  | ~ aElement0(X2) )
              & ! [X3] :
                  ( aElementOf0(sdtpldt0(X1,X3),X0)
                  | ~ aElementOf0(X3,X0) ) )
            | ~ aElementOf0(X1,X0) )
        & aSet0(X0) ) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
            | sz00 = X3 )
          & sdtpldt0(sdtasdt0(X2,X1),X3) = X0
          & aElement0(X3)
          & aElement0(X2) )
      | sz00 = X1
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
            | sz00 = X3 )
          & sdtpldt0(sdtasdt0(X2,X1),X3) = X0
          & aElement0(X3)
          & aElement0(X2) )
      | sz00 = X1
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f98]) ).

fof(f109,plain,
    ( ! [X0] :
        ( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
        | sz00 = X0
        | ~ aElementOf0(X0,xI) )
    & sz00 != xu
    & aElementOf0(xu,xI) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f110,plain,
    ( ! [X0] :
        ( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
        | sz00 = X0
        | ~ aElementOf0(X0,xI) )
    & sz00 != xu
    & aElementOf0(xu,xI) ),
    inference(flattening,[],[f109]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
        & sz00 != X1 )
      | xb != sdtpldt0(sdtasdt0(X0,xu),X1)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f132,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X1] :
              ( ( ! [X2] :
                    ( aElementOf0(sdtasdt0(X2,X1),X0)
                    | ~ aElement0(X2) )
                & ! [X3] :
                    ( aElementOf0(sdtpldt0(X1,X3),X0)
                    | ~ aElementOf0(X3,X0) ) )
              | ~ aElementOf0(X1,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(nnf_transformation,[],[f89]) ).

fof(f133,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X1] :
              ( ( ! [X2] :
                    ( aElementOf0(sdtasdt0(X2,X1),X0)
                    | ~ aElement0(X2) )
                & ! [X3] :
                    ( aElementOf0(sdtpldt0(X1,X3),X0)
                    | ~ aElementOf0(X3,X0) ) )
              | ~ aElementOf0(X1,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(flattening,[],[f132]) ).

fof(f134,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X4] :
              ( ( ! [X5] :
                    ( aElementOf0(sdtasdt0(X5,X4),X0)
                    | ~ aElement0(X5) )
                & ! [X6] :
                    ( aElementOf0(sdtpldt0(X4,X6),X0)
                    | ~ aElementOf0(X6,X0) ) )
              | ~ aElementOf0(X4,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(rectify,[],[f133]) ).

fof(f135,plain,
    ! [X0] :
      ( ? [X1] :
          ( ( ? [X2] :
                ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                & aElement0(X2) )
            | ? [X3] :
                ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                & aElementOf0(X3,X0) ) )
          & aElementOf0(X1,X0) )
     => ( ( ? [X2] :
              ( ~ aElementOf0(sdtasdt0(X2,sK10(X0)),X0)
              & aElement0(X2) )
          | ? [X3] :
              ( ~ aElementOf0(sdtpldt0(sK10(X0),X3),X0)
              & aElementOf0(X3,X0) ) )
        & aElementOf0(sK10(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ! [X0] :
      ( ? [X2] :
          ( ~ aElementOf0(sdtasdt0(X2,sK10(X0)),X0)
          & aElement0(X2) )
     => ( ~ aElementOf0(sdtasdt0(sK11(X0),sK10(X0)),X0)
        & aElement0(sK11(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f137,plain,
    ! [X0] :
      ( ? [X3] :
          ( ~ aElementOf0(sdtpldt0(sK10(X0),X3),X0)
          & aElementOf0(X3,X0) )
     => ( ~ aElementOf0(sdtpldt0(sK10(X0),sK12(X0)),X0)
        & aElementOf0(sK12(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f138,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ( ( ( ~ aElementOf0(sdtasdt0(sK11(X0),sK10(X0)),X0)
              & aElement0(sK11(X0)) )
            | ( ~ aElementOf0(sdtpldt0(sK10(X0),sK12(X0)),X0)
              & aElementOf0(sK12(X0),X0) ) )
          & aElementOf0(sK10(X0),X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X4] :
              ( ( ! [X5] :
                    ( aElementOf0(sdtasdt0(X5,X4),X0)
                    | ~ aElement0(X5) )
                & ! [X6] :
                    ( aElementOf0(sdtpldt0(X4,X6),X0)
                    | ~ aElementOf0(X6,X0) ) )
              | ~ aElementOf0(X4,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f134,f137,f136,f135]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( ( iLess0(sbrdtbr0(X3),sbrdtbr0(X1))
            | sz00 = X3 )
          & sdtpldt0(sdtasdt0(X2,X1),X3) = X0
          & aElement0(X3)
          & aElement0(X2) )
     => ( ( iLess0(sbrdtbr0(sK16(X0,X1)),sbrdtbr0(X1))
          | sz00 = sK16(X0,X1) )
        & sdtpldt0(sdtasdt0(sK15(X0,X1),X1),sK16(X0,X1)) = X0
        & aElement0(sK16(X0,X1))
        & aElement0(sK15(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( ( ( iLess0(sbrdtbr0(sK16(X0,X1)),sbrdtbr0(X1))
          | sz00 = sK16(X0,X1) )
        & sdtpldt0(sdtasdt0(sK15(X0,X1),X1),sK16(X0,X1)) = X0
        & aElement0(sK16(X0,X1))
        & aElement0(sK15(X0,X1)) )
      | sz00 = X1
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f99,f144]) ).

fof(f169,plain,
    aElement0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f188,plain,
    ! [X0] :
      ( sz00 = sdtasdt0(X0,sz00)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f190,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f192,plain,
    ! [X0,X1] :
      ( aElement0(X1)
      | ~ aElementOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f216,plain,
    ! [X0] :
      ( aSet0(X0)
      | ~ aIdeal0(X0) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f234,plain,
    ! [X0,X1] :
      ( aElement0(sK15(X0,X1))
      | sz00 = X1
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f235,plain,
    ! [X0,X1] :
      ( aElement0(sK16(X0,X1))
      | sz00 = X1
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f236,plain,
    ! [X0,X1] :
      ( sdtpldt0(sdtasdt0(sK15(X0,X1),X1),sK16(X0,X1)) = X0
      | sz00 = X1
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f237,plain,
    ! [X0,X1] :
      ( iLess0(sbrdtbr0(sK16(X0,X1)),sbrdtbr0(X1))
      | sz00 = sK16(X0,X1)
      | sz00 = X1
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f145]) ).

fof(f261,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f39]) ).

fof(f264,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[],[f42]) ).

fof(f272,plain,
    aElementOf0(xu,xI),
    inference(cnf_transformation,[],[f110]) ).

fof(f273,plain,
    sz00 != xu,
    inference(cnf_transformation,[],[f110]) ).

fof(f281,plain,
    ! [X0,X1] :
      ( sz00 != X1
      | xb != sdtpldt0(sdtasdt0(X0,xu),X1)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f282,plain,
    ! [X0,X1] :
      ( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
      | xb != sdtpldt0(sdtasdt0(X0,xu),X1)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f295,plain,
    ! [X0] :
      ( xb != sdtpldt0(sdtasdt0(X0,xu),sz00)
      | ~ aElement0(sz00)
      | ~ aElement0(X0) ),
    inference(equality_resolution,[],[f281]) ).

cnf(c_49,plain,
    aElement0(sz00),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_69,plain,
    ( ~ aElement0(X0)
    | sdtasdt0(X0,sz00) = sz00 ),
    inference(cnf_transformation,[],[f188]) ).

cnf(c_70,plain,
    ( sdtasdt0(X0,X1) != sz00
    | ~ aElement0(X0)
    | ~ aElement0(X1)
    | X0 = sz00
    | X1 = sz00 ),
    inference(cnf_transformation,[],[f190]) ).

cnf(c_72,plain,
    ( ~ aElementOf0(X0,X1)
    | ~ aSet0(X1)
    | aElement0(X0) ),
    inference(cnf_transformation,[],[f192]) ).

cnf(c_103,plain,
    ( ~ aIdeal0(X0)
    | aSet0(X0) ),
    inference(cnf_transformation,[],[f216]) ).

cnf(c_114,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(X1)
    | sK16(X0,X1) = sz00
    | X1 = sz00
    | iLess0(sbrdtbr0(sK16(X0,X1)),sbrdtbr0(X1)) ),
    inference(cnf_transformation,[],[f237]) ).

cnf(c_115,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(X1)
    | sdtpldt0(sdtasdt0(sK15(X0,X1),X1),sK16(X0,X1)) = X0
    | X1 = sz00 ),
    inference(cnf_transformation,[],[f236]) ).

cnf(c_116,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(X1)
    | X1 = sz00
    | aElement0(sK16(X0,X1)) ),
    inference(cnf_transformation,[],[f235]) ).

cnf(c_117,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(X1)
    | X1 = sz00
    | aElement0(sK15(X0,X1)) ),
    inference(cnf_transformation,[],[f234]) ).

cnf(c_140,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f261]) ).

cnf(c_145,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[],[f264]) ).

cnf(c_153,plain,
    sz00 != xu,
    inference(cnf_transformation,[],[f273]) ).

cnf(c_154,plain,
    aElementOf0(xu,xI),
    inference(cnf_transformation,[],[f272]) ).

cnf(c_161,negated_conjecture,
    ( sdtpldt0(sdtasdt0(X0,xu),X1) != xb
    | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu))
    | ~ aElement0(X0)
    | ~ aElement0(X1) ),
    inference(cnf_transformation,[],[f282]) ).

cnf(c_162,negated_conjecture,
    ( sdtpldt0(sdtasdt0(X0,xu),sz00) != xb
    | ~ aElement0(X0)
    | ~ aElement0(sz00) ),
    inference(cnf_transformation,[],[f295]) ).

cnf(c_170,plain,
    ( ~ aElement0(sz00)
    | sdtasdt0(sz00,sz00) = sz00 ),
    inference(instantiation,[status(thm)],[c_69]) ).

cnf(c_223,plain,
    ( sdtasdt0(sz00,sz00) != sz00
    | ~ aElement0(sz00)
    | sz00 = sz00 ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_243,plain,
    ( ~ aElement0(X0)
    | sdtpldt0(sdtasdt0(X0,xu),sz00) != xb ),
    inference(global_subsumption_just,[status(thm)],[c_162,c_49,c_162]) ).

cnf(c_244,negated_conjecture,
    ( sdtpldt0(sdtasdt0(X0,xu),sz00) != xb
    | ~ aElement0(X0) ),
    inference(renaming,[status(thm)],[c_243]) ).

cnf(c_267,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_269,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_272,plain,
    ( X0 != X1
    | X2 != X3
    | sdtpldt0(X0,X2) = sdtpldt0(X1,X3) ),
    theory(equality) ).

cnf(c_308,plain,
    ( ~ aIdeal0(xI)
    | aSet0(xI) ),
    inference(instantiation,[status(thm)],[c_103]) ).

cnf(c_327,plain,
    ( sz00 != X0
    | xu != X0
    | sz00 = xu ),
    inference(instantiation,[status(thm)],[c_269]) ).

cnf(c_328,plain,
    ( sz00 != sz00
    | xu != sz00
    | sz00 = xu ),
    inference(instantiation,[status(thm)],[c_327]) ).

cnf(c_329,plain,
    ( sdtpldt0(sdtasdt0(X0,xu),sz00) != X1
    | xb != X1
    | sdtpldt0(sdtasdt0(X0,xu),sz00) = xb ),
    inference(instantiation,[status(thm)],[c_269]) ).

cnf(c_415,plain,
    ( X0 != X1
    | xb != X1
    | xb = X0 ),
    inference(instantiation,[status(thm)],[c_269]) ).

cnf(c_894,plain,
    sdtasdt0(X0,X1) = sdtasdt0(X0,X1),
    inference(instantiation,[status(thm)],[c_267]) ).

cnf(c_918,plain,
    ( ~ aSet0(xI)
    | aElement0(xu) ),
    inference(resolution,[status(thm)],[c_72,c_154]) ).

cnf(c_1043,plain,
    ( X0 != xb
    | xb != xb
    | xb = X0 ),
    inference(instantiation,[status(thm)],[c_415]) ).

cnf(c_1044,plain,
    xb = xb,
    inference(instantiation,[status(thm)],[c_267]) ).

cnf(c_1224,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(xu)
    | sdtpldt0(sdtasdt0(sK15(X0,xu),xu),sK16(X0,xu)) = X0
    | xu = sz00 ),
    inference(instantiation,[status(thm)],[c_115]) ).

cnf(c_1227,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(xu)
    | xu = sz00
    | aElement0(sK15(X0,xu)) ),
    inference(instantiation,[status(thm)],[c_117]) ).

cnf(c_1228,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(xu)
    | xu = sz00
    | aElement0(sK16(X0,xu)) ),
    inference(instantiation,[status(thm)],[c_116]) ).

cnf(c_2859,plain,
    ( sdtpldt0(sdtasdt0(X0,xu),sz00) != sdtpldt0(X1,X2)
    | xb != sdtpldt0(X1,X2)
    | sdtpldt0(sdtasdt0(X0,xu),sz00) = xb ),
    inference(instantiation,[status(thm)],[c_329]) ).

cnf(c_2860,plain,
    ( sdtasdt0(X0,xu) != X1
    | sz00 != X2
    | sdtpldt0(sdtasdt0(X0,xu),sz00) = sdtpldt0(X1,X2) ),
    inference(instantiation,[status(thm)],[c_272]) ).

cnf(c_3535,plain,
    ( X0 != X1
    | X1 = X0 ),
    inference(resolution,[status(thm)],[c_269,c_267]) ).

cnf(c_4884,plain,
    ( sdtasdt0(X0,xu) != sdtasdt0(X1,X2)
    | sz00 != X3
    | sdtpldt0(sdtasdt0(X0,xu),sz00) = sdtpldt0(sdtasdt0(X1,X2),X3) ),
    inference(instantiation,[status(thm)],[c_2860]) ).

cnf(c_8761,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xu)
    | sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) = xb
    | xu = sz00 ),
    inference(instantiation,[status(thm)],[c_1224]) ).

cnf(c_8764,plain,
    ( sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) != xb
    | xb != xb
    | xb = sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) ),
    inference(instantiation,[status(thm)],[c_1043]) ).

cnf(c_9910,plain,
    ( sdtasdt0(X0,xu) != sdtasdt0(X0,xu)
    | sz00 != X1
    | sdtpldt0(sdtasdt0(X0,xu),sz00) = sdtpldt0(sdtasdt0(X0,xu),X1) ),
    inference(instantiation,[status(thm)],[c_4884]) ).

cnf(c_9911,plain,
    sdtasdt0(X0,xu) = sdtasdt0(X0,xu),
    inference(instantiation,[status(thm)],[c_894]) ).

cnf(c_10640,plain,
    ( sdtpldt0(sdtasdt0(X0,xu),sz00) != sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu))
    | xb != sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu))
    | sdtpldt0(sdtasdt0(X0,xu),sz00) = xb ),
    inference(instantiation,[status(thm)],[c_2859]) ).

cnf(c_14072,plain,
    ( ~ iLess0(sbrdtbr0(sK16(xb,xu)),sbrdtbr0(xu))
    | ~ aElement0(sK16(xb,xu))
    | ~ aElement0(sK15(xb,xu))
    | ~ aElement0(xb)
    | ~ aElement0(xu)
    | xu = sz00 ),
    inference(resolution,[status(thm)],[c_161,c_115]) ).

cnf(c_14087,plain,
    ( ~ aElement0(sK15(xb,xu))
    | ~ aElement0(sK16(xb,xu))
    | ~ iLess0(sbrdtbr0(sK16(xb,xu)),sbrdtbr0(xu)) ),
    inference(global_subsumption_just,[status(thm)],[c_14072,c_145,c_140,c_49,c_153,c_170,c_223,c_308,c_328,c_918,c_14072]) ).

cnf(c_14088,plain,
    ( ~ iLess0(sbrdtbr0(sK16(xb,xu)),sbrdtbr0(xu))
    | ~ aElement0(sK16(xb,xu))
    | ~ aElement0(sK15(xb,xu)) ),
    inference(renaming,[status(thm)],[c_14087]) ).

cnf(c_14109,plain,
    ( ~ aElement0(sK16(xb,xu))
    | ~ aElement0(sK15(xb,xu))
    | ~ aElement0(xb)
    | ~ aElement0(xu)
    | sK16(xb,xu) = sz00
    | xu = sz00 ),
    inference(resolution,[status(thm)],[c_14088,c_114]) ).

cnf(c_14121,plain,
    ( sK16(xb,xu) = sz00
    | ~ aElement0(sK15(xb,xu))
    | ~ aElement0(sK16(xb,xu)) ),
    inference(global_subsumption_just,[status(thm)],[c_14109,c_145,c_140,c_49,c_153,c_170,c_223,c_308,c_328,c_918,c_14109]) ).

cnf(c_14122,plain,
    ( ~ aElement0(sK16(xb,xu))
    | ~ aElement0(sK15(xb,xu))
    | sK16(xb,xu) = sz00 ),
    inference(renaming,[status(thm)],[c_14121]) ).

cnf(c_14164,plain,
    ( ~ aElement0(sK16(xb,xu))
    | ~ aElement0(sK15(xb,xu))
    | sz00 = sK16(xb,xu) ),
    inference(resolution,[status(thm)],[c_14122,c_3535]) ).

cnf(c_17594,plain,
    ( sdtasdt0(sK15(xb,xu),xu) != sdtasdt0(sK15(xb,xu),xu)
    | sz00 != sK16(xb,xu)
    | sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sz00) = sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu)) ),
    inference(instantiation,[status(thm)],[c_9910]) ).

cnf(c_17595,plain,
    ( sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sz00) != sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu))
    | xb != sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sK16(xb,xu))
    | sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sz00) = xb ),
    inference(instantiation,[status(thm)],[c_10640]) ).

cnf(c_19756,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xu)
    | xu = sz00
    | aElement0(sK16(xb,xu)) ),
    inference(instantiation,[status(thm)],[c_1228]) ).

cnf(c_29644,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xu)
    | xu = sz00
    | aElement0(sK15(xb,xu)) ),
    inference(instantiation,[status(thm)],[c_1227]) ).

cnf(c_30850,plain,
    sdtasdt0(sK15(xb,xu),xu) = sdtasdt0(sK15(xb,xu),xu),
    inference(instantiation,[status(thm)],[c_9911]) ).

cnf(c_34400,plain,
    ( sdtpldt0(sdtasdt0(sK15(xb,xu),xu),sz00) != xb
    | ~ aElement0(sK15(xb,xu)) ),
    inference(instantiation,[status(thm)],[c_244]) ).

cnf(c_34401,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_34400,c_30850,c_29644,c_19756,c_17595,c_17594,c_14164,c_8764,c_8761,c_1044,c_918,c_328,c_308,c_223,c_170,c_153,c_49,c_140,c_145]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : RNG118+1 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n014.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 : Thu May  2 21:13:32 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 57.79/8.20  % SZS status Started for theBenchmark.p
% 57.79/8.20  % SZS status Theorem for theBenchmark.p
% 57.79/8.20  
% 57.79/8.20  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 57.79/8.20  
% 57.79/8.20  ------  iProver source info
% 57.79/8.20  
% 57.79/8.20  git: date: 2024-05-02 19:28:25 +0000
% 57.79/8.20  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 57.79/8.20  git: non_committed_changes: false
% 57.79/8.20  
% 57.79/8.20  ------ Parsing...
% 57.79/8.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 57.79/8.20  
% 57.79/8.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e 
% 57.79/8.20  
% 57.79/8.20  ------ Preprocessing...
% 57.79/8.20  
% 57.79/8.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 57.79/8.20  ------ Proving...
% 57.79/8.20  ------ Problem Properties 
% 57.79/8.20  
% 57.79/8.20  
% 57.79/8.20  clauses                                 114
% 57.79/8.20  conjectures                             2
% 57.79/8.20  EPR                                     28
% 57.79/8.20  Horn                                    90
% 57.79/8.20  unary                                   21
% 57.79/8.20  binary                                  19
% 57.79/8.20  lits                                    376
% 57.79/8.20  lits eq                                 53
% 57.79/8.20  fd_pure                                 0
% 57.79/8.20  fd_pseudo                               0
% 57.79/8.20  fd_cond                                 5
% 57.79/8.20  fd_pseudo_cond                          11
% 57.79/8.20  AC symbols                              0
% 57.79/8.20  
% 57.79/8.20  ------ Input Options Time Limit: Unbounded
% 57.79/8.20  
% 57.79/8.20  
% 57.79/8.20  ------ 
% 57.79/8.20  Current options:
% 57.79/8.20  ------ 
% 57.79/8.20  
% 57.79/8.20  
% 57.79/8.20  
% 57.79/8.20  
% 57.79/8.20  ------ Proving...
% 57.79/8.20  
% 57.79/8.20  
% 57.79/8.20  % SZS status Theorem for theBenchmark.p
% 57.79/8.20  
% 57.79/8.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 57.79/8.20  
% 57.79/8.20  
%------------------------------------------------------------------------------