TSTP Solution File: RNG122+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : RNG122+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 02:39:03 EST 2010

% Result   : Theorem 3.73s
% Output   : CNFRefutation 3.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   60
%            Number of leaves      :   21
% Syntax   : Number of formulae    :  209 (  33 unt;   0 def)
%            Number of atoms       :  656 ( 190 equ)
%            Maximal formula atoms :   29 (   3 avg)
%            Number of connectives :  761 ( 314   ~; 349   |;  79   &)
%                                         (   1 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   8 con; 0-2 aty)
%            Number of variables   :  201 (   3 sgn 104   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mEOfElem) ).

fof(3,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtasdt0(X1,sz00) = sz00
        & sz00 = sdtasdt0(sz00,X1) ) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mMulZero) ).

fof(4,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mAddComm) ).

fof(8,axiom,
    ! [X1,X2,X3] :
      ( ( aElement0(X1)
        & aElement0(X2)
        & aElement0(X3) )
     => ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
        & sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mAMDistr) ).

fof(12,axiom,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( aElementOf0(X1,xI)
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',m__2273) ).

fof(13,axiom,
    ( aElement0(xq)
    & aElement0(xr)
    & xb = sdtpldt0(sdtasdt0(xq,xu),xr)
    & ( xr = sz00
      | iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',m__2666) ).

fof(18,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtasdt0(X1,sz10) = X1
        & X1 = sdtasdt0(sz10,X1) ) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mMulUnit) ).

fof(21,axiom,
    ! [X1,X2,X3] :
      ( ( aElement0(X1)
        & aElement0(X2)
        & aElement0(X3) )
     => sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mAddAsso) ).

fof(27,axiom,
    aElement0(sz10),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mSortsC_01) ).

fof(28,axiom,
    ( aIdeal0(xI)
    & xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',m__2174) ).

fof(29,axiom,
    ! [X1] :
      ( aIdeal0(X1)
    <=> ( aSet0(X1)
        & ! [X2] :
            ( aElementOf0(X2,X1)
           => ( ! [X3] :
                  ( aElementOf0(X3,X1)
                 => aElementOf0(sdtpldt0(X2,X3),X1) )
              & ! [X3] :
                  ( aElement0(X3)
                 => aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mDefIdeal) ).

fof(31,axiom,
    ! [X1,X2,X3] :
      ( ( aElement0(X1)
        & aElement0(X2)
        & aElement0(X3) )
     => sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mMulAsso) ).

fof(33,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtpldt0(X1,smndt0(X1)) = sz00
        & sz00 = sdtpldt0(smndt0(X1),X1) ) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mAddInvr) ).

fof(34,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => aElement0(sdtasdt0(X1,X2)) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mSortsB_02) ).

fof(36,axiom,
    aElement0(sz00),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mSortsC) ).

fof(40,axiom,
    ( aElement0(xa)
    & aElement0(xb) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',m__2091) ).

fof(42,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mAddZero) ).

fof(43,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aElement0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mMulComm) ).

fof(47,axiom,
    aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',m__2690) ).

fof(50,axiom,
    ! [X1] :
      ( aElement0(X1)
     => aElement0(smndt0(X1)) ),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',mSortsU) ).

fof(53,conjecture,
    xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    file('/tmp/tmpqzSbcQ/sel_RNG122+1.p_1',m__) ).

fof(55,negated_conjecture,
    xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    inference(assume_negation,[status(cth)],[53]) ).

fof(57,plain,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ( aElementOf0(X1,xI)
          & X1 != sz00 )
       => ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).

fof(59,negated_conjecture,
    xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    inference(fof_simplification,[status(thm)],[55,theory(equality)]) ).

fof(60,plain,
    ! [X1] :
      ( ~ aSet0(X1)
      | ! [X2] :
          ( ~ aElementOf0(X2,X1)
          | aElement0(X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(61,plain,
    ! [X3] :
      ( ~ aSet0(X3)
      | ! [X4] :
          ( ~ aElementOf0(X4,X3)
          | aElement0(X4) ) ),
    inference(variable_rename,[status(thm)],[60]) ).

fof(62,plain,
    ! [X3,X4] :
      ( ~ aElementOf0(X4,X3)
      | aElement0(X4)
      | ~ aSet0(X3) ),
    inference(shift_quantors,[status(thm)],[61]) ).

cnf(63,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[62]) ).

fof(67,plain,
    ! [X1] :
      ( ~ aElement0(X1)
      | ( sdtasdt0(X1,sz00) = sz00
        & sz00 = sdtasdt0(sz00,X1) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(68,plain,
    ! [X2] :
      ( ~ aElement0(X2)
      | ( sdtasdt0(X2,sz00) = sz00
        & sz00 = sdtasdt0(sz00,X2) ) ),
    inference(variable_rename,[status(thm)],[67]) ).

fof(69,plain,
    ! [X2] :
      ( ( sdtasdt0(X2,sz00) = sz00
        | ~ aElement0(X2) )
      & ( sz00 = sdtasdt0(sz00,X2)
        | ~ aElement0(X2) ) ),
    inference(distribute,[status(thm)],[68]) ).

cnf(70,plain,
    ( sz00 = sdtasdt0(sz00,X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[69]) ).

cnf(71,plain,
    ( sdtasdt0(X1,sz00) = sz00
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[69]) ).

fof(72,plain,
    ! [X1,X2] :
      ( ~ aElement0(X1)
      | ~ aElement0(X2)
      | sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(73,plain,
    ! [X3,X4] :
      ( ~ aElement0(X3)
      | ~ aElement0(X4)
      | sdtpldt0(X3,X4) = sdtpldt0(X4,X3) ),
    inference(variable_rename,[status(thm)],[72]) ).

cnf(74,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[73]) ).

fof(88,plain,
    ! [X1,X2,X3] :
      ( ~ aElement0(X1)
      | ~ aElement0(X2)
      | ~ aElement0(X3)
      | ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
        & sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(89,plain,
    ! [X4,X5,X6] :
      ( ~ aElement0(X4)
      | ~ aElement0(X5)
      | ~ aElement0(X6)
      | ( sdtasdt0(X4,sdtpldt0(X5,X6)) = sdtpldt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
        & sdtasdt0(sdtpldt0(X5,X6),X4) = sdtpldt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4)) ) ),
    inference(variable_rename,[status(thm)],[88]) ).

fof(90,plain,
    ! [X4,X5,X6] :
      ( ( sdtasdt0(X4,sdtpldt0(X5,X6)) = sdtpldt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
        | ~ aElement0(X4)
        | ~ aElement0(X5)
        | ~ aElement0(X6) )
      & ( sdtasdt0(sdtpldt0(X5,X6),X4) = sdtpldt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
        | ~ aElement0(X4)
        | ~ aElement0(X5)
        | ~ aElement0(X6) ) ),
    inference(distribute,[status(thm)],[89]) ).

cnf(91,plain,
    ( sdtasdt0(sdtpldt0(X2,X1),X3) = sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3))
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[90]) ).

cnf(92,plain,
    ( sdtasdt0(X3,sdtpldt0(X2,X1)) = sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[90]) ).

fof(111,plain,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X1] :
        ( ~ aElementOf0(X1,xI)
        | X1 = sz00
        | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
    inference(fof_nnf,[status(thm)],[57]) ).

fof(112,plain,
    ( aElementOf0(xu,xI)
    & xu != sz00
    & ! [X2] :
        ( ~ aElementOf0(X2,xI)
        | X2 = sz00
        | ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) ) ),
    inference(variable_rename,[status(thm)],[111]) ).

fof(113,plain,
    ! [X2] :
      ( ( ~ aElementOf0(X2,xI)
        | X2 = sz00
        | ~ iLess0(sbrdtbr0(X2),sbrdtbr0(xu)) )
      & aElementOf0(xu,xI)
      & xu != sz00 ),
    inference(shift_quantors,[status(thm)],[112]) ).

cnf(115,plain,
    aElementOf0(xu,xI),
    inference(split_conjunct,[status(thm)],[113]) ).

cnf(118,plain,
    xb = sdtpldt0(sdtasdt0(xq,xu),xr),
    inference(split_conjunct,[status(thm)],[13]) ).

cnf(119,plain,
    aElement0(xr),
    inference(split_conjunct,[status(thm)],[13]) ).

cnf(120,plain,
    aElement0(xq),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(133,plain,
    ! [X1] :
      ( ~ aElement0(X1)
      | ( sdtasdt0(X1,sz10) = X1
        & X1 = sdtasdt0(sz10,X1) ) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(134,plain,
    ! [X2] :
      ( ~ aElement0(X2)
      | ( sdtasdt0(X2,sz10) = X2
        & X2 = sdtasdt0(sz10,X2) ) ),
    inference(variable_rename,[status(thm)],[133]) ).

fof(135,plain,
    ! [X2] :
      ( ( sdtasdt0(X2,sz10) = X2
        | ~ aElement0(X2) )
      & ( X2 = sdtasdt0(sz10,X2)
        | ~ aElement0(X2) ) ),
    inference(distribute,[status(thm)],[134]) ).

cnf(136,plain,
    ( X1 = sdtasdt0(sz10,X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[135]) ).

cnf(137,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[135]) ).

fof(146,plain,
    ! [X1,X2,X3] :
      ( ~ aElement0(X1)
      | ~ aElement0(X2)
      | ~ aElement0(X3)
      | sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(147,plain,
    ! [X4,X5,X6] :
      ( ~ aElement0(X4)
      | ~ aElement0(X5)
      | ~ aElement0(X6)
      | sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6)) ),
    inference(variable_rename,[status(thm)],[146]) ).

cnf(148,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aElement0(X3)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[147]) ).

cnf(175,plain,
    aElement0(sz10),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(177,plain,
    aIdeal0(xI),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(178,plain,
    ! [X1] :
      ( ( ~ aIdeal0(X1)
        | ( aSet0(X1)
          & ! [X2] :
              ( ~ aElementOf0(X2,X1)
              | ( ! [X3] :
                    ( ~ aElementOf0(X3,X1)
                    | aElementOf0(sdtpldt0(X2,X3),X1) )
                & ! [X3] :
                    ( ~ aElement0(X3)
                    | aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) )
      & ( ~ aSet0(X1)
        | ? [X2] :
            ( aElementOf0(X2,X1)
            & ( ? [X3] :
                  ( aElementOf0(X3,X1)
                  & ~ aElementOf0(sdtpldt0(X2,X3),X1) )
              | ? [X3] :
                  ( aElement0(X3)
                  & ~ aElementOf0(sdtasdt0(X3,X2),X1) ) ) )
        | aIdeal0(X1) ) ),
    inference(fof_nnf,[status(thm)],[29]) ).

fof(179,plain,
    ! [X4] :
      ( ( ~ aIdeal0(X4)
        | ( aSet0(X4)
          & ! [X5] :
              ( ~ aElementOf0(X5,X4)
              | ( ! [X6] :
                    ( ~ aElementOf0(X6,X4)
                    | aElementOf0(sdtpldt0(X5,X6),X4) )
                & ! [X7] :
                    ( ~ aElement0(X7)
                    | aElementOf0(sdtasdt0(X7,X5),X4) ) ) ) ) )
      & ( ~ aSet0(X4)
        | ? [X8] :
            ( aElementOf0(X8,X4)
            & ( ? [X9] :
                  ( aElementOf0(X9,X4)
                  & ~ aElementOf0(sdtpldt0(X8,X9),X4) )
              | ? [X10] :
                  ( aElement0(X10)
                  & ~ aElementOf0(sdtasdt0(X10,X8),X4) ) ) )
        | aIdeal0(X4) ) ),
    inference(variable_rename,[status(thm)],[178]) ).

fof(180,plain,
    ! [X4] :
      ( ( ~ aIdeal0(X4)
        | ( aSet0(X4)
          & ! [X5] :
              ( ~ aElementOf0(X5,X4)
              | ( ! [X6] :
                    ( ~ aElementOf0(X6,X4)
                    | aElementOf0(sdtpldt0(X5,X6),X4) )
                & ! [X7] :
                    ( ~ aElement0(X7)
                    | aElementOf0(sdtasdt0(X7,X5),X4) ) ) ) ) )
      & ( ~ aSet0(X4)
        | ( aElementOf0(esk11_1(X4),X4)
          & ( ( aElementOf0(esk12_1(X4),X4)
              & ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4) )
            | ( aElement0(esk13_1(X4))
              & ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4) ) ) )
        | aIdeal0(X4) ) ),
    inference(skolemize,[status(esa)],[179]) ).

fof(181,plain,
    ! [X4,X5,X6,X7] :
      ( ( ( ( ( ( ~ aElement0(X7)
                | aElementOf0(sdtasdt0(X7,X5),X4) )
              & ( ~ aElementOf0(X6,X4)
                | aElementOf0(sdtpldt0(X5,X6),X4) ) )
            | ~ aElementOf0(X5,X4) )
          & aSet0(X4) )
        | ~ aIdeal0(X4) )
      & ( ~ aSet0(X4)
        | ( aElementOf0(esk11_1(X4),X4)
          & ( ( aElementOf0(esk12_1(X4),X4)
              & ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4) )
            | ( aElement0(esk13_1(X4))
              & ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4) ) ) )
        | aIdeal0(X4) ) ),
    inference(shift_quantors,[status(thm)],[180]) ).

fof(182,plain,
    ! [X4,X5,X6,X7] :
      ( ( ~ aElement0(X7)
        | aElementOf0(sdtasdt0(X7,X5),X4)
        | ~ aElementOf0(X5,X4)
        | ~ aIdeal0(X4) )
      & ( ~ aElementOf0(X6,X4)
        | aElementOf0(sdtpldt0(X5,X6),X4)
        | ~ aElementOf0(X5,X4)
        | ~ aIdeal0(X4) )
      & ( aSet0(X4)
        | ~ aIdeal0(X4) )
      & ( aElementOf0(esk11_1(X4),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( aElement0(esk13_1(X4))
        | aElementOf0(esk12_1(X4),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4)
        | aElementOf0(esk12_1(X4),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( aElement0(esk13_1(X4))
        | ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) )
      & ( ~ aElementOf0(sdtasdt0(esk13_1(X4),esk11_1(X4)),X4)
        | ~ aElementOf0(sdtpldt0(esk11_1(X4),esk12_1(X4)),X4)
        | ~ aSet0(X4)
        | aIdeal0(X4) ) ),
    inference(distribute,[status(thm)],[181]) ).

cnf(188,plain,
    ( aSet0(X1)
    | ~ aIdeal0(X1) ),
    inference(split_conjunct,[status(thm)],[182]) ).

fof(205,plain,
    ! [X1,X2,X3] :
      ( ~ aElement0(X1)
      | ~ aElement0(X2)
      | ~ aElement0(X3)
      | sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
    inference(fof_nnf,[status(thm)],[31]) ).

fof(206,plain,
    ! [X4,X5,X6] :
      ( ~ aElement0(X4)
      | ~ aElement0(X5)
      | ~ aElement0(X6)
      | sdtasdt0(sdtasdt0(X4,X5),X6) = sdtasdt0(X4,sdtasdt0(X5,X6)) ),
    inference(variable_rename,[status(thm)],[205]) ).

cnf(207,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aElement0(X3)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[206]) ).

fof(212,plain,
    ! [X1] :
      ( ~ aElement0(X1)
      | ( sdtpldt0(X1,smndt0(X1)) = sz00
        & sz00 = sdtpldt0(smndt0(X1),X1) ) ),
    inference(fof_nnf,[status(thm)],[33]) ).

fof(213,plain,
    ! [X2] :
      ( ~ aElement0(X2)
      | ( sdtpldt0(X2,smndt0(X2)) = sz00
        & sz00 = sdtpldt0(smndt0(X2),X2) ) ),
    inference(variable_rename,[status(thm)],[212]) ).

fof(214,plain,
    ! [X2] :
      ( ( sdtpldt0(X2,smndt0(X2)) = sz00
        | ~ aElement0(X2) )
      & ( sz00 = sdtpldt0(smndt0(X2),X2)
        | ~ aElement0(X2) ) ),
    inference(distribute,[status(thm)],[213]) ).

cnf(216,plain,
    ( sdtpldt0(X1,smndt0(X1)) = sz00
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[214]) ).

fof(217,plain,
    ! [X1,X2] :
      ( ~ aElement0(X1)
      | ~ aElement0(X2)
      | aElement0(sdtasdt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[34]) ).

fof(218,plain,
    ! [X3,X4] :
      ( ~ aElement0(X3)
      | ~ aElement0(X4)
      | aElement0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[217]) ).

cnf(219,plain,
    ( aElement0(sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[218]) ).

cnf(221,plain,
    aElement0(sz00),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(239,plain,
    aElement0(xb),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(249,plain,
    ! [X1] :
      ( ~ aElement0(X1)
      | ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    inference(fof_nnf,[status(thm)],[42]) ).

fof(250,plain,
    ! [X2] :
      ( ~ aElement0(X2)
      | ( sdtpldt0(X2,sz00) = X2
        & X2 = sdtpldt0(sz00,X2) ) ),
    inference(variable_rename,[status(thm)],[249]) ).

fof(251,plain,
    ! [X2] :
      ( ( sdtpldt0(X2,sz00) = X2
        | ~ aElement0(X2) )
      & ( X2 = sdtpldt0(sz00,X2)
        | ~ aElement0(X2) ) ),
    inference(distribute,[status(thm)],[250]) ).

cnf(252,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[251]) ).

cnf(253,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[251]) ).

fof(254,plain,
    ! [X1,X2] :
      ( ~ aElement0(X1)
      | ~ aElement0(X2)
      | sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    inference(fof_nnf,[status(thm)],[43]) ).

fof(255,plain,
    ! [X3,X4] :
      ( ~ aElement0(X3)
      | ~ aElement0(X4)
      | sdtasdt0(X3,X4) = sdtasdt0(X4,X3) ),
    inference(variable_rename,[status(thm)],[254]) ).

cnf(256,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[255]) ).

cnf(267,plain,
    aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(274,plain,
    ! [X1] :
      ( ~ aElement0(X1)
      | aElement0(smndt0(X1)) ),
    inference(fof_nnf,[status(thm)],[50]) ).

fof(275,plain,
    ! [X2] :
      ( ~ aElement0(X2)
      | aElement0(smndt0(X2)) ),
    inference(variable_rename,[status(thm)],[274]) ).

cnf(276,plain,
    ( aElement0(smndt0(X1))
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[275]) ).

cnf(294,negated_conjecture,
    xr != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    inference(split_conjunct,[status(thm)],[59]) ).

cnf(296,plain,
    aSet0(xI),
    inference(spm,[status(thm)],[188,177,theory(equality)]) ).

cnf(299,plain,
    ( sz00 = smndt0(sz00)
    | ~ aElement0(smndt0(sz00))
    | ~ aElement0(sz00) ),
    inference(spm,[status(thm)],[252,216,theory(equality)]) ).

cnf(300,plain,
    ( sz00 = smndt0(sz00)
    | ~ aElement0(smndt0(sz00))
    | $false ),
    inference(rw,[status(thm)],[299,221,theory(equality)]) ).

cnf(301,plain,
    ( sz00 = smndt0(sz00)
    | ~ aElement0(smndt0(sz00)) ),
    inference(cn,[status(thm)],[300,theory(equality)]) ).

cnf(312,plain,
    ( aElement0(xu)
    | ~ aSet0(xI) ),
    inference(spm,[status(thm)],[63,115,theory(equality)]) ).

cnf(318,plain,
    ( aElement0(smndt0(sdtasdt0(xq,xu)))
    | ~ aSet0(xI) ),
    inference(spm,[status(thm)],[63,267,theory(equality)]) ).

cnf(406,plain,
    ( sdtpldt0(xr,sdtasdt0(xq,xu)) = xb
    | ~ aElement0(xr)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(spm,[status(thm)],[118,74,theory(equality)]) ).

cnf(410,negated_conjecture,
    ( sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) != xr
    | ~ aElement0(xb)
    | ~ aElement0(smndt0(sdtasdt0(xq,xu))) ),
    inference(spm,[status(thm)],[294,74,theory(equality)]) ).

cnf(420,plain,
    ( sdtpldt0(xr,sdtasdt0(xq,xu)) = xb
    | $false
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(rw,[status(thm)],[406,119,theory(equality)]) ).

cnf(421,plain,
    ( sdtpldt0(xr,sdtasdt0(xq,xu)) = xb
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[420,theory(equality)]) ).

cnf(424,negated_conjecture,
    ( sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) != xr
    | $false
    | ~ aElement0(smndt0(sdtasdt0(xq,xu))) ),
    inference(rw,[status(thm)],[410,239,theory(equality)]) ).

cnf(425,negated_conjecture,
    ( sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) != xr
    | ~ aElement0(smndt0(sdtasdt0(xq,xu))) ),
    inference(cn,[status(thm)],[424,theory(equality)]) ).

cnf(574,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
    | ~ aElement0(sdtasdt0(X1,X2))
    | ~ aElement0(sz10)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[137,207,theory(equality)]) ).

cnf(578,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1)
    | ~ aElement0(sz10) ),
    inference(spm,[status(thm)],[207,136,theory(equality)]) ).

cnf(579,plain,
    ( sdtasdt0(sz00,X2) = sdtasdt0(sz00,sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1)
    | ~ aElement0(sz00) ),
    inference(spm,[status(thm)],[207,70,theory(equality)]) ).

cnf(598,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
    | ~ aElement0(sdtasdt0(X1,X2))
    | $false
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(rw,[status(thm)],[574,175,theory(equality)]) ).

cnf(599,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
    | ~ aElement0(sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[598,theory(equality)]) ).

cnf(606,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1)
    | $false ),
    inference(rw,[status(thm)],[578,175,theory(equality)]) ).

cnf(607,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[606,theory(equality)]) ).

cnf(608,plain,
    ( sdtasdt0(sz00,X2) = sdtasdt0(sz00,sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1)
    | $false ),
    inference(rw,[status(thm)],[579,221,theory(equality)]) ).

cnf(609,plain,
    ( sdtasdt0(sz00,X2) = sdtasdt0(sz00,sdtasdt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[608,theory(equality)]) ).

cnf(610,plain,
    ( sdtpldt0(xb,X1) = sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(xr,X1))
    | ~ aElement0(X1)
    | ~ aElement0(xr)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(spm,[status(thm)],[148,118,theory(equality)]) ).

cnf(627,plain,
    ( sdtpldt0(xb,X1) = sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(xr,X1))
    | ~ aElement0(X1)
    | $false
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(rw,[status(thm)],[610,119,theory(equality)]) ).

cnf(628,plain,
    ( sdtpldt0(xb,X1) = sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(xr,X1))
    | ~ aElement0(X1)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[627,theory(equality)]) ).

cnf(641,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz00,X2)) = sdtasdt0(sz00,sdtpldt0(X1,X2))
    | ~ aElement0(sz00)
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(spm,[status(thm)],[92,70,theory(equality)]) ).

cnf(674,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz00,X2)) = sdtasdt0(sz00,sdtpldt0(X1,X2))
    | $false
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(rw,[status(thm)],[641,221,theory(equality)]) ).

cnf(675,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz00,X2)) = sdtasdt0(sz00,sdtpldt0(X1,X2))
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(cn,[status(thm)],[674,theory(equality)]) ).

cnf(682,plain,
    ( sdtpldt0(X1,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz10,X2),X1)
    | ~ aElement0(X1)
    | ~ aElement0(sz10)
    | ~ aElement0(X2) ),
    inference(spm,[status(thm)],[91,136,theory(equality)]) ).

cnf(684,plain,
    ( sdtpldt0(sz00,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz00,X2),X1)
    | ~ aElement0(X1)
    | ~ aElement0(sz00)
    | ~ aElement0(X2) ),
    inference(spm,[status(thm)],[91,70,theory(equality)]) ).

cnf(714,plain,
    ( sdtpldt0(X1,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz10,X2),X1)
    | ~ aElement0(X1)
    | $false
    | ~ aElement0(X2) ),
    inference(rw,[status(thm)],[682,175,theory(equality)]) ).

cnf(715,plain,
    ( sdtpldt0(X1,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz10,X2),X1)
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(cn,[status(thm)],[714,theory(equality)]) ).

cnf(718,plain,
    ( sdtpldt0(sz00,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz00,X2),X1)
    | ~ aElement0(X1)
    | $false
    | ~ aElement0(X2) ),
    inference(rw,[status(thm)],[684,221,theory(equality)]) ).

cnf(719,plain,
    ( sdtpldt0(sz00,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz00,X2),X1)
    | ~ aElement0(X1)
    | ~ aElement0(X2) ),
    inference(cn,[status(thm)],[718,theory(equality)]) ).

cnf(817,plain,
    ( aElement0(xu)
    | $false ),
    inference(rw,[status(thm)],[312,296,theory(equality)]) ).

cnf(818,plain,
    aElement0(xu),
    inference(cn,[status(thm)],[817,theory(equality)]) ).

cnf(844,plain,
    ( smndt0(sz00) = sz00
    | ~ aElement0(sz00) ),
    inference(spm,[status(thm)],[301,276,theory(equality)]) ).

cnf(845,plain,
    ( smndt0(sz00) = sz00
    | $false ),
    inference(rw,[status(thm)],[844,221,theory(equality)]) ).

cnf(846,plain,
    smndt0(sz00) = sz00,
    inference(cn,[status(thm)],[845,theory(equality)]) ).

cnf(853,plain,
    ( sdtpldt0(sz00,sz00) = sz00
    | ~ aElement0(sz00) ),
    inference(spm,[status(thm)],[216,846,theory(equality)]) ).

cnf(863,plain,
    ( sdtpldt0(sz00,sz00) = sz00
    | $false ),
    inference(rw,[status(thm)],[853,221,theory(equality)]) ).

cnf(864,plain,
    sdtpldt0(sz00,sz00) = sz00,
    inference(cn,[status(thm)],[863,theory(equality)]) ).

cnf(916,plain,
    ( aElement0(smndt0(sdtasdt0(xq,xu)))
    | $false ),
    inference(rw,[status(thm)],[318,296,theory(equality)]) ).

cnf(917,plain,
    aElement0(smndt0(sdtasdt0(xq,xu))),
    inference(cn,[status(thm)],[916,theory(equality)]) ).

cnf(921,negated_conjecture,
    ( sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) != xr
    | $false ),
    inference(rw,[status(thm)],[425,917,theory(equality)]) ).

cnf(922,negated_conjecture,
    sdtpldt0(xb,smndt0(sdtasdt0(xq,xu))) != xr,
    inference(cn,[status(thm)],[921,theory(equality)]) ).

cnf(963,plain,
    ( sdtpldt0(xb,X1) = sdtpldt0(xr,sdtpldt0(sdtasdt0(xq,xu),X1))
    | ~ aElement0(X1)
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElement0(xr) ),
    inference(spm,[status(thm)],[148,421,theory(equality)]) ).

cnf(973,plain,
    ( sdtpldt0(xb,X1) = sdtpldt0(xr,sdtpldt0(sdtasdt0(xq,xu),X1))
    | ~ aElement0(X1)
    | ~ aElement0(sdtasdt0(xq,xu))
    | $false ),
    inference(rw,[status(thm)],[963,119,theory(equality)]) ).

cnf(974,plain,
    ( sdtpldt0(xb,X1) = sdtpldt0(xr,sdtpldt0(sdtasdt0(xq,xu),X1))
    | ~ aElement0(X1)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[973,theory(equality)]) ).

cnf(1525,plain,
    ( sdtasdt0(sz10,sz00) = sz00
    | ~ aElement0(sz00)
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[607,71,theory(equality)]) ).

cnf(1551,plain,
    ( sdtasdt0(sz10,sz00) = sz00
    | $false
    | ~ aElement0(X1) ),
    inference(rw,[status(thm)],[1525,221,theory(equality)]) ).

cnf(1552,plain,
    ( sdtasdt0(sz10,sz00) = sz00
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[1551,theory(equality)]) ).

cnf(1581,plain,
    sdtasdt0(sz10,sz00) = sz00,
    inference(spm,[status(thm)],[1552,239,theory(equality)]) ).

cnf(1617,plain,
    ( sz00 = sdtasdt0(sz00,sz10)
    | ~ aElement0(sz00)
    | ~ aElement0(sz10) ),
    inference(spm,[status(thm)],[256,1581,theory(equality)]) ).

cnf(1623,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | ~ aElement0(sz10)
    | ~ aElement0(sz00)
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[92,1581,theory(equality)]) ).

cnf(1633,plain,
    ( sz00 = sdtasdt0(sz00,sz10)
    | $false
    | ~ aElement0(sz10) ),
    inference(rw,[status(thm)],[1617,221,theory(equality)]) ).

cnf(1634,plain,
    ( sz00 = sdtasdt0(sz00,sz10)
    | $false
    | $false ),
    inference(rw,[status(thm)],[1633,175,theory(equality)]) ).

cnf(1635,plain,
    sz00 = sdtasdt0(sz00,sz10),
    inference(cn,[status(thm)],[1634,theory(equality)]) ).

cnf(1650,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | $false
    | ~ aElement0(sz00)
    | ~ aElement0(X1) ),
    inference(rw,[status(thm)],[1623,175,theory(equality)]) ).

cnf(1651,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | $false
    | $false
    | ~ aElement0(X1) ),
    inference(rw,[status(thm)],[1650,221,theory(equality)]) ).

cnf(1652,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[1651,theory(equality)]) ).

cnf(3754,plain,
    ( sdtpldt0(sz00,X1) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[1652,136,theory(equality)]) ).

cnf(4178,plain,
    ( sdtasdt0(sz10,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
    | ~ aElement0(X1)
    | ~ aElement0(sz00) ),
    inference(spm,[status(thm)],[3754,74,theory(equality)]) ).

cnf(4211,plain,
    ( sdtasdt0(sz10,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
    | ~ aElement0(X1)
    | $false ),
    inference(rw,[status(thm)],[4178,221,theory(equality)]) ).

cnf(4212,plain,
    ( sdtasdt0(sz10,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[4211,theory(equality)]) ).

cnf(5951,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
    | ~ aElement0(X2)
    | ~ aElement0(X1) ),
    inference(csr,[status(thm)],[599,219]) ).

cnf(5976,plain,
    ( sdtasdt0(sz10,X1) = sdtasdt0(X1,sz10)
    | ~ aElement0(sz10)
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[607,5951,theory(equality)]) ).

cnf(6022,plain,
    ( sdtasdt0(sz10,X1) = sdtasdt0(X1,sz10)
    | $false
    | ~ aElement0(X1) ),
    inference(rw,[status(thm)],[5976,175,theory(equality)]) ).

cnf(6023,plain,
    ( sdtasdt0(sz10,X1) = sdtasdt0(X1,sz10)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[6022,theory(equality)]) ).

cnf(6545,plain,
    ( sdtasdt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz00,sz10)
    | ~ aElement0(sz10)
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[609,6023,theory(equality)]) ).

cnf(6614,plain,
    ( sdtasdt0(sz00,sdtasdt0(sz10,X1)) = sz00
    | ~ aElement0(sz10)
    | ~ aElement0(X1) ),
    inference(rw,[status(thm)],[6545,1635,theory(equality)]) ).

cnf(6615,plain,
    ( sdtasdt0(sz00,sdtasdt0(sz10,X1)) = sz00
    | $false
    | ~ aElement0(X1) ),
    inference(rw,[status(thm)],[6614,175,theory(equality)]) ).

cnf(6616,plain,
    ( sdtasdt0(sz00,sdtasdt0(sz10,X1)) = sz00
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[6615,theory(equality)]) ).

cnf(12238,plain,
    ( sdtpldt0(sdtasdt0(xq,xu),xr) = sdtpldt0(xb,sz00)
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElement0(sz00)
    | ~ aElement0(xr) ),
    inference(spm,[status(thm)],[628,253,theory(equality)]) ).

cnf(12255,plain,
    ( xb = sdtpldt0(xb,sz00)
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElement0(sz00)
    | ~ aElement0(xr) ),
    inference(rw,[status(thm)],[12238,118,theory(equality)]) ).

cnf(12256,plain,
    ( xb = sdtpldt0(xb,sz00)
    | ~ aElement0(sdtasdt0(xq,xu))
    | $false
    | ~ aElement0(xr) ),
    inference(rw,[status(thm)],[12255,221,theory(equality)]) ).

cnf(12257,plain,
    ( xb = sdtpldt0(xb,sz00)
    | ~ aElement0(sdtasdt0(xq,xu))
    | $false
    | $false ),
    inference(rw,[status(thm)],[12256,119,theory(equality)]) ).

cnf(12258,plain,
    ( xb = sdtpldt0(xb,sz00)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[12257,theory(equality)]) ).

cnf(12403,plain,
    ( sdtasdt0(sz10,xb) = xb
    | ~ aElement0(xb)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(spm,[status(thm)],[4212,12258,theory(equality)]) ).

cnf(12451,plain,
    ( sdtasdt0(sz10,xb) = xb
    | $false
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(rw,[status(thm)],[12403,239,theory(equality)]) ).

cnf(12452,plain,
    ( sdtasdt0(sz10,xb) = xb
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[12451,theory(equality)]) ).

cnf(12668,plain,
    ( sdtasdt0(sz10,xb) = xb
    | ~ aElement0(xu)
    | ~ aElement0(xq) ),
    inference(spm,[status(thm)],[12452,219,theory(equality)]) ).

cnf(12674,plain,
    ( sdtasdt0(sz10,xb) = xb
    | $false
    | ~ aElement0(xq) ),
    inference(rw,[status(thm)],[12668,818,theory(equality)]) ).

cnf(12675,plain,
    ( sdtasdt0(sz10,xb) = xb
    | $false
    | $false ),
    inference(rw,[status(thm)],[12674,120,theory(equality)]) ).

cnf(12676,plain,
    sdtasdt0(sz10,xb) = xb,
    inference(cn,[status(thm)],[12675,theory(equality)]) ).

cnf(12719,plain,
    ( sdtasdt0(sz00,xb) = sz00
    | ~ aElement0(xb) ),
    inference(spm,[status(thm)],[6616,12676,theory(equality)]) ).

cnf(12827,plain,
    ( sdtasdt0(sz00,xb) = sz00
    | $false ),
    inference(rw,[status(thm)],[12719,239,theory(equality)]) ).

cnf(12828,plain,
    sdtasdt0(sz00,xb) = sz00,
    inference(cn,[status(thm)],[12827,theory(equality)]) ).

cnf(23042,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz00,xr)) = sdtasdt0(sz00,xb)
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElement0(xr) ),
    inference(spm,[status(thm)],[675,118,theory(equality)]) ).

cnf(23207,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz00,xr)) = sz00
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElement0(xr) ),
    inference(rw,[status(thm)],[23042,12828,theory(equality)]) ).

cnf(23208,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz00,xr)) = sz00
    | ~ aElement0(sdtasdt0(xq,xu))
    | $false ),
    inference(rw,[status(thm)],[23207,119,theory(equality)]) ).

cnf(23209,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz00,xr)) = sz00
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[23208,theory(equality)]) ).

cnf(86125,plain,
    ( sz00 = sdtasdt0(sdtpldt0(sz00,sz00),xr)
    | ~ aElement0(xr)
    | ~ aElement0(sz00)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(spm,[status(thm)],[719,23209,theory(equality)]) ).

cnf(86199,plain,
    ( sz00 = sdtasdt0(sz00,xr)
    | ~ aElement0(xr)
    | ~ aElement0(sz00)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(rw,[status(thm)],[86125,864,theory(equality)]) ).

cnf(86200,plain,
    ( sz00 = sdtasdt0(sz00,xr)
    | $false
    | ~ aElement0(sz00)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(rw,[status(thm)],[86199,119,theory(equality)]) ).

cnf(86201,plain,
    ( sz00 = sdtasdt0(sz00,xr)
    | $false
    | $false
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(rw,[status(thm)],[86200,221,theory(equality)]) ).

cnf(86202,plain,
    ( sz00 = sdtasdt0(sz00,xr)
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[86201,theory(equality)]) ).

cnf(86212,plain,
    ( sdtasdt0(sz00,xr) = sz00
    | ~ aElement0(xu)
    | ~ aElement0(xq) ),
    inference(spm,[status(thm)],[86202,219,theory(equality)]) ).

cnf(86219,plain,
    ( sdtasdt0(sz00,xr) = sz00
    | $false
    | ~ aElement0(xq) ),
    inference(rw,[status(thm)],[86212,818,theory(equality)]) ).

cnf(86220,plain,
    ( sdtasdt0(sz00,xr) = sz00
    | $false
    | $false ),
    inference(rw,[status(thm)],[86219,120,theory(equality)]) ).

cnf(86221,plain,
    sdtasdt0(sz00,xr) = sz00,
    inference(cn,[status(thm)],[86220,theory(equality)]) ).

cnf(86286,plain,
    ( sdtpldt0(xr,sz00) = sdtasdt0(sdtpldt0(sz10,sz00),xr)
    | ~ aElement0(xr)
    | ~ aElement0(sz00) ),
    inference(spm,[status(thm)],[715,86221,theory(equality)]) ).

cnf(86485,plain,
    ( sdtpldt0(xr,sz00) = sdtasdt0(sdtpldt0(sz10,sz00),xr)
    | $false
    | ~ aElement0(sz00) ),
    inference(rw,[status(thm)],[86286,119,theory(equality)]) ).

cnf(86486,plain,
    ( sdtpldt0(xr,sz00) = sdtasdt0(sdtpldt0(sz10,sz00),xr)
    | $false
    | $false ),
    inference(rw,[status(thm)],[86485,221,theory(equality)]) ).

cnf(86487,plain,
    sdtpldt0(xr,sz00) = sdtasdt0(sdtpldt0(sz10,sz00),xr),
    inference(cn,[status(thm)],[86486,theory(equality)]) ).

cnf(87847,plain,
    ( sdtasdt0(sz10,xr) = sdtpldt0(xr,sz00)
    | ~ aElement0(sz10) ),
    inference(spm,[status(thm)],[86487,253,theory(equality)]) ).

cnf(87922,plain,
    ( sdtasdt0(sz10,xr) = sdtpldt0(xr,sz00)
    | $false ),
    inference(rw,[status(thm)],[87847,175,theory(equality)]) ).

cnf(87923,plain,
    sdtasdt0(sz10,xr) = sdtpldt0(xr,sz00),
    inference(cn,[status(thm)],[87922,theory(equality)]) ).

cnf(88150,plain,
    ( sdtasdt0(sz10,xr) = xr
    | ~ aElement0(xr) ),
    inference(spm,[status(thm)],[253,87923,theory(equality)]) ).

cnf(88193,plain,
    ( sdtasdt0(sz10,xr) = xr
    | $false ),
    inference(rw,[status(thm)],[88150,119,theory(equality)]) ).

cnf(88194,plain,
    sdtasdt0(sz10,xr) = xr,
    inference(cn,[status(thm)],[88193,theory(equality)]) ).

cnf(102890,plain,
    ( sdtpldt0(xr,sz00) = sdtpldt0(xb,smndt0(sdtasdt0(xq,xu)))
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElement0(smndt0(sdtasdt0(xq,xu))) ),
    inference(spm,[status(thm)],[974,216,theory(equality)]) ).

cnf(102971,plain,
    ( xr = sdtpldt0(xb,smndt0(sdtasdt0(xq,xu)))
    | ~ aElement0(sdtasdt0(xq,xu))
    | ~ aElement0(smndt0(sdtasdt0(xq,xu))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[102890,87923,theory(equality)]),88194,theory(equality)]) ).

cnf(102972,plain,
    ( xr = sdtpldt0(xb,smndt0(sdtasdt0(xq,xu)))
    | ~ aElement0(sdtasdt0(xq,xu))
    | $false ),
    inference(rw,[status(thm)],[102971,917,theory(equality)]) ).

cnf(102973,plain,
    ( xr = sdtpldt0(xb,smndt0(sdtasdt0(xq,xu)))
    | ~ aElement0(sdtasdt0(xq,xu)) ),
    inference(cn,[status(thm)],[102972,theory(equality)]) ).

cnf(102974,plain,
    ~ aElement0(sdtasdt0(xq,xu)),
    inference(sr,[status(thm)],[102973,922,theory(equality)]) ).

cnf(103120,plain,
    ( ~ aElement0(xu)
    | ~ aElement0(xq) ),
    inference(spm,[status(thm)],[102974,219,theory(equality)]) ).

cnf(103128,plain,
    ( $false
    | ~ aElement0(xq) ),
    inference(rw,[status(thm)],[103120,818,theory(equality)]) ).

cnf(103129,plain,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[103128,120,theory(equality)]) ).

cnf(103130,plain,
    $false,
    inference(cn,[status(thm)],[103129,theory(equality)]) ).

cnf(103131,plain,
    $false,
    103130,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG122+1.p
% --creating new selector for []
% -running prover on /tmp/tmpqzSbcQ/sel_RNG122+1.p_1 with time limit 29
% -prover status Theorem
% Problem RNG122+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG122+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG122+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------