TSTP Solution File: RNG105+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG105+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 02:23:24 EST 2010
% Result : Theorem 12.33s
% Output : CNFRefutation 12.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 155
% Number of leaves : 27
% Syntax : Number of formulae : 556 ( 89 unt; 0 def)
% Number of atoms : 1769 ( 560 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 2045 ( 832 ~;1089 |; 102 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 447 ( 0 sgn 138 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mMulZero) ).
fof(4,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mAddComm) ).
fof(6,axiom,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',m__2043) ).
fof(7,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/tmp5xwDFN/sel_RNG105+1.p_1',mAMDistr) ).
fof(8,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X1,X3) = X2 ) ) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mDefDiv) ).
fof(10,axiom,
( aElementOf0(xx,slsdtgt0(xc))
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',m__1933) ).
fof(12,axiom,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',m__2010) ).
fof(15,axiom,
( aElement0(xv)
& sdtasdt0(xc,xv) = xy ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',m__1979) ).
fof(16,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mMulUnit) ).
fof(19,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mAddAsso) ).
fof(21,axiom,
sz10 != sz00,
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mUnNeZr) ).
fof(22,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( X2 = slsdtgt0(X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(X1,X4) = X3 ) ) ) ) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mDefPrIdeal) ).
fof(23,axiom,
aElement0(sz10),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mSortsC_01) ).
fof(26,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mMulAsso) ).
fof(27,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mAddInvr) ).
fof(28,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mSortsB_02) ).
fof(29,axiom,
aElement0(sz00),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mSortsC) ).
fof(30,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mSortsB) ).
fof(33,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2)
& X2 != sz00 )
=> ? [X3,X4] :
( aElement0(X3)
& aElement0(X4)
& X1 = sdtpldt0(sdtasdt0(X3,X2),X4)
& ( X4 != sz00
=> iLess0(sbrdtbr0(X4),sbrdtbr0(X2)) ) ) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mDivision) ).
fof(34,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mAddZero) ).
fof(35,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mMulComm) ).
fof(36,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mCancel) ).
fof(38,axiom,
aElement0(xc),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',m__1905) ).
fof(39,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mMulMnOne) ).
fof(40,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',mSortsU) ).
fof(43,conjecture,
( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',m__) ).
fof(44,axiom,
( aElement0(xu)
& sdtasdt0(xc,xu) = xx ),
file('/tmp/tmp5xwDFN/sel_RNG105+1.p_1',m__1956) ).
fof(45,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(assume_negation,[status(cth)],[43]) ).
fof(53,plain,
! [X1] :
( ~ aElement0(X1)
| ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(54,plain,
! [X2] :
( ~ aElement0(X2)
| ( sdtasdt0(X2,sz00) = sz00
& sz00 = sdtasdt0(sz00,X2) ) ),
inference(variable_rename,[status(thm)],[53]) ).
fof(55,plain,
! [X2] :
( ( sdtasdt0(X2,sz00) = sz00
| ~ aElement0(X2) )
& ( sz00 = sdtasdt0(sz00,X2)
| ~ aElement0(X2) ) ),
inference(distribute,[status(thm)],[54]) ).
cnf(56,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(57,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(58,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(59,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| sdtpldt0(X3,X4) = sdtpldt0(X4,X3) ),
inference(variable_rename,[status(thm)],[58]) ).
cnf(60,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[59]) ).
cnf(72,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(split_conjunct,[status(thm)],[6]) ).
fof(73,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)],[7]) ).
fof(74,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)],[73]) ).
fof(75,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)],[74]) ).
cnf(76,plain,
( sdtasdt0(sdtpldt0(X2,X1),X3) = sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[75]) ).
cnf(77,plain,
( sdtasdt0(X3,sdtpldt0(X2,X1)) = sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[75]) ).
fof(78,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| ( ( ~ doDivides0(X1,X2)
| ? [X3] :
( aElement0(X3)
& sdtasdt0(X1,X3) = X2 ) )
& ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X1,X3) != X2 )
| doDivides0(X1,X2) ) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(79,plain,
! [X4,X5] :
( ~ aElement0(X4)
| ~ aElement0(X5)
| ( ( ~ doDivides0(X4,X5)
| ? [X6] :
( aElement0(X6)
& sdtasdt0(X4,X6) = X5 ) )
& ( ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(X4,X7) != X5 )
| doDivides0(X4,X5) ) ) ),
inference(variable_rename,[status(thm)],[78]) ).
fof(80,plain,
! [X4,X5] :
( ~ aElement0(X4)
| ~ aElement0(X5)
| ( ( ~ doDivides0(X4,X5)
| ( aElement0(esk3_2(X4,X5))
& sdtasdt0(X4,esk3_2(X4,X5)) = X5 ) )
& ( ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(X4,X7) != X5 )
| doDivides0(X4,X5) ) ) ),
inference(skolemize,[status(esa)],[79]) ).
fof(81,plain,
! [X4,X5,X7] :
( ( ( ~ aElement0(X7)
| sdtasdt0(X4,X7) != X5
| doDivides0(X4,X5) )
& ( ~ doDivides0(X4,X5)
| ( aElement0(esk3_2(X4,X5))
& sdtasdt0(X4,esk3_2(X4,X5)) = X5 ) ) )
| ~ aElement0(X4)
| ~ aElement0(X5) ),
inference(shift_quantors,[status(thm)],[80]) ).
fof(82,plain,
! [X4,X5,X7] :
( ( ~ aElement0(X7)
| sdtasdt0(X4,X7) != X5
| doDivides0(X4,X5)
| ~ aElement0(X4)
| ~ aElement0(X5) )
& ( aElement0(esk3_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aElement0(X4)
| ~ aElement0(X5) )
& ( sdtasdt0(X4,esk3_2(X4,X5)) = X5
| ~ doDivides0(X4,X5)
| ~ aElement0(X4)
| ~ aElement0(X5) ) ),
inference(distribute,[status(thm)],[81]) ).
cnf(83,plain,
( sdtasdt0(X2,esk3_2(X2,X1)) = X1
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[82]) ).
cnf(84,plain,
( aElement0(esk3_2(X2,X1))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[82]) ).
cnf(85,plain,
( doDivides0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X2,X3) != X1
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[82]) ).
cnf(94,plain,
aElement0(xz),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(100,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(split_conjunct,[status(thm)],[12]) ).
cnf(107,plain,
sdtasdt0(xc,xv) = xy,
inference(split_conjunct,[status(thm)],[15]) ).
cnf(108,plain,
aElement0(xv),
inference(split_conjunct,[status(thm)],[15]) ).
fof(109,plain,
! [X1] :
( ~ aElement0(X1)
| ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(110,plain,
! [X2] :
( ~ aElement0(X2)
| ( sdtasdt0(X2,sz10) = X2
& X2 = sdtasdt0(sz10,X2) ) ),
inference(variable_rename,[status(thm)],[109]) ).
fof(111,plain,
! [X2] :
( ( sdtasdt0(X2,sz10) = X2
| ~ aElement0(X2) )
& ( X2 = sdtasdt0(sz10,X2)
| ~ aElement0(X2) ) ),
inference(distribute,[status(thm)],[110]) ).
cnf(112,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
cnf(113,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[111]) ).
fof(122,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)],[19]) ).
fof(123,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)],[122]) ).
cnf(124,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[123]) ).
cnf(132,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[21]) ).
fof(133,plain,
! [X1] :
( ~ aElement0(X1)
| ! [X2] :
( ( X2 != slsdtgt0(X1)
| ( aSet0(X2)
& ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ? [X4] :
( aElement0(X4)
& sdtasdt0(X1,X4) = X3 ) )
& ( ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(X1,X4) != X3 )
| aElementOf0(X3,X2) ) ) ) )
& ( ~ aSet0(X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X2)
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(X1,X4) != X3 ) )
& ( aElementOf0(X3,X2)
| ? [X4] :
( aElement0(X4)
& sdtasdt0(X1,X4) = X3 ) ) )
| X2 = slsdtgt0(X1) ) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(134,plain,
! [X5] :
( ~ aElement0(X5)
| ! [X6] :
( ( X6 != slsdtgt0(X5)
| ( aSet0(X6)
& ! [X7] :
( ( ~ aElementOf0(X7,X6)
| ? [X8] :
( aElement0(X8)
& sdtasdt0(X5,X8) = X7 ) )
& ( ! [X9] :
( ~ aElement0(X9)
| sdtasdt0(X5,X9) != X7 )
| aElementOf0(X7,X6) ) ) ) )
& ( ~ aSet0(X6)
| ? [X10] :
( ( ~ aElementOf0(X10,X6)
| ! [X11] :
( ~ aElement0(X11)
| sdtasdt0(X5,X11) != X10 ) )
& ( aElementOf0(X10,X6)
| ? [X12] :
( aElement0(X12)
& sdtasdt0(X5,X12) = X10 ) ) )
| X6 = slsdtgt0(X5) ) ) ),
inference(variable_rename,[status(thm)],[133]) ).
fof(135,plain,
! [X5] :
( ~ aElement0(X5)
| ! [X6] :
( ( X6 != slsdtgt0(X5)
| ( aSet0(X6)
& ! [X7] :
( ( ~ aElementOf0(X7,X6)
| ( aElement0(esk6_3(X5,X6,X7))
& sdtasdt0(X5,esk6_3(X5,X6,X7)) = X7 ) )
& ( ! [X9] :
( ~ aElement0(X9)
| sdtasdt0(X5,X9) != X7 )
| aElementOf0(X7,X6) ) ) ) )
& ( ~ aSet0(X6)
| ( ( ~ aElementOf0(esk7_2(X5,X6),X6)
| ! [X11] :
( ~ aElement0(X11)
| sdtasdt0(X5,X11) != esk7_2(X5,X6) ) )
& ( aElementOf0(esk7_2(X5,X6),X6)
| ( aElement0(esk8_2(X5,X6))
& sdtasdt0(X5,esk8_2(X5,X6)) = esk7_2(X5,X6) ) ) )
| X6 = slsdtgt0(X5) ) ) ),
inference(skolemize,[status(esa)],[134]) ).
fof(136,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ aElement0(X11)
| sdtasdt0(X5,X11) != esk7_2(X5,X6)
| ~ aElementOf0(esk7_2(X5,X6),X6) )
& ( aElementOf0(esk7_2(X5,X6),X6)
| ( aElement0(esk8_2(X5,X6))
& sdtasdt0(X5,esk8_2(X5,X6)) = esk7_2(X5,X6) ) ) )
| ~ aSet0(X6)
| X6 = slsdtgt0(X5) )
& ( ( ( ~ aElement0(X9)
| sdtasdt0(X5,X9) != X7
| aElementOf0(X7,X6) )
& ( ~ aElementOf0(X7,X6)
| ( aElement0(esk6_3(X5,X6,X7))
& sdtasdt0(X5,esk6_3(X5,X6,X7)) = X7 ) )
& aSet0(X6) )
| X6 != slsdtgt0(X5) ) )
| ~ aElement0(X5) ),
inference(shift_quantors,[status(thm)],[135]) ).
fof(137,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ aElement0(X11)
| sdtasdt0(X5,X11) != esk7_2(X5,X6)
| ~ aElementOf0(esk7_2(X5,X6),X6)
| ~ aSet0(X6)
| X6 = slsdtgt0(X5)
| ~ aElement0(X5) )
& ( aElement0(esk8_2(X5,X6))
| aElementOf0(esk7_2(X5,X6),X6)
| ~ aSet0(X6)
| X6 = slsdtgt0(X5)
| ~ aElement0(X5) )
& ( sdtasdt0(X5,esk8_2(X5,X6)) = esk7_2(X5,X6)
| aElementOf0(esk7_2(X5,X6),X6)
| ~ aSet0(X6)
| X6 = slsdtgt0(X5)
| ~ aElement0(X5) )
& ( ~ aElement0(X9)
| sdtasdt0(X5,X9) != X7
| aElementOf0(X7,X6)
| X6 != slsdtgt0(X5)
| ~ aElement0(X5) )
& ( aElement0(esk6_3(X5,X6,X7))
| ~ aElementOf0(X7,X6)
| X6 != slsdtgt0(X5)
| ~ aElement0(X5) )
& ( sdtasdt0(X5,esk6_3(X5,X6,X7)) = X7
| ~ aElementOf0(X7,X6)
| X6 != slsdtgt0(X5)
| ~ aElement0(X5) )
& ( aSet0(X6)
| X6 != slsdtgt0(X5)
| ~ aElement0(X5) ) ),
inference(distribute,[status(thm)],[136]) ).
cnf(141,plain,
( aElementOf0(X3,X2)
| ~ aElement0(X1)
| X2 != slsdtgt0(X1)
| sdtasdt0(X1,X4) != X3
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(145,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[23]) ).
fof(173,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)],[26]) ).
fof(174,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)],[173]) ).
cnf(175,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[174]) ).
fof(176,plain,
! [X1] :
( ~ aElement0(X1)
| ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
inference(fof_nnf,[status(thm)],[27]) ).
fof(177,plain,
! [X2] :
( ~ aElement0(X2)
| ( sdtpldt0(X2,smndt0(X2)) = sz00
& sz00 = sdtpldt0(smndt0(X2),X2) ) ),
inference(variable_rename,[status(thm)],[176]) ).
fof(178,plain,
! [X2] :
( ( sdtpldt0(X2,smndt0(X2)) = sz00
| ~ aElement0(X2) )
& ( sz00 = sdtpldt0(smndt0(X2),X2)
| ~ aElement0(X2) ) ),
inference(distribute,[status(thm)],[177]) ).
cnf(179,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[178]) ).
cnf(180,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[178]) ).
fof(181,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(182,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| aElement0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[181]) ).
cnf(183,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[182]) ).
cnf(184,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[29]) ).
fof(185,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| aElement0(sdtpldt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(186,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| aElement0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[185]) ).
cnf(187,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[186]) ).
fof(202,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| X2 = sz00
| ? [X3,X4] :
( aElement0(X3)
& aElement0(X4)
& X1 = sdtpldt0(sdtasdt0(X3,X2),X4)
& ( X4 = sz00
| iLess0(sbrdtbr0(X4),sbrdtbr0(X2)) ) ) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(203,plain,
! [X5,X6] :
( ~ aElement0(X5)
| ~ aElement0(X6)
| X6 = sz00
| ? [X7,X8] :
( aElement0(X7)
& aElement0(X8)
& X5 = sdtpldt0(sdtasdt0(X7,X6),X8)
& ( X8 = sz00
| iLess0(sbrdtbr0(X8),sbrdtbr0(X6)) ) ) ),
inference(variable_rename,[status(thm)],[202]) ).
fof(204,plain,
! [X5,X6] :
( ~ aElement0(X5)
| ~ aElement0(X6)
| X6 = sz00
| ( aElement0(esk18_2(X5,X6))
& aElement0(esk19_2(X5,X6))
& X5 = sdtpldt0(sdtasdt0(esk18_2(X5,X6),X6),esk19_2(X5,X6))
& ( esk19_2(X5,X6) = sz00
| iLess0(sbrdtbr0(esk19_2(X5,X6)),sbrdtbr0(X6)) ) ) ),
inference(skolemize,[status(esa)],[203]) ).
fof(205,plain,
! [X5,X6] :
( ( aElement0(esk18_2(X5,X6))
| ~ aElement0(X5)
| ~ aElement0(X6)
| X6 = sz00 )
& ( aElement0(esk19_2(X5,X6))
| ~ aElement0(X5)
| ~ aElement0(X6)
| X6 = sz00 )
& ( X5 = sdtpldt0(sdtasdt0(esk18_2(X5,X6),X6),esk19_2(X5,X6))
| ~ aElement0(X5)
| ~ aElement0(X6)
| X6 = sz00 )
& ( esk19_2(X5,X6) = sz00
| iLess0(sbrdtbr0(esk19_2(X5,X6)),sbrdtbr0(X6))
| ~ aElement0(X5)
| ~ aElement0(X6)
| X6 = sz00 ) ),
inference(distribute,[status(thm)],[204]) ).
cnf(207,plain,
( X1 = sz00
| X2 = sdtpldt0(sdtasdt0(esk18_2(X2,X1),X1),esk19_2(X2,X1))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[205]) ).
cnf(208,plain,
( X1 = sz00
| aElement0(esk19_2(X2,X1))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[205]) ).
cnf(209,plain,
( X1 = sz00
| aElement0(esk18_2(X2,X1))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[205]) ).
fof(210,plain,
! [X1] :
( ~ aElement0(X1)
| ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(211,plain,
! [X2] :
( ~ aElement0(X2)
| ( sdtpldt0(X2,sz00) = X2
& X2 = sdtpldt0(sz00,X2) ) ),
inference(variable_rename,[status(thm)],[210]) ).
fof(212,plain,
! [X2] :
( ( sdtpldt0(X2,sz00) = X2
| ~ aElement0(X2) )
& ( X2 = sdtpldt0(sz00,X2)
| ~ aElement0(X2) ) ),
inference(distribute,[status(thm)],[211]) ).
cnf(213,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[212]) ).
cnf(214,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[212]) ).
fof(215,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(216,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| sdtasdt0(X3,X4) = sdtasdt0(X4,X3) ),
inference(variable_rename,[status(thm)],[215]) ).
cnf(217,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[216]) ).
fof(218,plain,
! [X1,X2] :
( ~ aElement0(X1)
| ~ aElement0(X2)
| sdtasdt0(X1,X2) != sz00
| X1 = sz00
| X2 = sz00 ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(219,plain,
! [X3,X4] :
( ~ aElement0(X3)
| ~ aElement0(X4)
| sdtasdt0(X3,X4) != sz00
| X3 = sz00
| X4 = sz00 ),
inference(variable_rename,[status(thm)],[218]) ).
cnf(220,plain,
( X1 = sz00
| X2 = sz00
| sdtasdt0(X2,X1) != sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[219]) ).
cnf(224,plain,
aElement0(xc),
inference(split_conjunct,[status(thm)],[38]) ).
fof(225,plain,
! [X1] :
( ~ aElement0(X1)
| ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
inference(fof_nnf,[status(thm)],[39]) ).
fof(226,plain,
! [X2] :
( ~ aElement0(X2)
| ( sdtasdt0(smndt0(sz10),X2) = smndt0(X2)
& smndt0(X2) = sdtasdt0(X2,smndt0(sz10)) ) ),
inference(variable_rename,[status(thm)],[225]) ).
fof(227,plain,
! [X2] :
( ( sdtasdt0(smndt0(sz10),X2) = smndt0(X2)
| ~ aElement0(X2) )
& ( smndt0(X2) = sdtasdt0(X2,smndt0(sz10))
| ~ aElement0(X2) ) ),
inference(distribute,[status(thm)],[226]) ).
cnf(228,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[227]) ).
cnf(229,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[227]) ).
fof(230,plain,
! [X1] :
( ~ aElement0(X1)
| aElement0(smndt0(X1)) ),
inference(fof_nnf,[status(thm)],[40]) ).
fof(231,plain,
! [X2] :
( ~ aElement0(X2)
| aElement0(smndt0(X2)) ),
inference(variable_rename,[status(thm)],[230]) ).
cnf(232,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[231]) ).
fof(250,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(fof_nnf,[status(thm)],[45]) ).
cnf(251,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(split_conjunct,[status(thm)],[250]) ).
cnf(252,plain,
sdtasdt0(xc,xu) = xx,
inference(split_conjunct,[status(thm)],[44]) ).
cnf(253,plain,
aElement0(xu),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(254,plain,
( sz00 = smndt0(sz00)
| ~ aElement0(smndt0(sz00))
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[213,180,theory(equality)]) ).
cnf(255,plain,
( sz00 = smndt0(sz00)
| ~ aElement0(smndt0(sz00))
| $false ),
inference(rw,[status(thm)],[254,184,theory(equality)]) ).
cnf(256,plain,
( sz00 = smndt0(sz00)
| ~ aElement0(smndt0(sz00)) ),
inference(cn,[status(thm)],[255,theory(equality)]) ).
cnf(270,plain,
( aElement0(xx)
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[183,252,theory(equality)]) ).
cnf(271,plain,
( aElement0(xy)
| ~ aElement0(xv)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[183,107,theory(equality)]) ).
cnf(272,plain,
( aElement0(sdtasdt0(xz,xx))
| ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[183,72,theory(equality)]) ).
cnf(280,plain,
( aElement0(xx)
| $false
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[270,253,theory(equality)]) ).
cnf(281,plain,
( aElement0(xx)
| $false
| $false ),
inference(rw,[status(thm)],[280,224,theory(equality)]) ).
cnf(282,plain,
aElement0(xx),
inference(cn,[status(thm)],[281,theory(equality)]) ).
cnf(283,plain,
( aElement0(xy)
| $false
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[271,108,theory(equality)]) ).
cnf(284,plain,
( aElement0(xy)
| $false
| $false ),
inference(rw,[status(thm)],[283,224,theory(equality)]) ).
cnf(285,plain,
aElement0(xy),
inference(cn,[status(thm)],[284,theory(equality)]) ).
cnf(286,plain,
( aElement0(sdtasdt0(xz,xx))
| ~ aElement0(sdtasdt0(xu,xz))
| $false ),
inference(rw,[status(thm)],[272,224,theory(equality)]) ).
cnf(287,plain,
( aElement0(sdtasdt0(xz,xx))
| ~ aElement0(sdtasdt0(xu,xz)) ),
inference(cn,[status(thm)],[286,theory(equality)]) ).
cnf(306,plain,
( sz00 = smndt0(sz10)
| sz00 = X1
| smndt0(X1) != sz00
| ~ aElement0(X1)
| ~ aElement0(smndt0(sz10)) ),
inference(spm,[status(thm)],[220,228,theory(equality)]) ).
cnf(427,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| slsdtgt0(X1) != X3
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(er,[status(thm)],[141,theory(equality)]) ).
cnf(429,plain,
( aElementOf0(X1,X2)
| xy != X1
| slsdtgt0(xc) != X2
| ~ aElement0(xv)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[141,107,theory(equality)]) ).
cnf(443,plain,
( aElementOf0(X1,X2)
| xy != X1
| slsdtgt0(xc) != X2
| $false
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[429,108,theory(equality)]) ).
cnf(444,plain,
( aElementOf0(X1,X2)
| xy != X1
| slsdtgt0(xc) != X2
| $false
| $false ),
inference(rw,[status(thm)],[443,224,theory(equality)]) ).
cnf(445,plain,
( aElementOf0(X1,X2)
| xy != X1
| slsdtgt0(xc) != X2 ),
inference(cn,[status(thm)],[444,theory(equality)]) ).
cnf(464,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(sdtasdt0(X1,X2)) ),
inference(er,[status(thm)],[85,theory(equality)]) ).
cnf(503,plain,
( aElementOf0(X1,X2)
| X4 != X1
| slsdtgt0(X3) != X2
| ~ aElement0(esk3_2(X3,X4))
| ~ aElement0(X3)
| ~ doDivides0(X3,X4)
| ~ aElement0(X4) ),
inference(spm,[status(thm)],[141,83,theory(equality)]) ).
cnf(509,plain,
( aElementOf0(X1,X2)
| slsdtgt0(X3) != X2
| ~ aElement0(esk3_2(X3,X1))
| ~ aElement0(X3)
| ~ doDivides0(X3,X1)
| ~ aElement0(X1) ),
inference(er,[status(thm)],[503,theory(equality)]) ).
cnf(531,plain,
( sdtasdt0(xx,X1) = sdtasdt0(xc,sdtasdt0(xu,X1))
| ~ aElement0(X1)
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[175,252,theory(equality)]) ).
cnf(540,plain,
( sdtasdt0(sz00,X2) = sdtasdt0(sz00,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[175,56,theory(equality)]) ).
cnf(544,plain,
( aElement0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aElement0(X3)
| ~ aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[183,175,theory(equality)]) ).
cnf(559,plain,
( sdtasdt0(xx,X1) = sdtasdt0(xc,sdtasdt0(xu,X1))
| ~ aElement0(X1)
| $false
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[531,253,theory(equality)]) ).
cnf(560,plain,
( sdtasdt0(xx,X1) = sdtasdt0(xc,sdtasdt0(xu,X1))
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[559,224,theory(equality)]) ).
cnf(561,plain,
( sdtasdt0(xx,X1) = sdtasdt0(xc,sdtasdt0(xu,X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[560,theory(equality)]) ).
cnf(579,plain,
( sdtasdt0(sz00,X2) = sdtasdt0(sz00,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[540,184,theory(equality)]) ).
cnf(580,plain,
( sdtasdt0(sz00,X2) = sdtasdt0(sz00,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[579,theory(equality)]) ).
cnf(583,plain,
( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[124,213,theory(equality)]) ).
cnf(584,plain,
( sdtpldt0(X1,sdtpldt0(X2,smndt0(sdtpldt0(X1,X2)))) = sz00
| ~ aElement0(sdtpldt0(X1,X2))
| ~ aElement0(smndt0(sdtpldt0(X1,X2)))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[180,124,theory(equality)]) ).
cnf(585,plain,
( sdtpldt0(sz00,X2) = sdtpldt0(X1,sdtpldt0(smndt0(X1),X2))
| ~ aElement0(X2)
| ~ aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[124,180,theory(equality)]) ).
cnf(586,plain,
( sdtpldt0(sz00,X2) = sdtpldt0(smndt0(X1),sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(smndt0(X1)) ),
inference(spm,[status(thm)],[124,179,theory(equality)]) ).
cnf(587,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aElement0(X3)
| ~ aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[60,124,theory(equality)]) ).
cnf(599,plain,
( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[583,184,theory(equality)]) ).
cnf(600,plain,
( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[599,theory(equality)]) ).
cnf(610,plain,
( sdtpldt0(esk18_2(X1,sz10),esk19_2(X1,sz10)) = X1
| sz00 = sz10
| ~ aElement0(X1)
| ~ aElement0(sz10)
| ~ aElement0(esk18_2(X1,sz10)) ),
inference(spm,[status(thm)],[207,113,theory(equality)]) ).
cnf(619,plain,
( sdtpldt0(esk18_2(X1,sz10),esk19_2(X1,sz10)) = X1
| sz00 = sz10
| ~ aElement0(X1)
| $false
| ~ aElement0(esk18_2(X1,sz10)) ),
inference(rw,[status(thm)],[610,145,theory(equality)]) ).
cnf(620,plain,
( sdtpldt0(esk18_2(X1,sz10),esk19_2(X1,sz10)) = X1
| sz00 = sz10
| ~ aElement0(X1)
| ~ aElement0(esk18_2(X1,sz10)) ),
inference(cn,[status(thm)],[619,theory(equality)]) ).
cnf(621,plain,
( sdtpldt0(esk18_2(X1,sz10),esk19_2(X1,sz10)) = X1
| ~ aElement0(X1)
| ~ aElement0(esk18_2(X1,sz10)) ),
inference(sr,[status(thm)],[620,132,theory(equality)]) ).
cnf(635,plain,
( sdtpldt0(xx,sdtasdt0(xc,X1)) = sdtasdt0(xc,sdtpldt0(xu,X1))
| ~ aElement0(xc)
| ~ aElement0(xu)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[77,252,theory(equality)]) ).
cnf(636,plain,
( sdtpldt0(sdtasdt0(xc,X1),xx) = sdtasdt0(xc,sdtpldt0(X1,xu))
| ~ aElement0(xc)
| ~ aElement0(X1)
| ~ aElement0(xu) ),
inference(spm,[status(thm)],[77,252,theory(equality)]) ).
cnf(637,plain,
( sdtpldt0(xy,sdtasdt0(xc,X1)) = sdtasdt0(xc,sdtpldt0(xv,X1))
| ~ aElement0(xc)
| ~ aElement0(xv)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[77,107,theory(equality)]) ).
cnf(643,plain,
( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
| ~ aElement0(X1)
| ~ aElement0(sz10)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[77,113,theory(equality)]) ).
cnf(644,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[77,113,theory(equality)]) ).
cnf(661,plain,
( aElement0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aElement0(sdtasdt0(X1,X3))
| ~ aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(spm,[status(thm)],[187,77,theory(equality)]) ).
cnf(670,plain,
( sdtpldt0(xx,sdtasdt0(xc,X1)) = sdtasdt0(xc,sdtpldt0(xu,X1))
| $false
| ~ aElement0(xu)
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[635,224,theory(equality)]) ).
cnf(671,plain,
( sdtpldt0(xx,sdtasdt0(xc,X1)) = sdtasdt0(xc,sdtpldt0(xu,X1))
| $false
| $false
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[670,253,theory(equality)]) ).
cnf(672,plain,
( sdtpldt0(xx,sdtasdt0(xc,X1)) = sdtasdt0(xc,sdtpldt0(xu,X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[671,theory(equality)]) ).
cnf(673,plain,
( sdtpldt0(sdtasdt0(xc,X1),xx) = sdtasdt0(xc,sdtpldt0(X1,xu))
| $false
| ~ aElement0(X1)
| ~ aElement0(xu) ),
inference(rw,[status(thm)],[636,224,theory(equality)]) ).
cnf(674,plain,
( sdtpldt0(sdtasdt0(xc,X1),xx) = sdtasdt0(xc,sdtpldt0(X1,xu))
| $false
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[673,253,theory(equality)]) ).
cnf(675,plain,
( sdtpldt0(sdtasdt0(xc,X1),xx) = sdtasdt0(xc,sdtpldt0(X1,xu))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[674,theory(equality)]) ).
cnf(676,plain,
( sdtpldt0(xy,sdtasdt0(xc,X1)) = sdtasdt0(xc,sdtpldt0(xv,X1))
| $false
| ~ aElement0(xv)
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[637,224,theory(equality)]) ).
cnf(677,plain,
( sdtpldt0(xy,sdtasdt0(xc,X1)) = sdtasdt0(xc,sdtpldt0(xv,X1))
| $false
| $false
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[676,108,theory(equality)]) ).
cnf(678,plain,
( sdtpldt0(xy,sdtasdt0(xc,X1)) = sdtasdt0(xc,sdtpldt0(xv,X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[677,theory(equality)]) ).
cnf(690,plain,
( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
| ~ aElement0(X1)
| $false
| ~ aElement0(X2) ),
inference(rw,[status(thm)],[643,145,theory(equality)]) ).
cnf(691,plain,
( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[690,theory(equality)]) ).
cnf(692,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aElement0(X1)
| ~ aElement0(X2)
| $false ),
inference(rw,[status(thm)],[644,145,theory(equality)]) ).
cnf(693,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[692,theory(equality)]) ).
cnf(706,plain,
( sdtpldt0(xx,sdtasdt0(X1,xu)) = sdtasdt0(sdtpldt0(xc,X1),xu)
| ~ aElement0(xu)
| ~ aElement0(xc)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[76,252,theory(equality)]) ).
cnf(716,plain,
( sdtpldt0(X1,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz10,X2),X1)
| ~ aElement0(X1)
| ~ aElement0(sz10)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[76,112,theory(equality)]) ).
cnf(717,plain,
( sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[76,112,theory(equality)]) ).
cnf(720,plain,
( sdtpldt0(sz00,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz00,X2),X1)
| ~ aElement0(X1)
| ~ aElement0(sz00)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[76,56,theory(equality)]) ).
cnf(742,plain,
( sdtpldt0(xx,sdtasdt0(X1,xu)) = sdtasdt0(sdtpldt0(xc,X1),xu)
| $false
| ~ aElement0(xc)
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[706,253,theory(equality)]) ).
cnf(743,plain,
( sdtpldt0(xx,sdtasdt0(X1,xu)) = sdtasdt0(sdtpldt0(xc,X1),xu)
| $false
| $false
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[742,224,theory(equality)]) ).
cnf(744,plain,
( sdtpldt0(xx,sdtasdt0(X1,xu)) = sdtasdt0(sdtpldt0(xc,X1),xu)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[743,theory(equality)]) ).
cnf(766,plain,
( sdtpldt0(X1,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz10,X2),X1)
| ~ aElement0(X1)
| $false
| ~ aElement0(X2) ),
inference(rw,[status(thm)],[716,145,theory(equality)]) ).
cnf(767,plain,
( sdtpldt0(X1,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz10,X2),X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[766,theory(equality)]) ).
cnf(768,plain,
( sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2)
| ~ aElement0(X2)
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[717,145,theory(equality)]) ).
cnf(769,plain,
( sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[768,theory(equality)]) ).
cnf(774,plain,
( sdtpldt0(sz00,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz00,X2),X1)
| ~ aElement0(X1)
| $false
| ~ aElement0(X2) ),
inference(rw,[status(thm)],[720,184,theory(equality)]) ).
cnf(775,plain,
( sdtpldt0(sz00,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz00,X2),X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[774,theory(equality)]) ).
cnf(818,plain,
( sdtpldt0(X1,X2) = sdtpldt0(esk18_2(X1,sz10),sdtpldt0(esk19_2(X1,sz10),X2))
| ~ aElement0(X2)
| ~ aElement0(esk19_2(X1,sz10))
| ~ aElement0(esk18_2(X1,sz10))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[124,621,theory(equality)]) ).
cnf(834,plain,
( smndt0(sz00) = sz00
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[256,232,theory(equality)]) ).
cnf(835,plain,
( smndt0(sz00) = sz00
| $false ),
inference(rw,[status(thm)],[834,184,theory(equality)]) ).
cnf(836,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[835,theory(equality)]) ).
cnf(843,plain,
( sdtpldt0(sz00,sz00) = sz00
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[180,836,theory(equality)]) ).
cnf(853,plain,
( sdtpldt0(sz00,sz00) = sz00
| $false ),
inference(rw,[status(thm)],[843,184,theory(equality)]) ).
cnf(854,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[853,theory(equality)]) ).
cnf(933,plain,
( sdtpldt0(esk18_2(X1,sz10),esk19_2(X1,sz10)) = sdtpldt0(X1,sz00)
| ~ aElement0(esk19_2(X1,sz10))
| ~ aElement0(esk18_2(X1,sz10))
| ~ aElement0(sz00)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[818,214,theory(equality)]) ).
cnf(941,plain,
( sdtpldt0(esk18_2(X1,sz10),esk19_2(X1,sz10)) = sdtpldt0(X1,sz00)
| ~ aElement0(esk19_2(X1,sz10))
| ~ aElement0(esk18_2(X1,sz10))
| $false
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[933,184,theory(equality)]) ).
cnf(942,plain,
( sdtpldt0(esk18_2(X1,sz10),esk19_2(X1,sz10)) = sdtpldt0(X1,sz00)
| ~ aElement0(esk19_2(X1,sz10))
| ~ aElement0(esk18_2(X1,sz10))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[941,theory(equality)]) ).
cnf(946,plain,
( aElement0(sdtpldt0(X1,sz00))
| ~ aElement0(esk19_2(X1,sz10))
| ~ aElement0(esk18_2(X1,sz10))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[187,942,theory(equality)]) ).
cnf(1083,plain,
( aElement0(sdtpldt0(X1,sz00))
| sz00 = sz10
| ~ aElement0(esk19_2(X1,sz10))
| ~ aElement0(X1)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[946,209,theory(equality)]) ).
cnf(1084,plain,
( aElement0(sdtpldt0(X1,sz00))
| sz00 = sz10
| ~ aElement0(esk19_2(X1,sz10))
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[1083,145,theory(equality)]) ).
cnf(1085,plain,
( aElement0(sdtpldt0(X1,sz00))
| sz00 = sz10
| ~ aElement0(esk19_2(X1,sz10))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[1084,theory(equality)]) ).
cnf(1086,plain,
( aElement0(sdtpldt0(X1,sz00))
| ~ aElement0(esk19_2(X1,sz10))
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[1085,132,theory(equality)]) ).
cnf(1087,plain,
( aElement0(sdtpldt0(X1,sz00))
| sz00 = sz10
| ~ aElement0(X1)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[1086,208,theory(equality)]) ).
cnf(1088,plain,
( aElement0(sdtpldt0(X1,sz00))
| sz00 = sz10
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[1087,145,theory(equality)]) ).
cnf(1089,plain,
( aElement0(sdtpldt0(X1,sz00))
| sz00 = sz10
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[1088,theory(equality)]) ).
cnf(1090,plain,
( aElement0(sdtpldt0(X1,sz00))
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[1089,132,theory(equality)]) ).
cnf(1097,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(X2,sz00)))
| ~ aElement0(sdtpldt0(X1,X2))
| ~ aElement0(sz00)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[1090,124,theory(equality)]) ).
cnf(1113,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(X2,sz00)))
| ~ aElement0(sdtpldt0(X1,X2))
| $false
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[1097,184,theory(equality)]) ).
cnf(1114,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(X2,sz00)))
| ~ aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[1113,theory(equality)]) ).
cnf(1172,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(X2,sz00)))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[1114,187]) ).
cnf(1180,plain,
( aElement0(sdtpldt0(sdtpldt0(X2,sz00),X1))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(sdtpldt0(X2,sz00)) ),
inference(spm,[status(thm)],[1172,60,theory(equality)]) ).
cnf(1183,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(X2,sdtpldt0(X3,sz00))))
| ~ aElement0(sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(sz00)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[1172,124,theory(equality)]) ).
cnf(1201,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(X2,sdtpldt0(X3,sz00))))
| ~ aElement0(sdtpldt0(X2,X3))
| ~ aElement0(X1)
| $false
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(rw,[status(thm)],[1183,184,theory(equality)]) ).
cnf(1202,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(X2,sdtpldt0(X3,sz00))))
| ~ aElement0(sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[1201,theory(equality)]) ).
cnf(1236,plain,
( aElement0(sdtasdt0(xz,xx))
| ~ aElement0(xz)
| ~ aElement0(xu) ),
inference(spm,[status(thm)],[287,183,theory(equality)]) ).
cnf(1240,plain,
( aElement0(sdtasdt0(xz,xx))
| $false
| ~ aElement0(xu) ),
inference(rw,[status(thm)],[1236,94,theory(equality)]) ).
cnf(1241,plain,
( aElement0(sdtasdt0(xz,xx))
| $false
| $false ),
inference(rw,[status(thm)],[1240,253,theory(equality)]) ).
cnf(1242,plain,
aElement0(sdtasdt0(xz,xx)),
inference(cn,[status(thm)],[1241,theory(equality)]) ).
cnf(1249,plain,
( aElement0(sdtasdt0(xx,xz))
| ~ aElement0(xx)
| ~ aElement0(xz) ),
inference(spm,[status(thm)],[1242,217,theory(equality)]) ).
cnf(1253,plain,
( aElement0(sdtasdt0(xx,xz))
| $false
| ~ aElement0(xz) ),
inference(rw,[status(thm)],[1249,282,theory(equality)]) ).
cnf(1254,plain,
( aElement0(sdtasdt0(xx,xz))
| $false
| $false ),
inference(rw,[status(thm)],[1253,94,theory(equality)]) ).
cnf(1255,plain,
aElement0(sdtasdt0(xx,xz)),
inference(cn,[status(thm)],[1254,theory(equality)]) ).
cnf(1267,plain,
( aElement0(sdtpldt0(sdtpldt0(X2,sz00),X1))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[1180,1090]) ).
cnf(1274,plain,
( aElement0(sdtpldt0(sdtpldt0(sz00,X1),X2))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[1267,60,theory(equality)]) ).
cnf(1291,plain,
( aElement0(sdtpldt0(sdtpldt0(sz00,X1),X2))
| ~ aElement0(X1)
| ~ aElement0(X2)
| $false ),
inference(rw,[status(thm)],[1274,184,theory(equality)]) ).
cnf(1292,plain,
( aElement0(sdtpldt0(sdtpldt0(sz00,X1),X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[1291,theory(equality)]) ).
cnf(1319,plain,
( aElement0(sdtpldt0(sz00,sdtpldt0(X1,X2)))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[1292,124,theory(equality)]) ).
cnf(1335,plain,
( aElement0(sdtpldt0(sz00,sdtpldt0(X1,X2)))
| ~ aElement0(X1)
| ~ aElement0(X2)
| $false ),
inference(rw,[status(thm)],[1319,184,theory(equality)]) ).
cnf(1336,plain,
( aElement0(sdtpldt0(sz00,sdtpldt0(X1,X2)))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(cn,[status(thm)],[1335,theory(equality)]) ).
cnf(1363,plain,
( aElementOf0(X1,slsdtgt0(xc))
| xy != X1 ),
inference(er,[status(thm)],[445,theory(equality)]) ).
cnf(1365,plain,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| xy != sdtpldt0(xx,xy) ),
inference(spm,[status(thm)],[251,1363,theory(equality)]) ).
cnf(1409,plain,
( aElement0(sdtpldt0(sz00,sdtasdt0(X1,sdtpldt0(X2,X3))))
| ~ aElement0(sdtasdt0(X1,X2))
| ~ aElement0(sdtasdt0(X1,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(spm,[status(thm)],[1336,77,theory(equality)]) ).
cnf(1557,plain,
( smndt0(sz10) = sz00
| sz00 = X1
| smndt0(X1) != sz00
| ~ aElement0(X1)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[306,232,theory(equality)]) ).
cnf(1560,plain,
( smndt0(sz10) = sz00
| sz00 = X1
| smndt0(X1) != sz00
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[1557,145,theory(equality)]) ).
cnf(1561,plain,
( smndt0(sz10) = sz00
| sz00 = X1
| smndt0(X1) != sz00
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[1560,theory(equality)]) ).
cnf(1562,plain,
( sdtpldt0(xx,xy) != xy
| ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc))
| ~ aElement0(xx)
| ~ aElement0(xz) ),
inference(spm,[status(thm)],[1365,217,theory(equality)]) ).
cnf(1567,plain,
( sdtpldt0(xx,xy) != xy
| ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc))
| $false
| ~ aElement0(xz) ),
inference(rw,[status(thm)],[1562,282,theory(equality)]) ).
cnf(1568,plain,
( sdtpldt0(xx,xy) != xy
| ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc))
| $false
| $false ),
inference(rw,[status(thm)],[1567,94,theory(equality)]) ).
cnf(1569,plain,
( sdtpldt0(xx,xy) != xy
| ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc)) ),
inference(cn,[status(thm)],[1568,theory(equality)]) ).
cnf(2589,plain,
( sdtasdt0(xx,xz) = sdtasdt0(xz,xx)
| ~ aElement0(xz) ),
inference(spm,[status(thm)],[72,561,theory(equality)]) ).
cnf(2591,plain,
( sdtasdt0(xc,sz00) = sdtasdt0(xx,sz00)
| ~ aElement0(sz00)
| ~ aElement0(xu) ),
inference(spm,[status(thm)],[561,57,theory(equality)]) ).
cnf(2594,plain,
( sz00 = sdtasdt0(xu,X1)
| sz00 = xc
| sdtasdt0(xx,X1) != sz00
| ~ aElement0(xc)
| ~ aElement0(sdtasdt0(xu,X1))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[220,561,theory(equality)]) ).
cnf(2609,plain,
( sdtasdt0(xx,xz) = sdtasdt0(xz,xx)
| $false ),
inference(rw,[status(thm)],[2589,94,theory(equality)]) ).
cnf(2610,plain,
sdtasdt0(xx,xz) = sdtasdt0(xz,xx),
inference(cn,[status(thm)],[2609,theory(equality)]) ).
cnf(2615,plain,
( sdtasdt0(xc,sz00) = sdtasdt0(xx,sz00)
| $false
| ~ aElement0(xu) ),
inference(rw,[status(thm)],[2591,184,theory(equality)]) ).
cnf(2616,plain,
( sdtasdt0(xc,sz00) = sdtasdt0(xx,sz00)
| $false
| $false ),
inference(rw,[status(thm)],[2615,253,theory(equality)]) ).
cnf(2617,plain,
sdtasdt0(xc,sz00) = sdtasdt0(xx,sz00),
inference(cn,[status(thm)],[2616,theory(equality)]) ).
cnf(2622,plain,
( sz00 = sdtasdt0(xu,X1)
| sz00 = xc
| sdtasdt0(xx,X1) != sz00
| $false
| ~ aElement0(sdtasdt0(xu,X1))
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[2594,224,theory(equality)]) ).
cnf(2623,plain,
( sz00 = sdtasdt0(xu,X1)
| sz00 = xc
| sdtasdt0(xx,X1) != sz00
| ~ aElement0(sdtasdt0(xu,X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[2622,theory(equality)]) ).
cnf(2790,plain,
sdtasdt0(xc,sdtasdt0(xu,xz)) = sdtasdt0(xx,xz),
inference(rw,[status(thm)],[72,2610,theory(equality)]) ).
cnf(2810,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(rw,[status(thm)],[251,2610,theory(equality)]) ).
cnf(2844,plain,
( sdtasdt0(xc,sz00) = sz00
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[57,2617,theory(equality)]) ).
cnf(2857,plain,
( sdtasdt0(xc,sz00) = sz00
| $false ),
inference(rw,[status(thm)],[2844,282,theory(equality)]) ).
cnf(2858,plain,
sdtasdt0(xc,sz00) = sz00,
inference(cn,[status(thm)],[2857,theory(equality)]) ).
cnf(2906,plain,
sdtasdt0(xx,sz00) = sz00,
inference(rw,[status(thm)],[2617,2858,theory(equality)]) ).
cnf(2947,plain,
( sz00 = sdtasdt0(sz00,xx)
| ~ aElement0(sz00)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[217,2906,theory(equality)]) ).
cnf(2962,plain,
( sz00 = sdtasdt0(sz00,xx)
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[2947,184,theory(equality)]) ).
cnf(2963,plain,
( sz00 = sdtasdt0(sz00,xx)
| $false
| $false ),
inference(rw,[status(thm)],[2962,282,theory(equality)]) ).
cnf(2964,plain,
sz00 = sdtasdt0(sz00,xx),
inference(cn,[status(thm)],[2963,theory(equality)]) ).
cnf(3408,plain,
( aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X1))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(er,[status(thm)],[427,theory(equality)]) ).
cnf(3824,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[464,183]) ).
cnf(3831,plain,
( doDivides0(xc,sz00)
| ~ aElement0(sz00)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[3824,2858,theory(equality)]) ).
cnf(3833,plain,
( doDivides0(xc,sdtasdt0(xx,xz))
| ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[3824,2790,theory(equality)]) ).
cnf(3870,plain,
( doDivides0(xc,sz00)
| $false
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[3831,184,theory(equality)]) ).
cnf(3871,plain,
( doDivides0(xc,sz00)
| $false
| $false ),
inference(rw,[status(thm)],[3870,224,theory(equality)]) ).
cnf(3872,plain,
doDivides0(xc,sz00),
inference(cn,[status(thm)],[3871,theory(equality)]) ).
cnf(3876,plain,
( doDivides0(xc,sdtasdt0(xx,xz))
| ~ aElement0(sdtasdt0(xu,xz))
| $false ),
inference(rw,[status(thm)],[3833,224,theory(equality)]) ).
cnf(3877,plain,
( doDivides0(xc,sdtasdt0(xx,xz))
| ~ aElement0(sdtasdt0(xu,xz)) ),
inference(cn,[status(thm)],[3876,theory(equality)]) ).
cnf(4070,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(X2,sdtpldt0(X3,sz00))))
| ~ aElement0(X1)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[1202,187]) ).
cnf(4072,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(X2,X3)))
| ~ aElement0(X1)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[4070,214,theory(equality)]) ).
cnf(4631,plain,
( aElementOf0(X1,X2)
| slsdtgt0(X3) != X2
| ~ doDivides0(X3,X1)
| ~ aElement0(X3)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[509,84]) ).
cnf(4636,plain,
( aElementOf0(sz00,X1)
| slsdtgt0(xc) != X1
| ~ aElement0(xc)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[4631,3872,theory(equality)]) ).
cnf(4680,plain,
( aElementOf0(sz00,X1)
| slsdtgt0(xc) != X1
| $false
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[4636,224,theory(equality)]) ).
cnf(4681,plain,
( aElementOf0(sz00,X1)
| slsdtgt0(xc) != X1
| $false
| $false ),
inference(rw,[status(thm)],[4680,184,theory(equality)]) ).
cnf(4682,plain,
( aElementOf0(sz00,X1)
| slsdtgt0(xc) != X1 ),
inference(cn,[status(thm)],[4681,theory(equality)]) ).
cnf(4776,plain,
aElementOf0(sz00,slsdtgt0(xc)),
inference(er,[status(thm)],[4682,theory(equality)]) ).
cnf(6647,plain,
( sdtasdt0(sz00,sdtasdt0(xx,xz)) = sdtasdt0(sz00,xx)
| ~ aElement0(xx)
| ~ aElement0(xz) ),
inference(spm,[status(thm)],[580,2610,theory(equality)]) ).
cnf(6709,plain,
( sdtasdt0(sz00,sdtasdt0(xx,xz)) = sz00
| ~ aElement0(xx)
| ~ aElement0(xz) ),
inference(rw,[status(thm)],[6647,2964,theory(equality)]) ).
cnf(6710,plain,
( sdtasdt0(sz00,sdtasdt0(xx,xz)) = sz00
| $false
| ~ aElement0(xz) ),
inference(rw,[status(thm)],[6709,282,theory(equality)]) ).
cnf(6711,plain,
( sdtasdt0(sz00,sdtasdt0(xx,xz)) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[6710,94,theory(equality)]) ).
cnf(6712,plain,
sdtasdt0(sz00,sdtasdt0(xx,xz)) = sz00,
inference(cn,[status(thm)],[6711,theory(equality)]) ).
cnf(7248,plain,
( sz00 = sdtasdt0(sz00,xz)
| ~ aElement0(xz)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[580,6712,theory(equality)]) ).
cnf(7303,plain,
( sz00 = sdtasdt0(sz00,xz)
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[7248,94,theory(equality)]) ).
cnf(7304,plain,
( sz00 = sdtasdt0(sz00,xz)
| $false
| $false ),
inference(rw,[status(thm)],[7303,282,theory(equality)]) ).
cnf(7305,plain,
sz00 = sdtasdt0(sz00,xz),
inference(cn,[status(thm)],[7304,theory(equality)]) ).
cnf(7618,plain,
( aElement0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[544,183]) ).
cnf(7625,plain,
( aElement0(sdtasdt0(X1,sz00))
| ~ aElement0(sz00)
| ~ aElement0(xc)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[7618,2858,theory(equality)]) ).
cnf(7708,plain,
( aElement0(sdtasdt0(X1,sz00))
| $false
| ~ aElement0(xc)
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[7625,184,theory(equality)]) ).
cnf(7709,plain,
( aElement0(sdtasdt0(X1,sz00))
| $false
| $false
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[7708,224,theory(equality)]) ).
cnf(7710,plain,
( aElement0(sdtasdt0(X1,sz00))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[7709,theory(equality)]) ).
cnf(11671,plain,
( sdtpldt0(X1,sdtpldt0(X2,smndt0(sdtpldt0(X1,X2)))) = sz00
| ~ aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[584,232]) ).
cnf(11672,plain,
( sdtpldt0(X1,sdtpldt0(X2,smndt0(sdtpldt0(X1,X2)))) = sz00
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[11671,187]) ).
cnf(11897,plain,
( sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[585,232]) ).
cnf(12132,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[586,232]) ).
cnf(12273,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[587,187]) ).
cnf(16636,plain,
( sdtpldt0(xx,sz00) = sdtasdt0(xc,sdtpldt0(xu,sz00))
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[672,2858,theory(equality)]) ).
cnf(16641,plain,
( sdtpldt0(xx,xc) = sdtasdt0(xc,sdtpldt0(xu,sz10))
| ~ aElement0(sz10)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[672,113,theory(equality)]) ).
cnf(16692,plain,
( sdtpldt0(xx,sz00) = sdtasdt0(xc,sdtpldt0(xu,sz00))
| $false ),
inference(rw,[status(thm)],[16636,184,theory(equality)]) ).
cnf(16693,plain,
sdtpldt0(xx,sz00) = sdtasdt0(xc,sdtpldt0(xu,sz00)),
inference(cn,[status(thm)],[16692,theory(equality)]) ).
cnf(16694,plain,
( sdtpldt0(xx,xc) = sdtasdt0(xc,sdtpldt0(xu,sz10))
| $false
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[16641,145,theory(equality)]) ).
cnf(16695,plain,
( sdtpldt0(xx,xc) = sdtasdt0(xc,sdtpldt0(xu,sz10))
| $false
| $false ),
inference(rw,[status(thm)],[16694,224,theory(equality)]) ).
cnf(16696,plain,
sdtpldt0(xx,xc) = sdtasdt0(xc,sdtpldt0(xu,sz10)),
inference(cn,[status(thm)],[16695,theory(equality)]) ).
cnf(16882,plain,
( sdtasdt0(xc,sdtpldt0(sz10,xu)) = sdtpldt0(xx,xc)
| ~ aElement0(sz10)
| ~ aElement0(xu) ),
inference(spm,[status(thm)],[16696,60,theory(equality)]) ).
cnf(16916,plain,
( sdtasdt0(xc,sdtpldt0(sz10,xu)) = sdtpldt0(xx,xc)
| $false
| ~ aElement0(xu) ),
inference(rw,[status(thm)],[16882,145,theory(equality)]) ).
cnf(16917,plain,
( sdtasdt0(xc,sdtpldt0(sz10,xu)) = sdtpldt0(xx,xc)
| $false
| $false ),
inference(rw,[status(thm)],[16916,253,theory(equality)]) ).
cnf(16918,plain,
sdtasdt0(xc,sdtpldt0(sz10,xu)) = sdtpldt0(xx,xc),
inference(cn,[status(thm)],[16917,theory(equality)]) ).
cnf(17077,plain,
( sdtpldt0(xc,xx) = sdtasdt0(xc,sdtpldt0(sz10,xu))
| ~ aElement0(sz10)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[675,113,theory(equality)]) ).
cnf(17132,plain,
( sdtpldt0(xc,xx) = sdtpldt0(xx,xc)
| ~ aElement0(sz10)
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[17077,16918,theory(equality)]) ).
cnf(17133,plain,
( sdtpldt0(xc,xx) = sdtpldt0(xx,xc)
| $false
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[17132,145,theory(equality)]) ).
cnf(17134,plain,
( sdtpldt0(xc,xx) = sdtpldt0(xx,xc)
| $false
| $false ),
inference(rw,[status(thm)],[17133,224,theory(equality)]) ).
cnf(17135,plain,
sdtpldt0(xc,xx) = sdtpldt0(xx,xc),
inference(cn,[status(thm)],[17134,theory(equality)]) ).
cnf(17219,plain,
( aElement0(sdtpldt0(xc,xx))
| ~ aElement0(xc)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[187,17135,theory(equality)]) ).
cnf(17224,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(xc,xx)))
| ~ aElement0(X1)
| ~ aElement0(xc)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[4072,17135,theory(equality)]) ).
cnf(17233,plain,
( sdtpldt0(sz00,sdtpldt0(xc,xx)) = sdtpldt0(xc,xx)
| ~ aElement0(xc)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[600,17135,theory(equality)]) ).
cnf(17235,plain,
( sdtpldt0(smndt0(xx),sdtpldt0(xc,xx)) = sdtpldt0(sz00,xc)
| ~ aElement0(xc)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[12132,17135,theory(equality)]) ).
cnf(17244,plain,
( aElement0(sdtpldt0(xc,xx))
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[17219,224,theory(equality)]) ).
cnf(17245,plain,
( aElement0(sdtpldt0(xc,xx))
| $false
| $false ),
inference(rw,[status(thm)],[17244,282,theory(equality)]) ).
cnf(17246,plain,
aElement0(sdtpldt0(xc,xx)),
inference(cn,[status(thm)],[17245,theory(equality)]) ).
cnf(17256,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(xc,xx)))
| ~ aElement0(X1)
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[17224,224,theory(equality)]) ).
cnf(17257,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(xc,xx)))
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[17256,282,theory(equality)]) ).
cnf(17258,plain,
( aElement0(sdtpldt0(X1,sdtpldt0(xc,xx)))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[17257,theory(equality)]) ).
cnf(17280,plain,
( sdtpldt0(sz00,sdtpldt0(xc,xx)) = sdtpldt0(xc,xx)
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[17233,224,theory(equality)]) ).
cnf(17281,plain,
( sdtpldt0(sz00,sdtpldt0(xc,xx)) = sdtpldt0(xc,xx)
| $false
| $false ),
inference(rw,[status(thm)],[17280,282,theory(equality)]) ).
cnf(17282,plain,
sdtpldt0(sz00,sdtpldt0(xc,xx)) = sdtpldt0(xc,xx),
inference(cn,[status(thm)],[17281,theory(equality)]) ).
cnf(17286,plain,
( sdtpldt0(smndt0(xx),sdtpldt0(xc,xx)) = sdtpldt0(sz00,xc)
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[17235,224,theory(equality)]) ).
cnf(17287,plain,
( sdtpldt0(smndt0(xx),sdtpldt0(xc,xx)) = sdtpldt0(sz00,xc)
| $false
| $false ),
inference(rw,[status(thm)],[17286,282,theory(equality)]) ).
cnf(17288,plain,
sdtpldt0(smndt0(xx),sdtpldt0(xc,xx)) = sdtpldt0(sz00,xc),
inference(cn,[status(thm)],[17287,theory(equality)]) ).
cnf(17575,plain,
( sdtpldt0(xy,sz00) = sdtasdt0(xc,sdtpldt0(xv,sz00))
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[678,2858,theory(equality)]) ).
cnf(17629,plain,
( sdtpldt0(xy,sz00) = sdtasdt0(xc,sdtpldt0(xv,sz00))
| $false ),
inference(rw,[status(thm)],[17575,184,theory(equality)]) ).
cnf(17630,plain,
sdtpldt0(xy,sz00) = sdtasdt0(xc,sdtpldt0(xv,sz00)),
inference(cn,[status(thm)],[17629,theory(equality)]) ).
cnf(17717,plain,
( aElement0(sdtpldt0(xx,sdtpldt0(X1,xc)))
| ~ aElement0(X1)
| ~ aElement0(xx)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[17258,12273,theory(equality)]) ).
cnf(17745,plain,
( aElement0(sdtpldt0(xx,sdtpldt0(X1,xc)))
| ~ aElement0(X1)
| $false
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[17717,282,theory(equality)]) ).
cnf(17746,plain,
( aElement0(sdtpldt0(xx,sdtpldt0(X1,xc)))
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[17745,224,theory(equality)]) ).
cnf(17747,plain,
( aElement0(sdtpldt0(xx,sdtpldt0(X1,xc)))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[17746,theory(equality)]) ).
cnf(19313,plain,
( aElement0(sdtpldt0(sz00,xc))
| ~ aElement0(smndt0(xx))
| ~ aElement0(xc)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[17747,11897,theory(equality)]) ).
cnf(19339,plain,
( aElement0(sdtpldt0(sz00,xc))
| ~ aElement0(smndt0(xx))
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[19313,224,theory(equality)]) ).
cnf(19340,plain,
( aElement0(sdtpldt0(sz00,xc))
| ~ aElement0(smndt0(xx))
| $false
| $false ),
inference(rw,[status(thm)],[19339,282,theory(equality)]) ).
cnf(19341,plain,
( aElement0(sdtpldt0(sz00,xc))
| ~ aElement0(smndt0(xx)) ),
inference(cn,[status(thm)],[19340,theory(equality)]) ).
cnf(19548,plain,
( sdtpldt0(xx,sz00) = sdtasdt0(xx,sdtpldt0(sz10,sz00))
| ~ aElement0(xx)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[691,2906,theory(equality)]) ).
cnf(19698,plain,
( sdtpldt0(xx,sz00) = sdtasdt0(xx,sdtpldt0(sz10,sz00))
| $false
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[19548,282,theory(equality)]) ).
cnf(19699,plain,
( sdtpldt0(xx,sz00) = sdtasdt0(xx,sdtpldt0(sz10,sz00))
| $false
| $false ),
inference(rw,[status(thm)],[19698,184,theory(equality)]) ).
cnf(19700,plain,
sdtpldt0(xx,sz00) = sdtasdt0(xx,sdtpldt0(sz10,sz00)),
inference(cn,[status(thm)],[19699,theory(equality)]) ).
cnf(20422,plain,
( aElement0(sdtpldt0(sz00,xc))
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[19341,232,theory(equality)]) ).
cnf(20427,plain,
( aElement0(sdtpldt0(sz00,xc))
| $false ),
inference(rw,[status(thm)],[20422,282,theory(equality)]) ).
cnf(20428,plain,
aElement0(sdtpldt0(sz00,xc)),
inference(cn,[status(thm)],[20427,theory(equality)]) ).
cnf(30872,plain,
( sdtasdt0(xc,xu) = sdtpldt0(xx,sz00)
| ~ aElement0(xu) ),
inference(spm,[status(thm)],[16693,214,theory(equality)]) ).
cnf(30922,plain,
( xx = sdtpldt0(xx,sz00)
| ~ aElement0(xu) ),
inference(rw,[status(thm)],[30872,252,theory(equality)]) ).
cnf(30923,plain,
( xx = sdtpldt0(xx,sz00)
| $false ),
inference(rw,[status(thm)],[30922,253,theory(equality)]) ).
cnf(30924,plain,
xx = sdtpldt0(xx,sz00),
inference(cn,[status(thm)],[30923,theory(equality)]) ).
cnf(31013,plain,
( xx = sdtpldt0(sz00,xx)
| ~ aElement0(sz00)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[60,30924,theory(equality)]) ).
cnf(31041,plain,
( sdtpldt0(smndt0(xx),xx) = sdtpldt0(sz00,sz00)
| ~ aElement0(sz00)
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[12132,30924,theory(equality)]) ).
cnf(31060,plain,
( xx = sdtpldt0(sz00,xx)
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[31013,184,theory(equality)]) ).
cnf(31061,plain,
( xx = sdtpldt0(sz00,xx)
| $false
| $false ),
inference(rw,[status(thm)],[31060,282,theory(equality)]) ).
cnf(31062,plain,
xx = sdtpldt0(sz00,xx),
inference(cn,[status(thm)],[31061,theory(equality)]) ).
cnf(31134,plain,
( sdtpldt0(smndt0(xx),xx) = sz00
| ~ aElement0(sz00)
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[31041,854,theory(equality)]) ).
cnf(31135,plain,
( sdtpldt0(smndt0(xx),xx) = sz00
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[31134,184,theory(equality)]) ).
cnf(31136,plain,
( sdtpldt0(smndt0(xx),xx) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[31135,282,theory(equality)]) ).
cnf(31137,plain,
sdtpldt0(smndt0(xx),xx) = sz00,
inference(cn,[status(thm)],[31136,theory(equality)]) ).
cnf(32683,plain,
( sdtpldt0(xx,sdtpldt0(sz00,xc)) = sdtpldt0(sz00,sdtpldt0(xc,xx))
| ~ aElement0(sdtpldt0(xc,xx))
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[11897,17288,theory(equality)]) ).
cnf(32738,plain,
( sdtpldt0(xx,sdtpldt0(sz00,xc)) = sdtpldt0(xc,xx)
| ~ aElement0(sdtpldt0(xc,xx))
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[32683,17282,theory(equality)]) ).
cnf(32739,plain,
( sdtpldt0(xx,sdtpldt0(sz00,xc)) = sdtpldt0(xc,xx)
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[32738,17246,theory(equality)]) ).
cnf(32740,plain,
( sdtpldt0(xx,sdtpldt0(sz00,xc)) = sdtpldt0(xc,xx)
| $false
| $false ),
inference(rw,[status(thm)],[32739,282,theory(equality)]) ).
cnf(32741,plain,
sdtpldt0(xx,sdtpldt0(sz00,xc)) = sdtpldt0(xc,xx),
inference(cn,[status(thm)],[32740,theory(equality)]) ).
cnf(32804,plain,
( sdtpldt0(smndt0(xx),sdtpldt0(xc,xx)) = sdtpldt0(sz00,sdtpldt0(sz00,xc))
| ~ aElement0(sdtpldt0(sz00,xc))
| ~ aElement0(xx) ),
inference(spm,[status(thm)],[12132,32741,theory(equality)]) ).
cnf(32897,plain,
( sdtpldt0(sz00,xc) = sdtpldt0(sz00,sdtpldt0(sz00,xc))
| ~ aElement0(sdtpldt0(sz00,xc))
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[32804,17288,theory(equality)]) ).
cnf(32898,plain,
( sdtpldt0(sz00,xc) = sdtpldt0(sz00,sdtpldt0(sz00,xc))
| $false
| ~ aElement0(xx) ),
inference(rw,[status(thm)],[32897,20428,theory(equality)]) ).
cnf(32899,plain,
( sdtpldt0(sz00,xc) = sdtpldt0(sz00,sdtpldt0(sz00,xc))
| $false
| $false ),
inference(rw,[status(thm)],[32898,282,theory(equality)]) ).
cnf(32900,plain,
sdtpldt0(sz00,xc) = sdtpldt0(sz00,sdtpldt0(sz00,xc)),
inference(cn,[status(thm)],[32899,theory(equality)]) ).
cnf(34136,plain,
( sdtasdt0(xc,xv) = sdtpldt0(xy,sz00)
| ~ aElement0(xv) ),
inference(spm,[status(thm)],[17630,214,theory(equality)]) ).
cnf(34187,plain,
( xy = sdtpldt0(xy,sz00)
| ~ aElement0(xv) ),
inference(rw,[status(thm)],[34136,107,theory(equality)]) ).
cnf(34188,plain,
( xy = sdtpldt0(xy,sz00)
| $false ),
inference(rw,[status(thm)],[34187,108,theory(equality)]) ).
cnf(34189,plain,
xy = sdtpldt0(xy,sz00),
inference(cn,[status(thm)],[34188,theory(equality)]) ).
cnf(34281,plain,
( xy = sdtpldt0(sz00,xy)
| ~ aElement0(sz00)
| ~ aElement0(xy) ),
inference(spm,[status(thm)],[60,34189,theory(equality)]) ).
cnf(34316,plain,
( xy = sdtpldt0(sz00,xy)
| $false
| ~ aElement0(xy) ),
inference(rw,[status(thm)],[34281,184,theory(equality)]) ).
cnf(34317,plain,
( xy = sdtpldt0(sz00,xy)
| $false
| $false ),
inference(rw,[status(thm)],[34316,285,theory(equality)]) ).
cnf(34318,plain,
xy = sdtpldt0(sz00,xy),
inference(cn,[status(thm)],[34317,theory(equality)]) ).
cnf(35161,plain,
( aElement0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aElement0(sdtasdt0(X1,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[661,183]) ).
cnf(35162,plain,
( aElement0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[35161,183]) ).
cnf(36316,plain,
( sdtpldt0(sz00,xc) = xc
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[32900,213,theory(equality)]) ).
cnf(36365,plain,
( sdtpldt0(sz00,xc) = xc
| $false ),
inference(rw,[status(thm)],[36316,224,theory(equality)]) ).
cnf(36366,plain,
sdtpldt0(sz00,xc) = xc,
inference(cn,[status(thm)],[36365,theory(equality)]) ).
cnf(36514,plain,
( sdtpldt0(xc,X1) = sdtpldt0(sz00,sdtpldt0(xc,X1))
| ~ aElement0(X1)
| ~ aElement0(xc)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[124,36366,theory(equality)]) ).
cnf(36534,plain,
( sdtpldt0(sz00,sdtpldt0(xc,smndt0(xc))) = sz00
| ~ aElement0(xc)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[11672,36366,theory(equality)]) ).
cnf(36543,plain,
( aElement0(sdtasdt0(X1,xc))
| ~ aElement0(X1)
| ~ aElement0(sz00)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[35162,36366,theory(equality)]) ).
cnf(36573,plain,
( sdtpldt0(xc,X1) = sdtpldt0(sz00,sdtpldt0(xc,X1))
| ~ aElement0(X1)
| $false
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[36514,224,theory(equality)]) ).
cnf(36574,plain,
( sdtpldt0(xc,X1) = sdtpldt0(sz00,sdtpldt0(xc,X1))
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[36573,184,theory(equality)]) ).
cnf(36575,plain,
( sdtpldt0(xc,X1) = sdtpldt0(sz00,sdtpldt0(xc,X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[36574,theory(equality)]) ).
cnf(36630,plain,
( sdtpldt0(sz00,sdtpldt0(xc,smndt0(xc))) = sz00
| $false
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[36534,224,theory(equality)]) ).
cnf(36631,plain,
( sdtpldt0(sz00,sdtpldt0(xc,smndt0(xc))) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[36630,184,theory(equality)]) ).
cnf(36632,plain,
sdtpldt0(sz00,sdtpldt0(xc,smndt0(xc))) = sz00,
inference(cn,[status(thm)],[36631,theory(equality)]) ).
cnf(36659,plain,
( aElement0(sdtasdt0(X1,xc))
| ~ aElement0(X1)
| $false
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[36543,184,theory(equality)]) ).
cnf(36660,plain,
( aElement0(sdtasdt0(X1,xc))
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[36659,224,theory(equality)]) ).
cnf(36661,plain,
( aElement0(sdtasdt0(X1,xc))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[36660,theory(equality)]) ).
cnf(36898,plain,
( aElement0(smndt0(xc))
| ~ aElement0(smndt0(sz10))
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[36661,229,theory(equality)]) ).
cnf(36918,plain,
( aElement0(smndt0(xc))
| ~ aElement0(smndt0(sz10))
| $false ),
inference(rw,[status(thm)],[36898,224,theory(equality)]) ).
cnf(36919,plain,
( aElement0(smndt0(xc))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[36918,theory(equality)]) ).
cnf(37113,plain,
( sz00 = sdtpldt0(xc,smndt0(xc))
| ~ aElement0(smndt0(xc))
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[600,36632,theory(equality)]) ).
cnf(37180,plain,
( sz00 = sdtpldt0(xc,smndt0(xc))
| ~ aElement0(smndt0(xc))
| $false ),
inference(rw,[status(thm)],[37113,224,theory(equality)]) ).
cnf(37181,plain,
( sz00 = sdtpldt0(xc,smndt0(xc))
| ~ aElement0(smndt0(xc)) ),
inference(cn,[status(thm)],[37180,theory(equality)]) ).
cnf(37478,plain,
( aElement0(smndt0(xc))
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[36919,232,theory(equality)]) ).
cnf(37482,plain,
( aElement0(smndt0(xc))
| $false ),
inference(rw,[status(thm)],[37478,145,theory(equality)]) ).
cnf(37483,plain,
aElement0(smndt0(xc)),
inference(cn,[status(thm)],[37482,theory(equality)]) ).
cnf(42122,plain,
sdtasdt0(xx,sdtpldt0(sz10,sz00)) = xx,
inference(rw,[status(thm)],[19700,30924,theory(equality)]) ).
cnf(42126,plain,
( sdtasdt0(xx,sdtpldt0(sz00,sz10)) = xx
| ~ aElement0(sz00)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[42122,60,theory(equality)]) ).
cnf(42186,plain,
( sdtasdt0(xx,sdtpldt0(sz00,sz10)) = xx
| $false
| ~ aElement0(sz10) ),
inference(rw,[status(thm)],[42126,184,theory(equality)]) ).
cnf(42187,plain,
( sdtasdt0(xx,sdtpldt0(sz00,sz10)) = xx
| $false
| $false ),
inference(rw,[status(thm)],[42186,145,theory(equality)]) ).
cnf(42188,plain,
sdtasdt0(xx,sdtpldt0(sz00,sz10)) = xx,
inference(cn,[status(thm)],[42187,theory(equality)]) ).
cnf(42622,plain,
( sdtpldt0(xx,xx) = sdtasdt0(sdtpldt0(xc,xc),xu)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[744,252,theory(equality)]) ).
cnf(42663,plain,
( sdtpldt0(xx,xx) = sdtasdt0(sdtpldt0(xc,xc),xu)
| $false ),
inference(rw,[status(thm)],[42622,224,theory(equality)]) ).
cnf(42664,plain,
sdtpldt0(xx,xx) = sdtasdt0(sdtpldt0(xc,xc),xu),
inference(cn,[status(thm)],[42663,theory(equality)]) ).
cnf(47419,plain,
( sdtpldt0(xz,sz00) = sdtasdt0(sdtpldt0(sz10,sz00),xz)
| ~ aElement0(xz)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[767,7305,theory(equality)]) ).
cnf(47691,plain,
( sdtpldt0(xz,sz00) = sdtasdt0(sdtpldt0(sz10,sz00),xz)
| $false
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[47419,94,theory(equality)]) ).
cnf(47692,plain,
( sdtpldt0(xz,sz00) = sdtasdt0(sdtpldt0(sz10,sz00),xz)
| $false
| $false ),
inference(rw,[status(thm)],[47691,184,theory(equality)]) ).
cnf(47693,plain,
sdtpldt0(xz,sz00) = sdtasdt0(sdtpldt0(sz10,sz00),xz),
inference(cn,[status(thm)],[47692,theory(equality)]) ).
cnf(48770,plain,
( sdtpldt0(sz00,xz) = sdtasdt0(sdtpldt0(sz00,sz10),xz)
| ~ aElement0(xz)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[769,7305,theory(equality)]) ).
cnf(49056,plain,
( sdtpldt0(sz00,xz) = sdtasdt0(sdtpldt0(sz00,sz10),xz)
| $false
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[48770,94,theory(equality)]) ).
cnf(49057,plain,
( sdtpldt0(sz00,xz) = sdtasdt0(sdtpldt0(sz00,sz10),xz)
| $false
| $false ),
inference(rw,[status(thm)],[49056,184,theory(equality)]) ).
cnf(49058,plain,
sdtpldt0(sz00,xz) = sdtasdt0(sdtpldt0(sz00,sz10),xz),
inference(cn,[status(thm)],[49057,theory(equality)]) ).
cnf(52151,plain,
( sdtpldt0(xc,smndt0(xc)) = sz00
| $false ),
inference(rw,[status(thm)],[37181,37483,theory(equality)]) ).
cnf(52152,plain,
sdtpldt0(xc,smndt0(xc)) = sz00,
inference(cn,[status(thm)],[52151,theory(equality)]) ).
cnf(52167,plain,
( sdtpldt0(xc,sdtpldt0(smndt0(xc),smndt0(sz00))) = sz00
| ~ aElement0(smndt0(xc))
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[11672,52152,theory(equality)]) ).
cnf(52228,plain,
( sdtpldt0(xc,sdtpldt0(smndt0(xc),sz00)) = sz00
| ~ aElement0(smndt0(xc))
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[52167,836,theory(equality)]) ).
cnf(52229,plain,
( sdtpldt0(xc,sdtpldt0(smndt0(xc),sz00)) = sz00
| $false
| ~ aElement0(xc) ),
inference(rw,[status(thm)],[52228,37483,theory(equality)]) ).
cnf(52230,plain,
( sdtpldt0(xc,sdtpldt0(smndt0(xc),sz00)) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[52229,224,theory(equality)]) ).
cnf(52231,plain,
sdtpldt0(xc,sdtpldt0(smndt0(xc),sz00)) = sz00,
inference(cn,[status(thm)],[52230,theory(equality)]) ).
cnf(53100,plain,
( sdtpldt0(xc,sdtpldt0(sz00,smndt0(xc))) = sz00
| ~ aElement0(sz00)
| ~ aElement0(smndt0(xc)) ),
inference(spm,[status(thm)],[52231,60,theory(equality)]) ).
cnf(53142,plain,
( sdtpldt0(xc,sdtpldt0(sz00,smndt0(xc))) = sz00
| $false
| ~ aElement0(smndt0(xc)) ),
inference(rw,[status(thm)],[53100,184,theory(equality)]) ).
cnf(53143,plain,
( sdtpldt0(xc,sdtpldt0(sz00,smndt0(xc))) = sz00
| $false
| $false ),
inference(rw,[status(thm)],[53142,37483,theory(equality)]) ).
cnf(53144,plain,
sdtpldt0(xc,sdtpldt0(sz00,smndt0(xc))) = sz00,
inference(cn,[status(thm)],[53143,theory(equality)]) ).
cnf(53277,plain,
( sdtpldt0(sz00,sdtpldt0(smndt0(xc),xc)) = sz00
| ~ aElement0(xc)
| ~ aElement0(smndt0(xc))
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[12273,53144,theory(equality)]) ).
cnf(53360,plain,
( sdtpldt0(sz00,sdtpldt0(smndt0(xc),xc)) = sz00
| $false
| ~ aElement0(smndt0(xc))
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[53277,224,theory(equality)]) ).
cnf(53361,plain,
( sdtpldt0(sz00,sdtpldt0(smndt0(xc),xc)) = sz00
| $false
| $false
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[53360,37483,theory(equality)]) ).
cnf(53362,plain,
( sdtpldt0(sz00,sdtpldt0(smndt0(xc),xc)) = sz00
| $false
| $false
| $false ),
inference(rw,[status(thm)],[53361,184,theory(equality)]) ).
cnf(53363,plain,
sdtpldt0(sz00,sdtpldt0(smndt0(xc),xc)) = sz00,
inference(cn,[status(thm)],[53362,theory(equality)]) ).
cnf(54264,plain,
( sz00 = sdtpldt0(smndt0(xc),xc)
| ~ aElement0(xc)
| ~ aElement0(smndt0(xc)) ),
inference(spm,[status(thm)],[600,53363,theory(equality)]) ).
cnf(54345,plain,
( sz00 = sdtpldt0(smndt0(xc),xc)
| $false
| ~ aElement0(smndt0(xc)) ),
inference(rw,[status(thm)],[54264,224,theory(equality)]) ).
cnf(54346,plain,
( sz00 = sdtpldt0(smndt0(xc),xc)
| $false
| $false ),
inference(rw,[status(thm)],[54345,37483,theory(equality)]) ).
cnf(54347,plain,
sz00 = sdtpldt0(smndt0(xc),xc),
inference(cn,[status(thm)],[54346,theory(equality)]) ).
cnf(54405,plain,
( sdtpldt0(smndt0(smndt0(xc)),sz00) = sdtpldt0(sz00,xc)
| ~ aElement0(xc)
| ~ aElement0(smndt0(xc)) ),
inference(spm,[status(thm)],[12132,54347,theory(equality)]) ).
cnf(54477,plain,
( sdtpldt0(smndt0(smndt0(xc)),sz00) = xc
| ~ aElement0(xc)
| ~ aElement0(smndt0(xc)) ),
inference(rw,[status(thm)],[54405,36366,theory(equality)]) ).
cnf(54478,plain,
( sdtpldt0(smndt0(smndt0(xc)),sz00) = xc
| $false
| ~ aElement0(smndt0(xc)) ),
inference(rw,[status(thm)],[54477,224,theory(equality)]) ).
cnf(54479,plain,
( sdtpldt0(smndt0(smndt0(xc)),sz00) = xc
| $false
| $false ),
inference(rw,[status(thm)],[54478,37483,theory(equality)]) ).
cnf(54480,plain,
sdtpldt0(smndt0(smndt0(xc)),sz00) = xc,
inference(cn,[status(thm)],[54479,theory(equality)]) ).
cnf(54525,plain,
( xc = smndt0(smndt0(xc))
| ~ aElement0(smndt0(smndt0(xc))) ),
inference(spm,[status(thm)],[214,54480,theory(equality)]) ).
cnf(77369,plain,
( smndt0(smndt0(xc)) = xc
| ~ aElement0(smndt0(xc)) ),
inference(spm,[status(thm)],[54525,232,theory(equality)]) ).
cnf(77375,plain,
( smndt0(smndt0(xc)) = xc
| $false ),
inference(rw,[status(thm)],[77369,37483,theory(equality)]) ).
cnf(77376,plain,
smndt0(smndt0(xc)) = xc,
inference(cn,[status(thm)],[77375,theory(equality)]) ).
cnf(79856,plain,
( sdtasdt0(sz10,xz) = sdtpldt0(xz,sz00)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[47693,214,theory(equality)]) ).
cnf(79928,plain,
( sdtasdt0(sz10,xz) = sdtpldt0(xz,sz00)
| $false ),
inference(rw,[status(thm)],[79856,145,theory(equality)]) ).
cnf(79929,plain,
sdtasdt0(sz10,xz) = sdtpldt0(xz,sz00),
inference(cn,[status(thm)],[79928,theory(equality)]) ).
cnf(80108,plain,
( sdtasdt0(sz10,xz) = xz
| ~ aElement0(xz) ),
inference(spm,[status(thm)],[214,79929,theory(equality)]) ).
cnf(80147,plain,
sdtasdt0(sdtpldt0(sz10,sz00),xz) = sdtasdt0(sz10,xz),
inference(rw,[status(thm)],[47693,79929,theory(equality)]) ).
cnf(80149,plain,
( sdtasdt0(sz10,xz) = xz
| $false ),
inference(rw,[status(thm)],[80108,94,theory(equality)]) ).
cnf(80150,plain,
sdtasdt0(sz10,xz) = xz,
inference(cn,[status(thm)],[80149,theory(equality)]) ).
cnf(80589,plain,
sdtasdt0(sdtpldt0(sz10,sz00),xz) = xz,
inference(rw,[status(thm)],[80147,80150,theory(equality)]) ).
cnf(80826,plain,
( sdtasdt0(sdtpldt0(sz00,sz10),xz) = xz
| ~ aElement0(sz00)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[80589,60,theory(equality)]) ).
cnf(80904,plain,
( sdtasdt0(sdtpldt0(sz00,sz10),xz) = xz
| $false
| ~ aElement0(sz10) ),
inference(rw,[status(thm)],[80826,184,theory(equality)]) ).
cnf(80905,plain,
( sdtasdt0(sdtpldt0(sz00,sz10),xz) = xz
| $false
| $false ),
inference(rw,[status(thm)],[80904,145,theory(equality)]) ).
cnf(80906,plain,
sdtasdt0(sdtpldt0(sz00,sz10),xz) = xz,
inference(cn,[status(thm)],[80905,theory(equality)]) ).
cnf(85694,plain,
xz = sdtpldt0(sz00,xz),
inference(rw,[status(thm)],[49058,80906,theory(equality)]) ).
cnf(114269,plain,
( aElement0(sdtpldt0(sz00,sdtasdt0(X1,sdtpldt0(X2,X3))))
| ~ aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[1409,183]) ).
cnf(114270,plain,
( aElement0(sdtpldt0(sz00,sdtasdt0(X1,sdtpldt0(X2,X3))))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[114269,183]) ).
cnf(114367,plain,
( aElement0(sdtpldt0(sz00,sdtasdt0(X1,xz)))
| ~ aElement0(X1)
| ~ aElement0(sz00)
| ~ aElement0(xz) ),
inference(spm,[status(thm)],[114270,85694,theory(equality)]) ).
cnf(114919,plain,
( aElement0(sdtpldt0(sz00,sdtasdt0(X1,xz)))
| ~ aElement0(X1)
| $false
| ~ aElement0(xz) ),
inference(rw,[status(thm)],[114367,184,theory(equality)]) ).
cnf(114920,plain,
( aElement0(sdtpldt0(sz00,sdtasdt0(X1,xz)))
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[114919,94,theory(equality)]) ).
cnf(114921,plain,
( aElement0(sdtpldt0(sz00,sdtasdt0(X1,xz)))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[114920,theory(equality)]) ).
cnf(116912,plain,
( smndt0(sz10) = sz00
| sz00 = smndt0(xc)
| xc != sz00
| ~ aElement0(smndt0(xc)) ),
inference(spm,[status(thm)],[1561,77376,theory(equality)]) ).
cnf(116916,plain,
( smndt0(sz10) = sz00
| sz00 = smndt0(xc)
| xc != sz00
| $false ),
inference(rw,[status(thm)],[116912,37483,theory(equality)]) ).
cnf(116917,plain,
( smndt0(sz10) = sz00
| sz00 = smndt0(xc)
| xc != sz00 ),
inference(cn,[status(thm)],[116916,theory(equality)]) ).
cnf(116922,plain,
( sdtpldt0(sz00,sz10) = sz00
| smndt0(xc) = sz00
| ~ aElement0(sz10)
| xc != sz00 ),
inference(spm,[status(thm)],[179,116917,theory(equality)]) ).
cnf(116966,plain,
( sdtpldt0(sz00,sz10) = sz00
| smndt0(xc) = sz00
| $false
| xc != sz00 ),
inference(rw,[status(thm)],[116922,145,theory(equality)]) ).
cnf(116967,plain,
( sdtpldt0(sz00,sz10) = sz00
| smndt0(xc) = sz00
| xc != sz00 ),
inference(cn,[status(thm)],[116966,theory(equality)]) ).
cnf(119217,plain,
( aElement0(sdtasdt0(sdtpldt0(sz00,X1),xz))
| ~ aElement0(X1)
| ~ aElement0(xz) ),
inference(spm,[status(thm)],[114921,775,theory(equality)]) ).
cnf(119296,plain,
( aElement0(sdtasdt0(sdtpldt0(sz00,X1),xz))
| ~ aElement0(X1)
| $false ),
inference(rw,[status(thm)],[119217,94,theory(equality)]) ).
cnf(119297,plain,
( aElement0(sdtasdt0(sdtpldt0(sz00,X1),xz))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[119296,theory(equality)]) ).
cnf(149616,plain,
( sdtpldt0(xc,X1) = sdtpldt0(X1,sdtpldt0(sz00,xc))
| ~ aElement0(X1)
| ~ aElement0(xc)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[12273,36575,theory(equality)]) ).
cnf(149802,plain,
( sdtpldt0(xc,X1) = sdtpldt0(X1,xc)
| ~ aElement0(X1)
| ~ aElement0(xc)
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[149616,36366,theory(equality)]) ).
cnf(149803,plain,
( sdtpldt0(xc,X1) = sdtpldt0(X1,xc)
| ~ aElement0(X1)
| $false
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[149802,224,theory(equality)]) ).
cnf(149804,plain,
( sdtpldt0(xc,X1) = sdtpldt0(X1,xc)
| ~ aElement0(X1)
| $false
| $false ),
inference(rw,[status(thm)],[149803,184,theory(equality)]) ).
cnf(149805,plain,
( sdtpldt0(xc,X1) = sdtpldt0(X1,xc)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[149804,theory(equality)]) ).
cnf(150067,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(xc,X1)) = sdtpldt0(sz00,xc)
| ~ aElement0(xc)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[12132,149805,theory(equality)]) ).
cnf(150213,plain,
( sdtpldt0(sz00,sdtpldt0(xc,xc)) = sdtpldt0(xc,xc)
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[36575,149805,theory(equality)]) ).
cnf(150629,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(xc,X1)) = xc
| ~ aElement0(xc)
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[150067,36366,theory(equality)]) ).
cnf(150630,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(xc,X1)) = xc
| $false
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[150629,224,theory(equality)]) ).
cnf(150631,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(xc,X1)) = xc
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[150630,theory(equality)]) ).
cnf(150983,plain,
( sdtpldt0(sz00,sdtpldt0(xc,xc)) = sdtpldt0(xc,xc)
| $false ),
inference(rw,[status(thm)],[150213,224,theory(equality)]) ).
cnf(150984,plain,
sdtpldt0(sz00,sdtpldt0(xc,xc)) = sdtpldt0(xc,xc),
inference(cn,[status(thm)],[150983,theory(equality)]) ).
cnf(163522,plain,
( sdtpldt0(sz00,sdtpldt0(xc,xc)) = xc
| sdtpldt0(sz00,sz10) = sz00
| ~ aElement0(xc)
| xc != sz00 ),
inference(spm,[status(thm)],[150631,116967,theory(equality)]) ).
cnf(163662,plain,
( sdtpldt0(xc,xc) = xc
| sdtpldt0(sz00,sz10) = sz00
| ~ aElement0(xc)
| xc != sz00 ),
inference(rw,[status(thm)],[163522,150984,theory(equality)]) ).
cnf(163663,plain,
( sdtpldt0(xc,xc) = xc
| sdtpldt0(sz00,sz10) = sz00
| $false
| xc != sz00 ),
inference(rw,[status(thm)],[163662,224,theory(equality)]) ).
cnf(163664,plain,
( sdtpldt0(xc,xc) = xc
| sdtpldt0(sz00,sz10) = sz00
| xc != sz00 ),
inference(cn,[status(thm)],[163663,theory(equality)]) ).
cnf(164309,plain,
( sdtasdt0(xc,xu) = sdtpldt0(xx,xx)
| sdtpldt0(sz00,sz10) = sz00
| xc != sz00 ),
inference(spm,[status(thm)],[42664,163664,theory(equality)]) ).
cnf(164406,plain,
( xx = sdtpldt0(xx,xx)
| sdtpldt0(sz00,sz10) = sz00
| xc != sz00 ),
inference(rw,[status(thm)],[164309,252,theory(equality)]) ).
cnf(164612,plain,
( sdtpldt0(smndt0(xx),xx) = sdtpldt0(sz00,xx)
| sdtpldt0(sz00,sz10) = sz00
| ~ aElement0(xx)
| xc != sz00 ),
inference(spm,[status(thm)],[12132,164406,theory(equality)]) ).
cnf(164716,plain,
( sz00 = sdtpldt0(sz00,xx)
| sdtpldt0(sz00,sz10) = sz00
| ~ aElement0(xx)
| xc != sz00 ),
inference(rw,[status(thm)],[164612,31137,theory(equality)]) ).
cnf(164717,plain,
( sz00 = xx
| sdtpldt0(sz00,sz10) = sz00
| ~ aElement0(xx)
| xc != sz00 ),
inference(rw,[status(thm)],[164716,31062,theory(equality)]) ).
cnf(164718,plain,
( sz00 = xx
| sdtpldt0(sz00,sz10) = sz00
| $false
| xc != sz00 ),
inference(rw,[status(thm)],[164717,282,theory(equality)]) ).
cnf(164719,plain,
( sz00 = xx
| sdtpldt0(sz00,sz10) = sz00
| xc != sz00 ),
inference(cn,[status(thm)],[164718,theory(equality)]) ).
cnf(165107,plain,
( sdtasdt0(xx,sz00) = xx
| xx = sz00
| xc != sz00 ),
inference(spm,[status(thm)],[42188,164719,theory(equality)]) ).
cnf(165176,plain,
( sz00 = xx
| xx = sz00
| xc != sz00 ),
inference(rw,[status(thm)],[165107,2906,theory(equality)]) ).
cnf(165177,plain,
( sz00 = xx
| xc != sz00 ),
inference(cn,[status(thm)],[165176,theory(equality)]) ).
cnf(165688,plain,
( sdtpldt0(sz00,xy) != xy
| ~ aElementOf0(sdtasdt0(sz00,xz),slsdtgt0(xc))
| xc != sz00 ),
inference(spm,[status(thm)],[1569,165177,theory(equality)]) ).
cnf(166173,plain,
( $false
| ~ aElementOf0(sdtasdt0(sz00,xz),slsdtgt0(xc))
| xc != sz00 ),
inference(rw,[status(thm)],[165688,34318,theory(equality)]) ).
cnf(166174,plain,
( $false
| $false
| xc != sz00 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[166173,7305,theory(equality)]),4776,theory(equality)]) ).
cnf(166175,plain,
xc != sz00,
inference(cn,[status(thm)],[166174,theory(equality)]) ).
cnf(169419,plain,
( sdtasdt0(xu,X1) = sz00
| sdtasdt0(xx,X1) != sz00
| ~ aElement0(sdtasdt0(xu,X1))
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[2623,166175,theory(equality)]) ).
cnf(169441,plain,
( sdtasdt0(xu,sz00) = sz00
| sdtasdt0(xx,sz00) != sz00
| ~ aElement0(sz00)
| ~ aElement0(xu) ),
inference(spm,[status(thm)],[169419,7710,theory(equality)]) ).
cnf(169526,plain,
( sdtasdt0(xu,sz00) = sz00
| $false
| ~ aElement0(sz00)
| ~ aElement0(xu) ),
inference(rw,[status(thm)],[169441,2906,theory(equality)]) ).
cnf(169527,plain,
( sdtasdt0(xu,sz00) = sz00
| $false
| $false
| ~ aElement0(xu) ),
inference(rw,[status(thm)],[169526,184,theory(equality)]) ).
cnf(169528,plain,
( sdtasdt0(xu,sz00) = sz00
| $false
| $false
| $false ),
inference(rw,[status(thm)],[169527,253,theory(equality)]) ).
cnf(169529,plain,
sdtasdt0(xu,sz00) = sz00,
inference(cn,[status(thm)],[169528,theory(equality)]) ).
cnf(169901,plain,
( sdtpldt0(xu,sz00) = sdtasdt0(xu,sdtpldt0(sz10,sz00))
| ~ aElement0(xu)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[691,169529,theory(equality)]) ).
cnf(169902,plain,
( sdtpldt0(sz00,xu) = sdtasdt0(xu,sdtpldt0(sz00,sz10))
| ~ aElement0(xu)
| ~ aElement0(sz00) ),
inference(spm,[status(thm)],[693,169529,theory(equality)]) ).
cnf(170042,plain,
( sdtpldt0(xu,sz00) = sdtasdt0(xu,sdtpldt0(sz10,sz00))
| $false
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[169901,253,theory(equality)]) ).
cnf(170043,plain,
( sdtpldt0(xu,sz00) = sdtasdt0(xu,sdtpldt0(sz10,sz00))
| $false
| $false ),
inference(rw,[status(thm)],[170042,184,theory(equality)]) ).
cnf(170044,plain,
sdtpldt0(xu,sz00) = sdtasdt0(xu,sdtpldt0(sz10,sz00)),
inference(cn,[status(thm)],[170043,theory(equality)]) ).
cnf(170045,plain,
( sdtpldt0(sz00,xu) = sdtasdt0(xu,sdtpldt0(sz00,sz10))
| $false
| ~ aElement0(sz00) ),
inference(rw,[status(thm)],[169902,253,theory(equality)]) ).
cnf(170046,plain,
( sdtpldt0(sz00,xu) = sdtasdt0(xu,sdtpldt0(sz00,sz10))
| $false
| $false ),
inference(rw,[status(thm)],[170045,184,theory(equality)]) ).
cnf(170047,plain,
sdtpldt0(sz00,xu) = sdtasdt0(xu,sdtpldt0(sz00,sz10)),
inference(cn,[status(thm)],[170046,theory(equality)]) ).
cnf(192559,plain,
( sdtasdt0(xu,sz10) = sdtpldt0(xu,sz00)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[170044,214,theory(equality)]) ).
cnf(192640,plain,
( sdtasdt0(xu,sz10) = sdtpldt0(xu,sz00)
| $false ),
inference(rw,[status(thm)],[192559,145,theory(equality)]) ).
cnf(192641,plain,
sdtasdt0(xu,sz10) = sdtpldt0(xu,sz00),
inference(cn,[status(thm)],[192640,theory(equality)]) ).
cnf(192820,plain,
( sdtasdt0(xu,sz10) = xu
| ~ aElement0(xu) ),
inference(spm,[status(thm)],[214,192641,theory(equality)]) ).
cnf(192876,plain,
sdtasdt0(xu,sdtpldt0(sz10,sz00)) = sdtasdt0(xu,sz10),
inference(rw,[status(thm)],[170044,192641,theory(equality)]) ).
cnf(192886,plain,
( sdtasdt0(xu,sz10) = xu
| $false ),
inference(rw,[status(thm)],[192820,253,theory(equality)]) ).
cnf(192887,plain,
sdtasdt0(xu,sz10) = xu,
inference(cn,[status(thm)],[192886,theory(equality)]) ).
cnf(193395,plain,
sdtasdt0(xu,sdtpldt0(sz10,sz00)) = xu,
inference(rw,[status(thm)],[192876,192887,theory(equality)]) ).
cnf(193399,plain,
( sdtasdt0(xu,sdtpldt0(sz00,sz10)) = xu
| ~ aElement0(sz00)
| ~ aElement0(sz10) ),
inference(spm,[status(thm)],[193395,60,theory(equality)]) ).
cnf(193485,plain,
( sdtasdt0(xu,sdtpldt0(sz00,sz10)) = xu
| $false
| ~ aElement0(sz10) ),
inference(rw,[status(thm)],[193399,184,theory(equality)]) ).
cnf(193486,plain,
( sdtasdt0(xu,sdtpldt0(sz00,sz10)) = xu
| $false
| $false ),
inference(rw,[status(thm)],[193485,145,theory(equality)]) ).
cnf(193487,plain,
sdtasdt0(xu,sdtpldt0(sz00,sz10)) = xu,
inference(cn,[status(thm)],[193486,theory(equality)]) ).
cnf(197806,plain,
xu = sdtpldt0(sz00,xu),
inference(rw,[status(thm)],[170047,193487,theory(equality)]) ).
cnf(197852,plain,
( aElement0(sdtasdt0(xu,xz))
| ~ aElement0(xu) ),
inference(spm,[status(thm)],[119297,197806,theory(equality)]) ).
cnf(198002,plain,
( aElement0(sdtasdt0(xu,xz))
| $false ),
inference(rw,[status(thm)],[197852,253,theory(equality)]) ).
cnf(198003,plain,
aElement0(sdtasdt0(xu,xz)),
inference(cn,[status(thm)],[198002,theory(equality)]) ).
cnf(198150,plain,
( doDivides0(xc,sdtasdt0(xx,xz))
| $false ),
inference(rw,[status(thm)],[3877,198003,theory(equality)]) ).
cnf(198151,plain,
doDivides0(xc,sdtasdt0(xx,xz)),
inference(cn,[status(thm)],[198150,theory(equality)]) ).
cnf(198201,plain,
( aElementOf0(sdtasdt0(xx,xz),X1)
| slsdtgt0(xc) != X1
| ~ aElement0(xc)
| ~ aElement0(sdtasdt0(xx,xz)) ),
inference(spm,[status(thm)],[4631,198151,theory(equality)]) ).
cnf(198210,plain,
( aElementOf0(sdtasdt0(xx,xz),X1)
| slsdtgt0(xc) != X1
| $false
| ~ aElement0(sdtasdt0(xx,xz)) ),
inference(rw,[status(thm)],[198201,224,theory(equality)]) ).
cnf(198211,plain,
( aElementOf0(sdtasdt0(xx,xz),X1)
| slsdtgt0(xc) != X1
| $false
| $false ),
inference(rw,[status(thm)],[198210,1255,theory(equality)]) ).
cnf(198212,plain,
( aElementOf0(sdtasdt0(xx,xz),X1)
| slsdtgt0(xc) != X1 ),
inference(cn,[status(thm)],[198211,theory(equality)]) ).
cnf(240669,plain,
aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc)),
inference(er,[status(thm)],[198212,theory(equality)]) ).
cnf(240694,negated_conjecture,
( $false
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(rw,[status(thm)],[2810,240669,theory(equality)]) ).
cnf(240695,negated_conjecture,
~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)),
inference(cn,[status(thm)],[240694,theory(equality)]) ).
cnf(241385,plain,
( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElement0(sdtpldt0(xu,xv))
| ~ aElement0(xc) ),
inference(spm,[status(thm)],[3408,100,theory(equality)]) ).
cnf(241881,plain,
( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElement0(sdtpldt0(xu,xv))
| $false ),
inference(rw,[status(thm)],[241385,224,theory(equality)]) ).
cnf(241882,plain,
( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElement0(sdtpldt0(xu,xv)) ),
inference(cn,[status(thm)],[241881,theory(equality)]) ).
cnf(241883,plain,
~ aElement0(sdtpldt0(xu,xv)),
inference(sr,[status(thm)],[241882,240695,theory(equality)]) ).
cnf(243200,plain,
( ~ aElement0(xv)
| ~ aElement0(xu) ),
inference(spm,[status(thm)],[241883,187,theory(equality)]) ).
cnf(243211,plain,
( $false
| ~ aElement0(xu) ),
inference(rw,[status(thm)],[243200,108,theory(equality)]) ).
cnf(243212,plain,
( $false
| $false ),
inference(rw,[status(thm)],[243211,253,theory(equality)]) ).
cnf(243213,plain,
$false,
inference(cn,[status(thm)],[243212,theory(equality)]) ).
cnf(243214,plain,
$false,
243213,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG105+1.p
% --creating new selector for []
% -running prover on /tmp/tmp5xwDFN/sel_RNG105+1.p_1 with time limit 29
% -prover status Theorem
% Problem RNG105+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG105+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG105+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
%
%------------------------------------------------------------------------------