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