TSTP Solution File: RNG049+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : RNG049+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 01:47:15 EST 2010
% Result : Theorem 1.44s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 17
% Syntax : Number of formulae : 139 ( 24 unt; 0 def)
% Number of atoms : 518 ( 147 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 600 ( 221 ~; 299 |; 63 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 69 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
aScalar0(sz0z00),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mSZeroSc) ).
fof(5,axiom,
! [X1] :
( aScalar0(X1)
=> ( sdtpldt0(X1,sz0z00) = X1
& sdtpldt0(sz0z00,X1) = X1
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtpldt0(smndt0(X1),X1) = sz0z00
& smndt0(smndt0(X1)) = X1
& smndt0(sz0z00) = sz0z00 ) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mScZero) ).
fof(6,axiom,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',m__1568) ).
fof(9,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mLEASm) ).
fof(10,axiom,
aVector0(xs),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',m__1542) ).
fof(11,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X2) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
& sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ) ) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mPosMon) ).
fof(12,axiom,
! [X1,X2] :
( ( aVector0(X1)
& aNaturalNumber0(X2) )
=> aScalar0(sdtlbdtrb0(X1,X2)) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mElmSc) ).
fof(18,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1) ) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mLETot) ).
fof(25,axiom,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( aVector0(X2)
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) ) ) ) ) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mDefInit) ).
fof(26,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mDimNat) ).
fof(29,axiom,
! [X1,X2] :
( ( aVector0(X1)
& aVector0(X2) )
=> ( aDimensionOf0(X1) = aDimensionOf0(X2)
=> aScalar0(sdtasasdt0(X1,X2)) ) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mScPr) ).
fof(31,conjecture,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',m__) ).
fof(33,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mMulSc) ).
fof(35,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mSqPos) ).
fof(37,axiom,
( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
& sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',m__1590) ).
fof(40,axiom,
aDimensionOf0(xs) != sz00,
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',m__1542_01) ).
fof(41,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/tmp/tmpVY0sHk/sel_RNG049+1.p_1',mLERef) ).
fof(43,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(assume_negation,[status(cth)],[31]) ).
fof(44,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(fof_simplification,[status(thm)],[43,theory(equality)]) ).
cnf(54,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[4]) ).
fof(55,plain,
! [X1] :
( ~ aScalar0(X1)
| ( sdtpldt0(X1,sz0z00) = X1
& sdtpldt0(sz0z00,X1) = X1
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtpldt0(smndt0(X1),X1) = sz0z00
& smndt0(smndt0(X1)) = X1
& smndt0(sz0z00) = sz0z00 ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(56,plain,
! [X2] :
( ~ aScalar0(X2)
| ( sdtpldt0(X2,sz0z00) = X2
& sdtpldt0(sz0z00,X2) = X2
& sdtasdt0(X2,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X2) = sz0z00
& sdtpldt0(X2,smndt0(X2)) = sz0z00
& sdtpldt0(smndt0(X2),X2) = sz0z00
& smndt0(smndt0(X2)) = X2
& smndt0(sz0z00) = sz0z00 ) ),
inference(variable_rename,[status(thm)],[55]) ).
fof(57,plain,
! [X2] :
( ( sdtpldt0(X2,sz0z00) = X2
| ~ aScalar0(X2) )
& ( sdtpldt0(sz0z00,X2) = X2
| ~ aScalar0(X2) )
& ( sdtasdt0(X2,sz0z00) = sz0z00
| ~ aScalar0(X2) )
& ( sdtasdt0(sz0z00,X2) = sz0z00
| ~ aScalar0(X2) )
& ( sdtpldt0(X2,smndt0(X2)) = sz0z00
| ~ aScalar0(X2) )
& ( sdtpldt0(smndt0(X2),X2) = sz0z00
| ~ aScalar0(X2) )
& ( smndt0(smndt0(X2)) = X2
| ~ aScalar0(X2) )
& ( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X2) ) ),
inference(distribute,[status(thm)],[56]) ).
cnf(63,plain,
( sdtasdt0(X1,sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(66,plain,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(split_conjunct,[status(thm)],[6]) ).
fof(73,plain,
! [X1,X2] :
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1)
| X1 = X2 ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(74,plain,
! [X3,X4] :
( ~ aScalar0(X3)
| ~ aScalar0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| X3 = X4 ),
inference(variable_rename,[status(thm)],[73]) ).
cnf(75,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[74]) ).
cnf(76,plain,
aVector0(xs),
inference(split_conjunct,[status(thm)],[10]) ).
fof(77,plain,
! [X1,X2] :
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
& sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(78,plain,
! [X3,X4] :
( ~ aScalar0(X3)
| ~ aScalar0(X4)
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(sz0z00,X4)
| ( sdtlseqdt0(sz0z00,sdtpldt0(X3,X4))
& sdtlseqdt0(sz0z00,sdtasdt0(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[77]) ).
fof(79,plain,
! [X3,X4] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(X3,X4))
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(sz0z00,X4)
| ~ aScalar0(X3)
| ~ aScalar0(X4) )
& ( sdtlseqdt0(sz0z00,sdtasdt0(X3,X4))
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(sz0z00,X4)
| ~ aScalar0(X3)
| ~ aScalar0(X4) ) ),
inference(distribute,[status(thm)],[78]) ).
cnf(81,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X2,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2) ),
inference(split_conjunct,[status(thm)],[79]) ).
fof(82,plain,
! [X1,X2] :
( ~ aVector0(X1)
| ~ aNaturalNumber0(X2)
| aScalar0(sdtlbdtrb0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(83,plain,
! [X3,X4] :
( ~ aVector0(X3)
| ~ aNaturalNumber0(X4)
| aScalar0(sdtlbdtrb0(X3,X4)) ),
inference(variable_rename,[status(thm)],[82]) ).
cnf(84,plain,
( aScalar0(sdtlbdtrb0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[83]) ).
fof(102,plain,
! [X1,X2] :
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(103,plain,
! [X3,X4] :
( ~ aScalar0(X3)
| ~ aScalar0(X4)
| sdtlseqdt0(X3,X4)
| sdtlseqdt0(X4,X3) ),
inference(variable_rename,[status(thm)],[102]) ).
cnf(104,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[103]) ).
fof(125,plain,
! [X1] :
( ~ aVector0(X1)
| aDimensionOf0(X1) = sz00
| ! [X2] :
( ( X2 != sziznziztdt0(X1)
| ( aVector0(X2)
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& ! [X3] :
( ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) ) ) )
& ( ~ aVector0(X2)
| szszuzczcdt0(aDimensionOf0(X2)) != aDimensionOf0(X1)
| ? [X3] :
( aNaturalNumber0(X3)
& sdtlbdtrb0(X2,X3) != sdtlbdtrb0(X1,X3) )
| X2 = sziznziztdt0(X1) ) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(126,plain,
! [X4] :
( ~ aVector0(X4)
| aDimensionOf0(X4) = sz00
| ! [X5] :
( ( X5 != sziznziztdt0(X4)
| ( aVector0(X5)
& szszuzczcdt0(aDimensionOf0(X5)) = aDimensionOf0(X4)
& ! [X6] :
( ~ aNaturalNumber0(X6)
| sdtlbdtrb0(X5,X6) = sdtlbdtrb0(X4,X6) ) ) )
& ( ~ aVector0(X5)
| szszuzczcdt0(aDimensionOf0(X5)) != aDimensionOf0(X4)
| ? [X7] :
( aNaturalNumber0(X7)
& sdtlbdtrb0(X5,X7) != sdtlbdtrb0(X4,X7) )
| X5 = sziznziztdt0(X4) ) ) ),
inference(variable_rename,[status(thm)],[125]) ).
fof(127,plain,
! [X4] :
( ~ aVector0(X4)
| aDimensionOf0(X4) = sz00
| ! [X5] :
( ( X5 != sziznziztdt0(X4)
| ( aVector0(X5)
& szszuzczcdt0(aDimensionOf0(X5)) = aDimensionOf0(X4)
& ! [X6] :
( ~ aNaturalNumber0(X6)
| sdtlbdtrb0(X5,X6) = sdtlbdtrb0(X4,X6) ) ) )
& ( ~ aVector0(X5)
| szszuzczcdt0(aDimensionOf0(X5)) != aDimensionOf0(X4)
| ( aNaturalNumber0(esk1_2(X4,X5))
& sdtlbdtrb0(X5,esk1_2(X4,X5)) != sdtlbdtrb0(X4,esk1_2(X4,X5)) )
| X5 = sziznziztdt0(X4) ) ) ),
inference(skolemize,[status(esa)],[126]) ).
fof(128,plain,
! [X4,X5,X6] :
( ( ( ( ( ~ aNaturalNumber0(X6)
| sdtlbdtrb0(X5,X6) = sdtlbdtrb0(X4,X6) )
& aVector0(X5)
& szszuzczcdt0(aDimensionOf0(X5)) = aDimensionOf0(X4) )
| X5 != sziznziztdt0(X4) )
& ( ~ aVector0(X5)
| szszuzczcdt0(aDimensionOf0(X5)) != aDimensionOf0(X4)
| ( aNaturalNumber0(esk1_2(X4,X5))
& sdtlbdtrb0(X5,esk1_2(X4,X5)) != sdtlbdtrb0(X4,esk1_2(X4,X5)) )
| X5 = sziznziztdt0(X4) ) )
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) ),
inference(shift_quantors,[status(thm)],[127]) ).
fof(129,plain,
! [X4,X5,X6] :
( ( ~ aNaturalNumber0(X6)
| sdtlbdtrb0(X5,X6) = sdtlbdtrb0(X4,X6)
| X5 != sziznziztdt0(X4)
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) )
& ( aVector0(X5)
| X5 != sziznziztdt0(X4)
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) )
& ( szszuzczcdt0(aDimensionOf0(X5)) = aDimensionOf0(X4)
| X5 != sziznziztdt0(X4)
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) )
& ( aNaturalNumber0(esk1_2(X4,X5))
| ~ aVector0(X5)
| szszuzczcdt0(aDimensionOf0(X5)) != aDimensionOf0(X4)
| X5 = sziznziztdt0(X4)
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) )
& ( sdtlbdtrb0(X5,esk1_2(X4,X5)) != sdtlbdtrb0(X4,esk1_2(X4,X5))
| ~ aVector0(X5)
| szszuzczcdt0(aDimensionOf0(X5)) != aDimensionOf0(X4)
| X5 = sziznziztdt0(X4)
| aDimensionOf0(X4) = sz00
| ~ aVector0(X4) ) ),
inference(distribute,[status(thm)],[128]) ).
cnf(133,plain,
( aDimensionOf0(X1) = sz00
| aVector0(X2)
| ~ aVector0(X1)
| X2 != sziznziztdt0(X1) ),
inference(split_conjunct,[status(thm)],[129]) ).
fof(135,plain,
! [X1] :
( ~ aVector0(X1)
| aNaturalNumber0(aDimensionOf0(X1)) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(136,plain,
! [X2] :
( ~ aVector0(X2)
| aNaturalNumber0(aDimensionOf0(X2)) ),
inference(variable_rename,[status(thm)],[135]) ).
cnf(137,plain,
( aNaturalNumber0(aDimensionOf0(X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[136]) ).
fof(147,plain,
! [X1,X2] :
( ~ aVector0(X1)
| ~ aVector0(X2)
| aDimensionOf0(X1) != aDimensionOf0(X2)
| aScalar0(sdtasasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[29]) ).
fof(148,plain,
! [X3,X4] :
( ~ aVector0(X3)
| ~ aVector0(X4)
| aDimensionOf0(X3) != aDimensionOf0(X4)
| aScalar0(sdtasasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[147]) ).
cnf(149,plain,
( aScalar0(sdtasasdt0(X1,X2))
| aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[148]) ).
cnf(155,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(split_conjunct,[status(thm)],[44]) ).
fof(159,plain,
! [X1,X2] :
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(fof_nnf,[status(thm)],[33]) ).
fof(160,plain,
! [X3,X4] :
( ~ aScalar0(X3)
| ~ aScalar0(X4)
| aScalar0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[159]) ).
cnf(161,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[160]) ).
fof(167,plain,
! [X1] :
( ~ aScalar0(X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(168,plain,
! [X2] :
( ~ aScalar0(X2)
| sdtlseqdt0(sz0z00,sdtasdt0(X2,X2)) ),
inference(variable_rename,[status(thm)],[167]) ).
cnf(169,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[168]) ).
cnf(173,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(174,plain,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(181,plain,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[40]) ).
fof(182,plain,
! [X1] :
( ~ aScalar0(X1)
| sdtlseqdt0(X1,X1) ),
inference(fof_nnf,[status(thm)],[41]) ).
fof(183,plain,
! [X2] :
( ~ aScalar0(X2)
| sdtlseqdt0(X2,X2) ),
inference(variable_rename,[status(thm)],[182]) ).
cnf(184,plain,
( sdtlseqdt0(X1,X1)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[183]) ).
cnf(188,plain,
( sdtlseqdt0(sz0z00,sz0z00)
| ~ aScalar0(sz0z00) ),
inference(spm,[status(thm)],[169,63,theory(equality)]) ).
cnf(190,plain,
( sdtlseqdt0(sz0z00,sz0z00)
| $false ),
inference(rw,[status(thm)],[188,54,theory(equality)]) ).
cnf(191,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[190,theory(equality)]) ).
cnf(242,plain,
( aDimensionOf0(X1) = sz00
| aVector0(sziznziztdt0(X1))
| ~ aVector0(X1) ),
inference(er,[status(thm)],[133,theory(equality)]) ).
cnf(244,plain,
( sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| ~ sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(spm,[status(thm)],[75,174,theory(equality)]) ).
cnf(245,plain,
( sdtasdt0(X1,X1) = sz0z00
| ~ sdtlseqdt0(sdtasdt0(X1,X1),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[75,169,theory(equality)]) ).
cnf(248,plain,
( sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| ~ sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| $false
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(rw,[status(thm)],[244,54,theory(equality)]) ).
cnf(249,plain,
( sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| ~ sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(cn,[status(thm)],[248,theory(equality)]) ).
cnf(250,plain,
( sdtasdt0(X1,X1) = sz0z00
| ~ sdtlseqdt0(sdtasdt0(X1,X1),sz0z00)
| $false
| ~ aScalar0(sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(rw,[status(thm)],[245,54,theory(equality)]) ).
cnf(251,plain,
( sdtasdt0(X1,X1) = sz0z00
| ~ sdtlseqdt0(sdtasdt0(X1,X1),sz0z00)
| ~ aScalar0(sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[250,theory(equality)]) ).
cnf(260,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(sz0z00,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[81,184,theory(equality)]) ).
cnf(262,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
| sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(sz0z00) ),
inference(spm,[status(thm)],[81,104,theory(equality)]) ).
cnf(264,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(sz0z00,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| $false
| ~ aScalar0(X1) ),
inference(rw,[status(thm)],[260,54,theory(equality)]) ).
cnf(265,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(sz0z00,X1))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[264,theory(equality)]) ).
cnf(266,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
| sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| $false ),
inference(rw,[status(thm)],[262,54,theory(equality)]) ).
cnf(267,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
| sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[266,theory(equality)]) ).
cnf(339,plain,
( aScalar0(sdtasasdt0(X1,X1))
| ~ aVector0(X1) ),
inference(er,[status(thm)],[149,theory(equality)]) ).
cnf(639,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(spm,[status(thm)],[265,173,theory(equality)]) ).
cnf(929,plain,
( sdtasdt0(X1,X1) = sz0z00
| ~ sdtlseqdt0(sdtasdt0(X1,X1),sz0z00)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[251,161,theory(equality)]) ).
cnf(1664,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,sz0z00))
| sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(sz0z00) ),
inference(spm,[status(thm)],[267,191,theory(equality)]) ).
cnf(1669,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
| sdtlseqdt0(X1,sz0z00)
| sdtlseqdt0(X2,sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(sz0z00) ),
inference(spm,[status(thm)],[267,104,theory(equality)]) ).
cnf(1677,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,sz0z00))
| sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1)
| $false ),
inference(rw,[status(thm)],[1664,54,theory(equality)]) ).
cnf(1678,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,sz0z00))
| sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[1677,theory(equality)]) ).
cnf(1681,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
| sdtlseqdt0(X1,sz0z00)
| sdtlseqdt0(X2,sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| $false ),
inference(rw,[status(thm)],[1669,54,theory(equality)]) ).
cnf(1682,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
| sdtlseqdt0(X1,sz0z00)
| sdtlseqdt0(X2,sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[1681,theory(equality)]) ).
cnf(2731,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(spm,[status(thm)],[1682,66,theory(equality)]) ).
cnf(2758,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(sr,[status(thm)],[2731,155,theory(equality)]) ).
cnf(2782,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aVector0(sziznziztdt0(xs)) ),
inference(spm,[status(thm)],[2758,339,theory(equality)]) ).
cnf(2898,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| aDimensionOf0(xs) = sz00
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aVector0(xs) ),
inference(spm,[status(thm)],[2782,242,theory(equality)]) ).
cnf(2899,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| aDimensionOf0(xs) = sz00
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| $false ),
inference(rw,[status(thm)],[2898,76,theory(equality)]) ).
cnf(2900,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| aDimensionOf0(xs) = sz00
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(cn,[status(thm)],[2899,theory(equality)]) ).
cnf(2901,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(sr,[status(thm)],[2900,181,theory(equality)]) ).
cnf(2902,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(spm,[status(thm)],[2901,161,theory(equality)]) ).
cnf(2905,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(spm,[status(thm)],[2902,84,theory(equality)]) ).
cnf(2906,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aNaturalNumber0(aDimensionOf0(xs))
| $false ),
inference(rw,[status(thm)],[2905,76,theory(equality)]) ).
cnf(2907,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ),
inference(cn,[status(thm)],[2906,theory(equality)]) ).
cnf(2908,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aVector0(xs) ),
inference(spm,[status(thm)],[2907,137,theory(equality)]) ).
cnf(2909,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| $false ),
inference(rw,[status(thm)],[2908,76,theory(equality)]) ).
cnf(2910,plain,
( sdtlseqdt0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),sz0z00)
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00) ),
inference(cn,[status(thm)],[2909,theory(equality)]) ).
cnf(2928,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))) ),
inference(spm,[status(thm)],[929,2910,theory(equality)]) ).
cnf(2939,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(spm,[status(thm)],[2928,84,theory(equality)]) ).
cnf(2940,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aNaturalNumber0(aDimensionOf0(xs))
| $false ),
inference(rw,[status(thm)],[2939,76,theory(equality)]) ).
cnf(2941,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aNaturalNumber0(aDimensionOf0(xs)) ),
inference(cn,[status(thm)],[2940,theory(equality)]) ).
cnf(2942,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| ~ aVector0(xs) ),
inference(spm,[status(thm)],[2941,137,theory(equality)]) ).
cnf(2943,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| $false ),
inference(rw,[status(thm)],[2942,76,theory(equality)]) ).
cnf(2944,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00) ),
inference(cn,[status(thm)],[2943,theory(equality)]) ).
cnf(2945,plain,
( sz0z00 = sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))
| sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sz0z00) ),
inference(spm,[status(thm)],[75,2944,theory(equality)]) ).
cnf(2950,plain,
( sz0z00 = sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))
| sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| $false
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sz0z00) ),
inference(rw,[status(thm)],[2945,174,theory(equality)]) ).
cnf(2951,plain,
( sz0z00 = sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))
| sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| $false
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| $false ),
inference(rw,[status(thm)],[2950,54,theory(equality)]) ).
cnf(2952,plain,
( sz0z00 = sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))
| sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(cn,[status(thm)],[2951,theory(equality)]) ).
cnf(3111,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| ~ aVector0(sziznziztdt0(xs)) ),
inference(spm,[status(thm)],[2952,339,theory(equality)]) ).
cnf(3112,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| aDimensionOf0(xs) = sz00
| ~ aVector0(xs) ),
inference(spm,[status(thm)],[3111,242,theory(equality)]) ).
cnf(3113,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| aDimensionOf0(xs) = sz00
| $false ),
inference(rw,[status(thm)],[3112,76,theory(equality)]) ).
cnf(3114,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| aDimensionOf0(xs) = sz00 ),
inference(cn,[status(thm)],[3113,theory(equality)]) ).
cnf(3115,plain,
( sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))) = sz0z00
| sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00 ),
inference(sr,[status(thm)],[3114,181,theory(equality)]) ).
cnf(3117,plain,
( sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00) = sdtasasdt0(xs,xs)
| sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00 ),
inference(spm,[status(thm)],[66,3115,theory(equality)]) ).
cnf(3170,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(spm,[status(thm)],[1678,3117,theory(equality)]) ).
cnf(3182,plain,
( sdtlseqdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sz0z00)
| sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(sr,[status(thm)],[3170,155,theory(equality)]) ).
cnf(3240,plain,
( sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
inference(csr,[status(thm)],[3182,249]) ).
cnf(3241,plain,
( sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| ~ aVector0(sziznziztdt0(xs)) ),
inference(spm,[status(thm)],[3240,339,theory(equality)]) ).
cnf(3242,plain,
( sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| aDimensionOf0(xs) = sz00
| ~ aVector0(xs) ),
inference(spm,[status(thm)],[3241,242,theory(equality)]) ).
cnf(3243,plain,
( sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| aDimensionOf0(xs) = sz00
| $false ),
inference(rw,[status(thm)],[3242,76,theory(equality)]) ).
cnf(3244,plain,
( sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00
| aDimensionOf0(xs) = sz00 ),
inference(cn,[status(thm)],[3243,theory(equality)]) ).
cnf(3245,plain,
sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)) = sz0z00,
inference(sr,[status(thm)],[3244,181,theory(equality)]) ).
cnf(3247,plain,
sdtpldt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs),
inference(rw,[status(thm)],[66,3245,theory(equality)]) ).
cnf(35612,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(rw,[status(thm)],[639,3247,theory(equality)]) ).
cnf(35613,plain,
~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(sr,[status(thm)],[35612,155,theory(equality)]) ).
cnf(35614,plain,
~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(spm,[status(thm)],[35613,161,theory(equality)]) ).
cnf(35617,plain,
( ~ aNaturalNumber0(aDimensionOf0(xs))
| ~ aVector0(xs) ),
inference(spm,[status(thm)],[35614,84,theory(equality)]) ).
cnf(35618,plain,
( ~ aNaturalNumber0(aDimensionOf0(xs))
| $false ),
inference(rw,[status(thm)],[35617,76,theory(equality)]) ).
cnf(35619,plain,
~ aNaturalNumber0(aDimensionOf0(xs)),
inference(cn,[status(thm)],[35618,theory(equality)]) ).
cnf(35620,plain,
~ aVector0(xs),
inference(spm,[status(thm)],[35619,137,theory(equality)]) ).
cnf(35621,plain,
$false,
inference(rw,[status(thm)],[35620,76,theory(equality)]) ).
cnf(35622,plain,
$false,
inference(cn,[status(thm)],[35621,theory(equality)]) ).
cnf(35623,plain,
$false,
35622,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/RNG/RNG049+1.p
% --creating new selector for []
% -running prover on /tmp/tmpVY0sHk/sel_RNG049+1.p_1 with time limit 29
% -prover status Theorem
% Problem RNG049+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/RNG/RNG049+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/RNG/RNG049+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
%
%------------------------------------------------------------------------------