TPTP Problem File: RNG098+2.p
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%------------------------------------------------------------------------------
% File : RNG098+2 : TPTP v8.2.0. Released v4.0.0.
% Domain : Ring Theory
% Problem : Chinese remainder theorem in a ring 05_03_03, 01 expansion
% Version : Especial.
% English :
% Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% Source : [Pas08]
% Names : chines_05_03_03.01 [Pas08]
% Status : Theorem
% Rating : 0.56 v8.2.0, 0.53 v8.1.0, 0.50 v7.5.0, 0.59 v7.4.0, 0.43 v7.3.0, 0.52 v7.0.0, 0.50 v6.4.0, 0.54 v6.3.0, 0.46 v6.2.0, 0.48 v6.1.0, 0.57 v6.0.0, 0.61 v5.5.0, 0.74 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0, 0.75 v5.1.0, 0.81 v5.0.0, 0.83 v4.0.1, 0.96 v4.0.0
% Syntax : Number of formulae : 35 ( 7 unt; 4 def)
% Number of atoms : 125 ( 28 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 91 ( 1 ~; 1 |; 45 &)
% ( 6 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 63 ( 59 !; 4 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Problem generated by the SAD system [VLP07]
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fof(mElmSort,axiom,
! [W0] :
( aElement0(W0)
=> $true ) ).
fof(mSortsC,axiom,
aElement0(sz00) ).
fof(mSortsC_01,axiom,
aElement0(sz10) ).
fof(mSortsU,axiom,
! [W0] :
( aElement0(W0)
=> aElement0(smndt0(W0)) ) ).
fof(mSortsB,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) ) ).
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ) ).
fof(mAddComm,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ).
fof(mAddZero,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ) ).
fof(mAddInvr,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ).
fof(mMulUnit,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ) ).
fof(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ).
fof(mMulMnOne,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
& smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ).
fof(mMulZero,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ) ).
fof(mCancel,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W0 = sz00
| W1 = sz00 ) ) ) ).
fof(mUnNeZr,axiom,
sz10 != sz00 ).
fof(mSetSort,axiom,
! [W0] :
( aSet0(W0)
=> $true ) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ) ).
fof(mSetEq,axiom,
! [W0,W1] :
( ( aSet0(W0)
& aSet0(W1) )
=> ( ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(W2,W1) )
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) )
=> W0 = W1 ) ) ).
fof(mDefSSum,definition,
! [W0,W1] :
( ( aSet0(W0)
& aSet0(W1) )
=> ! [W2] :
( W2 = sdtpldt1(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( aElementOf0(W4,W0)
& aElementOf0(W5,W1)
& sdtpldt0(W4,W5) = W3 ) ) ) ) ) ).
fof(mDefSInt,definition,
! [W0,W1] :
( ( aSet0(W0)
& aSet0(W1) )
=> ! [W2] :
( W2 = sdtasasdt0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,W0)
& aElementOf0(W3,W1) ) ) ) ) ) ).
fof(mDefIdeal,definition,
! [W0] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ).
fof(mIdeSum,axiom,
! [W0,W1] :
( ( aIdeal0(W0)
& aIdeal0(W1) )
=> aIdeal0(sdtpldt1(W0,W1)) ) ).
fof(mIdeInt,axiom,
! [W0,W1] :
( ( aIdeal0(W0)
& aIdeal0(W1) )
=> aIdeal0(sdtasasdt0(W0,W1)) ) ).
fof(mDefMod,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) ).
fof(m__1205,hypothesis,
( aSet0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) )
& ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) ) ) )
& aIdeal0(xJ) ) ).
fof(m__1205_03,hypothesis,
! [W0] :
( aElement0(W0)
=> ( ? [W1,W2] :
( aElementOf0(W1,xI)
& aElementOf0(W2,xJ)
& sdtpldt0(W1,W2) = W0 )
& aElementOf0(W0,sdtpldt1(xI,xJ)) ) ) ).
fof(m__1217,hypothesis,
( aElement0(xx)
& aElement0(xy) ) ).
fof(m__1294,hypothesis,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ) ).
fof(m__1319,hypothesis,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) ).
fof(m__1374,hypothesis,
sdtpldt0(xw,smndt0(xx)) = sdtpldt0(sdtasdt0(xy,xa),sdtpldt0(sdtasdt0(xx,xb),smndt0(xx))) ).
fof(m__1393,hypothesis,
aElementOf0(sdtasdt0(xx,sdtpldt0(xb,smndt0(sz10))),xI) ).
fof(m__,conjecture,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI) ).
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