TPTP Problem File: NUM436+3.p
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%------------------------------------------------------------------------------
% File : NUM436+3 : TPTP v9.0.0. Released v4.0.0.
% Domain : Number Theory
% Problem : Fuerstenberg's infinitude of primes 06_03, 02 expansion
% Version : Especial.
% English :
% Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% Source : [Pas08]
% Names : fuerst_06_03.02 [Pas08]
% Status : Theorem
% Rating : 0.30 v9.0.0, 0.28 v8.2.0, 0.25 v8.1.0, 0.19 v7.5.0, 0.22 v7.4.0, 0.20 v7.3.0, 0.28 v7.1.0, 0.30 v7.0.0, 0.27 v6.4.0, 0.31 v6.3.0, 0.33 v6.2.0, 0.32 v6.1.0, 0.40 v6.0.0, 0.35 v5.5.0, 0.52 v5.4.0, 0.54 v5.3.0, 0.56 v5.2.0, 0.50 v5.1.0, 0.57 v5.0.0, 0.58 v4.1.0, 0.65 v4.0.1, 0.83 v4.0.0
% Syntax : Number of formulae : 27 ( 2 unt; 2 def)
% Number of atoms : 104 ( 34 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 85 ( 8 ~; 5 |; 47 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 44 ( 40 !; 4 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Problem generated by the SAD system [VLP07]
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fof(mIntegers,axiom,
! [W0] :
( aInteger0(W0)
=> $true ) ).
fof(mIntZero,axiom,
aInteger0(sz00) ).
fof(mIntOne,axiom,
aInteger0(sz10) ).
fof(mIntNeg,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ) ).
fof(mIntPlus,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ) ).
fof(mIntMult,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtasdt0(W0,W1)) ) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ).
fof(mAddComm,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ).
fof(mAddZero,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ) ).
fof(mAddNeg,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> sdtasdt0(W0,sdtasdt0(W1,W2)) = sdtasdt0(sdtasdt0(W0,W1),W2) ) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ).
fof(mMulOne,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ) ).
fof(mDistrib,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ).
fof(mMulZero,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ) ).
fof(mMulMinOne,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
& smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ).
fof(mZeroDiv,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtasdt0(W0,W1) = sz00
=> ( W0 = sz00
| W1 = sz00 ) ) ) ).
fof(mDivisor,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& W1 != sz00
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W1,W2) = W0 ) ) ) ) ).
fof(mEquMod,definition,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& W2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ).
fof(mEquModRef,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1)
& W1 != sz00 )
=> sdteqdtlpzmzozddtrp0(W0,W0,W1) ) ).
fof(mEquModSym,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& W2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ) ).
fof(mEquModTrn,axiom,
! [W0,W1,W2,W3] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& W2 != sz00
& aInteger0(W3) )
=> ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) ) ) ).
fof(m__979,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ) ).
fof(m__1003,hypothesis,
( sdtasdt0(xp,xq) != sz00
& ? [W0] :
( aInteger0(W0)
& sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ) ).
fof(m__1032,hypothesis,
( aInteger0(xm)
& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ) ).
fof(m__1071,hypothesis,
( sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb))
& sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)) ) ).
fof(m__,conjecture,
( ( ? [W0] :
( aInteger0(W0)
& sdtasdt0(xp,W0) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xp) )
& ( ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
| sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ) ).
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