TPTP Problem File: NUM853+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : NUM853+2 : TPTP v8.2.0. Released v4.1.0.
% Domain : Number Theory
% Problem : holds(conseq(307),490,0)
% Version : Especial: Reduced > Especial.
% English :
% Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% : [Kue09] Kuehlwein (2009), Email to Geoff Sutcliffe
% : [KC+10] Kuehlwein et al. (2010), Premise Selection in the Napr
% Source : [Kue09]
% Names :
% Status : Theorem
% Rating : 0.25 v8.2.0, 0.31 v7.4.0, 0.37 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.35 v7.0.0, 0.30 v6.4.0, 0.38 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.33 v6.0.0, 0.35 v5.5.0, 0.33 v5.4.0, 0.32 v5.3.0, 0.41 v5.2.0, 0.25 v5.1.0, 0.29 v4.1.0
% Syntax : Number of formulae : 37 ( 14 unt; 0 def)
% Number of atoms : 63 ( 37 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 19 ~; 10 |; 3 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 0 prp; 2-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 74 !; 8 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : From the Landau in Naproche 0.45 collection.
% : This version uses a filtered set of axioms.
%------------------------------------------------------------------------------
fof('holds(conseq(307), 490, 0)',conjecture,
greater(vd486,vd488) ).
fof('holds(antec(307), 489, 0)',axiom,
greater(vmul(vd486,vd487),vmul(vd488,vd487)) ).
fof('ass(cond(299, 0), 0)',axiom,
! [Vd456,Vd465,Vd466] :
( less(Vd465,Vd466)
=> less(vmul(Vd465,Vd456),vmul(Vd466,Vd456)) ) ).
fof('ass(cond(299, 0), 1)',axiom,
! [Vd456,Vd461,Vd462] :
( Vd461 = Vd462
=> vmul(Vd461,Vd456) = vmul(Vd462,Vd456) ) ).
fof('ass(cond(299, 0), 2)',axiom,
! [Vd456,Vd457,Vd458] :
( greater(Vd457,Vd458)
=> greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456)) ) ).
fof('ass(cond(290, 0), 0)',axiom,
! [Vd444,Vd445,Vd446] : vmul(vmul(Vd444,Vd445),Vd446) = vmul(Vd444,vmul(Vd445,Vd446)) ).
fof('ass(cond(281, 0), 0)',axiom,
! [Vd432,Vd433,Vd434] : vmul(Vd432,vplus(Vd433,Vd434)) = vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)) ).
fof('ass(cond(270, 0), 0)',axiom,
! [Vd418,Vd419] : vmul(Vd418,Vd419) = vmul(Vd419,Vd418) ).
fof('ass(cond(261, 0), 0)',axiom,
! [Vd408,Vd409] : vmul(vsucc(Vd408),Vd409) = vplus(vmul(Vd408,Vd409),Vd409) ).
fof('ass(cond(253, 0), 0)',axiom,
! [Vd400] : vmul(v1,Vd400) = Vd400 ).
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [Vd396,Vd397] :
( vmul(Vd396,vsucc(Vd397)) = vplus(vmul(Vd396,Vd397),Vd396)
& vmul(Vd396,v1) = Vd396 ) ).
fof('ass(cond(241, 0), 0)',axiom,
! [Vd386,Vd387] :
( less(Vd386,vplus(Vd387,v1))
=> leq(Vd386,Vd387) ) ).
fof('ass(cond(234, 0), 0)',axiom,
! [Vd375,Vd376] :
( greater(Vd375,Vd376)
=> geq(Vd375,vplus(Vd376,v1)) ) ).
fof('ass(cond(228, 0), 0)',axiom,
! [Vd369] : geq(Vd369,v1) ).
fof('ass(cond(223, 0), 0)',axiom,
! [Vd362,Vd363,Vd365,Vd366] :
( ( geq(Vd365,Vd366)
& geq(Vd362,Vd363) )
=> geq(vplus(Vd362,Vd365),vplus(Vd363,Vd366)) ) ).
fof('ass(cond(147, 0), 0)',axiom,
! [Vd226,Vd227] :
( less(Vd226,Vd227)
=> greater(Vd227,Vd226) ) ).
fof('ass(cond(140, 0), 0)',axiom,
! [Vd208,Vd209] :
( greater(Vd208,Vd209)
=> less(Vd209,Vd208) ) ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [Vd203,Vd204] :
( Vd203 = Vd204
| greater(Vd203,Vd204)
| less(Vd203,Vd204) ) ).
fof('ass(cond(goal(130), 0), 1)',axiom,
! [Vd203,Vd204] :
( Vd203 != Vd204
| ~ less(Vd203,Vd204) ) ).
fof('ass(cond(goal(130), 0), 2)',axiom,
! [Vd203,Vd204] :
( ~ greater(Vd203,Vd204)
| ~ less(Vd203,Vd204) ) ).
fof('ass(cond(goal(130), 0), 3)',axiom,
! [Vd203,Vd204] :
( Vd203 != Vd204
| ~ greater(Vd203,Vd204) ) ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [Vd198,Vd199] :
( less(Vd199,Vd198)
<=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ) ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ) ).
fof('ass(cond(goal(88), 0), 0)',axiom,
! [Vd120,Vd121] :
( Vd120 = Vd121
| ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
fof('ass(cond(goal(88), 0), 1)',axiom,
! [Vd120,Vd121] :
( Vd120 != Vd121
| ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
fof('ass(cond(goal(88), 0), 2)',axiom,
! [Vd120,Vd121] :
( ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123)
| ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125) ) ).
fof('ass(cond(goal(88), 0), 3)',axiom,
! [Vd120,Vd121] :
( Vd120 != Vd121
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ) ).
fof('ass(cond(81, 0), 0)',axiom,
! [Vd104,Vd105] :
( Vd104 != Vd105
=> ! [Vd107] : vplus(Vd107,Vd104) != vplus(Vd107,Vd105) ) ).
fof('ass(cond(73, 0), 0)',axiom,
! [Vd92,Vd93] : Vd93 != vplus(Vd92,Vd93) ).
fof('ass(cond(61, 0), 0)',axiom,
! [Vd78,Vd79] : vplus(Vd79,Vd78) = vplus(Vd78,Vd79) ).
fof('ass(cond(52, 0), 0)',axiom,
! [Vd68,Vd69] : vplus(vsucc(Vd68),Vd69) = vsucc(vplus(Vd68,Vd69)) ).
fof('ass(cond(43, 0), 0)',axiom,
! [Vd59] : vplus(v1,Vd59) = vsucc(Vd59) ).
fof('ass(cond(33, 0), 0)',axiom,
! [Vd46,Vd47,Vd48] : vplus(vplus(Vd46,Vd47),Vd48) = vplus(Vd46,vplus(Vd47,Vd48)) ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [Vd42,Vd43] :
( vplus(Vd42,vsucc(Vd43)) = vsucc(vplus(Vd42,Vd43))
& vplus(Vd42,v1) = vsucc(Vd42) ) ).
fof('ass(cond(20, 0), 0)',axiom,
! [Vd24] :
( Vd24 != v1
=> Vd24 = vsucc(vskolem2(Vd24)) ) ).
fof('ass(cond(12, 0), 0)',axiom,
! [Vd16] : vsucc(Vd16) != Vd16 ).
fof('ass(cond(6, 0), 0)',axiom,
! [Vd7,Vd8] :
( Vd7 != Vd8
=> vsucc(Vd7) != vsucc(Vd8) ) ).
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