TPTP Problem File: NUM841+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : NUM841+1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Number Theory
% Problem : holds(214,352,0)
% Version : 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 : 0.22 v8.2.0, 0.28 v8.1.0, 0.25 v7.5.0, 0.22 v7.4.0, 0.20 v7.3.0, 0.21 v7.1.0, 0.26 v7.0.0, 0.27 v6.4.0, 0.35 v6.3.0, 0.29 v6.2.0, 0.32 v6.1.0, 0.43 v6.0.0, 0.35 v5.5.0, 0.41 v5.4.0, 0.39 v5.3.0, 0.56 v5.2.0, 0.35 v5.1.0, 0.33 v5.0.0, 0.42 v4.1.0
% Syntax : Number of formulae : 45 ( 15 unt; 0 def)
% Number of atoms : 84 ( 39 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 59 ( 20 ~; 13 |; 5 &)
% ( 4 <=>; 17 =>; 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; 5 con; 0-2 aty)
% Number of variables : 91 ( 83 !; 8 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : From the Landau in Naproche 0.45 collection.
%------------------------------------------------------------------------------
fof('holds(214, 352, 0)',conjecture,
greater(vplus(vd344,vd347),vplus(vd345,vd348)) ).
fof('holds(213, 351, 2)',axiom,
vplus(vd348,vd345) = vplus(vd345,vd348) ).
fof('holds(213, 351, 1)',axiom,
greater(vplus(vd347,vd345),vplus(vd348,vd345)) ).
fof('holds(213, 351, 0)',axiom,
vplus(vd345,vd347) = vplus(vd347,vd345) ).
fof('holds(212, 350, 0)',axiom,
greater(vplus(vd344,vd347),vplus(vd345,vd347)) ).
fof('holds(conjunct2(211), 349, 0)',axiom,
greater(vd347,vd348) ).
fof('holds(conjunct1(211), 346, 0)',axiom,
greater(vd344,vd345) ).
fof('ass(cond(goal(202), 0), 0)',axiom,
! [Vd328,Vd329,Vd330] :
( less(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
=> less(Vd328,Vd329) ) ).
fof('ass(cond(goal(202), 0), 1)',axiom,
! [Vd328,Vd329,Vd330] :
( vplus(Vd328,Vd330) = vplus(Vd329,Vd330)
=> Vd328 = Vd329 ) ).
fof('ass(cond(goal(202), 0), 2)',axiom,
! [Vd328,Vd329,Vd330] :
( greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))
=> greater(Vd328,Vd329) ) ).
fof('ass(cond(goal(193), 0), 0)',axiom,
! [Vd301,Vd302,Vd303] :
( less(Vd301,Vd302)
=> less(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ) ).
fof('ass(cond(goal(193), 0), 1)',axiom,
! [Vd301,Vd302,Vd303] :
( Vd301 = Vd302
=> vplus(Vd301,Vd303) = vplus(Vd302,Vd303) ) ).
fof('ass(cond(goal(193), 0), 2)',axiom,
! [Vd301,Vd302,Vd303] :
( greater(Vd301,Vd302)
=> greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)) ) ).
fof('ass(cond(189, 0), 0)',axiom,
! [Vd295,Vd296] : greater(vplus(Vd295,Vd296),Vd295) ).
fof('ass(cond(184, 0), 0)',axiom,
! [Vd289,Vd290,Vd292] :
( ( leq(Vd290,Vd292)
& leq(Vd289,Vd290) )
=> leq(Vd289,Vd292) ) ).
fof('ass(cond(goal(177), 0), 0)',axiom,
! [Vd281,Vd282,Vd283] :
( ( ( less(Vd282,Vd283)
& leq(Vd281,Vd282) )
| ( leq(Vd282,Vd283)
& less(Vd281,Vd282) ) )
=> less(Vd281,Vd283) ) ).
fof('ass(cond(168, 0), 0)',axiom,
! [Vd262,Vd263,Vd265] :
( ( less(Vd263,Vd265)
& less(Vd262,Vd263) )
=> less(Vd262,Vd265) ) ).
fof('ass(cond(163, 0), 0)',axiom,
! [Vd258,Vd259] :
( leq(Vd258,Vd259)
=> geq(Vd259,Vd258) ) ).
fof('ass(cond(158, 0), 0)',axiom,
! [Vd254,Vd255] :
( geq(Vd254,Vd255)
=> leq(Vd255,Vd254) ) ).
fof('def(cond(conseq(axiom(3)), 17), 1)',axiom,
! [Vd249,Vd250] :
( leq(Vd250,Vd249)
<=> ( less(Vd250,Vd249)
| Vd250 = Vd249 ) ) ).
fof('def(cond(conseq(axiom(3)), 16), 1)',axiom,
! [Vd244,Vd245] :
( geq(Vd245,Vd244)
<=> ( greater(Vd245,Vd244)
| Vd245 = Vd244 ) ) ).
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) ) ).
fof('qu(antec(axiom(3)), imp(antec(axiom(3))))',axiom,
! [Vd3,Vd4] :
( vsucc(Vd3) = vsucc(Vd4)
=> Vd3 = Vd4 ) ).
fof('qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))',axiom,
! [Vd1] : vsucc(Vd1) != v1 ).
%------------------------------------------------------------------------------