TPTP Problem File: NUM838+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : NUM838+1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Number Theory
% Problem : holds(conseq(195),305,0)
% 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 : 0.11 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.13 v7.3.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.17 v6.2.0, 0.20 v6.0.0, 0.22 v5.5.0, 0.15 v5.4.0, 0.14 v5.3.0, 0.22 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0
% Syntax : Number of formulae : 44 ( 10 unt; 0 def)
% Number of atoms : 87 ( 40 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 63 ( 20 ~; 13 |; 5 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 4 ( 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 : 103 ( 95 !; 8 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : From the Landau in Naproche 0.45 collection.
%------------------------------------------------------------------------------
fof('holds(conseq(195), 305, 0)',conjecture,
greater(vplus(vd301,vd303),vplus(vd302,vd303)) ).
fof('holds(antec(195), 304, 0)',axiom,
greater(vd301,vd302) ).
fof('ass(cond(proof(196), 0), 0)',axiom,
! [Vd310,Vd322,Vd323] :
( less(Vd322,Vd323)
=> less(vplus(Vd322,Vd310),vplus(Vd323,Vd310)) ) ).
fof('ass(cond(proof(196), 0), 1)',axiom,
! [Vd310,Vd322,Vd323] :
( less(Vd322,Vd323)
=> greater(vplus(Vd323,Vd310),vplus(Vd322,Vd310)) ) ).
fof('ass(cond(proof(196), 0), 2)',axiom,
! [Vd310,Vd322,Vd323] :
( less(Vd322,Vd323)
=> greater(Vd323,Vd322) ) ).
fof('ass(cond(proof(196), 0), 3)',axiom,
! [Vd310,Vd318,Vd319] :
( Vd318 = Vd319
=> vplus(Vd318,Vd310) = vplus(Vd319,Vd310) ) ).
fof('ass(cond(proof(196), 0), 4)',axiom,
! [Vd310,Vd311,Vd312] :
( greater(Vd311,Vd312)
=> greater(vplus(Vd311,Vd310),vplus(Vd312,Vd310)) ) ).
fof('ass(cond(proof(196), 0), 5)',axiom,
! [Vd310,Vd311,Vd312] :
( greater(Vd311,Vd312)
=> vplus(vskolem7(Vd311,Vd312),vplus(Vd312,Vd310)) = vplus(vplus(Vd312,Vd310),vskolem7(Vd311,Vd312)) ) ).
fof('ass(cond(proof(196), 0), 6)',axiom,
! [Vd310,Vd311,Vd312] :
( greater(Vd311,Vd312)
=> vplus(vplus(vskolem7(Vd311,Vd312),Vd312),Vd310) = vplus(vskolem7(Vd311,Vd312),vplus(Vd312,Vd310)) ) ).
fof('ass(cond(proof(196), 0), 7)',axiom,
! [Vd310,Vd311,Vd312] :
( greater(Vd311,Vd312)
=> vplus(vplus(Vd312,vskolem7(Vd311,Vd312)),Vd310) = vplus(vplus(vskolem7(Vd311,Vd312),Vd312),Vd310) ) ).
fof('ass(cond(proof(196), 0), 8)',axiom,
! [Vd310,Vd311,Vd312] :
( greater(Vd311,Vd312)
=> vplus(Vd311,Vd310) = vplus(vplus(Vd312,vskolem7(Vd311,Vd312)),Vd310) ) ).
fof('ass(cond(proof(196), 0), 9)',axiom,
! [Vd310,Vd311,Vd312] :
( greater(Vd311,Vd312)
=> Vd311 = vplus(Vd312,vskolem7(Vd311,Vd312)) ) ).
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 ).
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