TPTP Problem File: GEO497+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : GEO497+1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Geometry
% Problem : Property of a and b being on the same side of point p
% Version : Especial.
% English :
% Refs : [Urb16] Urban (2016), Email to Geoff Sutcliffe
% : [BW17] Beeson & Wos (2017), Finding Proofs in Tarskian Geomet
% Source : [Urb16]
% Names : Satz6.11a.in.p [BW17]
% Status : Theorem
% Rating : 0.55 v9.0.0, 0.61 v8.2.0, 0.64 v8.1.0, 0.56 v7.5.0, 0.66 v7.4.0, 0.50 v7.3.0, 0.52 v7.1.0, 0.48 v7.0.0
% Syntax : Number of formulae : 85 ( 15 unt; 0 def)
% Number of atoms : 339 ( 46 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 444 ( 190 ~; 212 |; 42 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 0 prp; 2-8 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-6 aty)
% Number of variables : 335 ( 335 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
include('Axioms/GEO011+0.ax').
%------------------------------------------------------------------------------
fof(aSatz2_1,axiom,
! [Xa,Xb] : s_e(Xa,Xb,Xa,Xb) ).
fof(aSatz2_2,axiom,
! [Xa,Xb,Xc,Xd] :
( ~ s_e(Xa,Xb,Xc,Xd)
| s_e(Xc,Xd,Xa,Xb) ) ).
fof(aSatz2_3,axiom,
! [Xa,Xb,Xc,Xd,Xe,Xf] :
( ~ s_e(Xa,Xb,Xc,Xd)
| ~ s_e(Xc,Xd,Xe,Xf)
| s_e(Xa,Xb,Xe,Xf) ) ).
fof(aSatz2_4,axiom,
! [Xa,Xb,Xc,Xd] :
( ~ s_e(Xa,Xb,Xc,Xd)
| s_e(Xb,Xa,Xc,Xd) ) ).
fof(aSatz2_5,axiom,
! [Xa,Xb,Xc,Xd] :
( ~ s_e(Xa,Xb,Xc,Xd)
| s_e(Xa,Xb,Xd,Xc) ) ).
fof(aSatz2_8,axiom,
! [Xa,Xb] : s_e(Xa,Xa,Xb,Xb) ).
fof(aSatz2_11,axiom,
! [Xa,Xb,Xc,Xa1,Xb1,Xc1] :
( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xa1,Xb1,Xc1)
| ~ s_e(Xa,Xb,Xa1,Xb1)
| ~ s_e(Xb,Xc,Xb1,Xc1)
| s_e(Xa,Xc,Xa1,Xc1) ) ).
fof(aSatz2_12,axiom,
! [Xq,Xa,Xd,Xb,Xc] :
( Xq = Xa
| ~ s_t(Xq,Xa,Xd)
| ~ s_e(Xa,Xd,Xb,Xc)
| Xd = ext(Xq,Xa,Xb,Xc) ) ).
fof(aSatz2_13,axiom,
! [Xb,Xc,Xa] :
( ~ s_e(Xb,Xc,Xa,Xa)
| Xb = Xc ) ).
fof(aSatz2_14,axiom,
! [Xa,Xb,Xc,Xd] :
( ~ s_e(Xa,Xb,Xc,Xd)
| s_e(Xb,Xa,Xd,Xc) ) ).
fof(aSatz2_15,axiom,
! [Xa,Xb,Xc,XA,XB,XC] :
( ~ s_t(Xa,Xb,Xc)
| ~ s_t(XA,XB,XC)
| ~ s_e(Xa,Xb,XB,XC)
| ~ s_e(Xb,Xc,XA,XB)
| s_e(Xa,Xc,XA,XC) ) ).
fof(aSatz3_1,axiom,
! [Xa,Xb] : s_t(Xa,Xb,Xb) ).
fof(aSatz3_2,axiom,
! [Xa,Xb,Xc] :
( ~ s_t(Xa,Xb,Xc)
| s_t(Xc,Xb,Xa) ) ).
fof(aSatz3_3,axiom,
! [Xa1,Xb1] : s_t(Xa1,Xa1,Xb1) ).
fof(aSatz3_4,axiom,
! [Xa,Xb,Xc] :
( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xb,Xa,Xc)
| Xa = Xb ) ).
fof(aSatz3_5a,axiom,
! [Xa,Xb,Xd,Xc] :
( ~ s_t(Xa,Xb,Xd)
| ~ s_t(Xb,Xc,Xd)
| s_t(Xa,Xb,Xc) ) ).
fof(aSatz3_6a,axiom,
! [Xa,Xb,Xc,Xd] :
( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xa,Xc,Xd)
| s_t(Xb,Xc,Xd) ) ).
fof(aSatz3_7a,axiom,
! [Xa,Xb,Xc,Xd] :
( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xb,Xc,Xd)
| Xb = Xc
| s_t(Xa,Xc,Xd) ) ).
fof(aSatz3_5b,axiom,
! [Xa,Xb,Xd,Xc] :
( ~ s_t(Xa,Xb,Xd)
| ~ s_t(Xb,Xc,Xd)
| s_t(Xa,Xc,Xd) ) ).
fof(aSatz3_6b,axiom,
! [Xa,Xb,Xc,Xd] :
( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xa,Xc,Xd)
| s_t(Xa,Xb,Xd) ) ).
fof(aSatz3_7b,axiom,
! [Xa,Xb,Xc,Xd] :
( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xb,Xc,Xd)
| Xb = Xc
| s_t(Xa,Xb,Xd) ) ).
fof(aSatz3_13a,axiom,
alpha != beta ).
fof(aSatz3_13b,axiom,
beta != gamma ).
fof(aSatz3_13c,axiom,
alpha != gamma ).
fof(aSatz3_14a,axiom,
! [Xa,Xb] : s_t(Xa,Xb,ext(Xa,Xb,alpha,gamma)) ).
fof(aSatz3_14b,axiom,
! [Xb,Xa] : Xb != ext(Xa,Xb,alpha,gamma) ).
fof(aSatz3_17,axiom,
! [Xa,Xb,Xc,Xa1,Xb1,Xp] :
( ( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xa1,Xb1,Xc)
| ~ s_t(Xa,Xp,Xa1)
| s_t(Xp,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xc) )
& ( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xa1,Xb1,Xc)
| ~ s_t(Xa,Xp,Xa1)
| s_t(Xb,crossbar(Xa,Xb,Xc,Xa1,Xb1,Xp),Xb1) ) ) ).
fof(aSatz4_2,axiom,
! [Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1] :
( ~ s_ifs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)
| s_e(Xb,Xd,Xb1,Xd1) ) ).
fof(aSatz4_3,axiom,
! [Xa,Xb,Xc,Xa1,Xb1,Xc1] :
( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xa1,Xb1,Xc1)
| ~ s_e(Xa,Xc,Xa1,Xc1)
| ~ s_e(Xb,Xc,Xb1,Xc1)
| s_e(Xa,Xb,Xa1,Xb1) ) ).
fof(aSatz4_5,axiom,
! [Xa,Xb,Xc,Xa1,Xc1] :
( ( ~ s_t(Xa,Xb,Xc)
| ~ s_e(Xa,Xc,Xa1,Xc1)
| s_t(Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) )
& ( ~ s_t(Xa,Xb,Xc)
| ~ s_e(Xa,Xc,Xa1,Xc1)
| s_e3(Xa,Xb,Xc,Xa1,insert(Xa,Xb,Xa1,Xc1),Xc1) ) ) ).
fof(aSatz4_6,axiom,
! [Xa,Xb,Xc,Xa1,Xb1,Xc1] :
( ~ s_t(Xa,Xb,Xc)
| ~ s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1)
| s_t(Xa1,Xb1,Xc1) ) ).
fof(aSatz4_11a,axiom,
! [Xa,Xb,Xc] :
( ~ s_col(Xa,Xb,Xc)
| s_col(Xb,Xc,Xa) ) ).
fof(aSatz4_11b,axiom,
! [Xa,Xb,Xc] :
( ~ s_col(Xa,Xb,Xc)
| s_col(Xc,Xa,Xb) ) ).
fof(aSatz4_11c,axiom,
! [Xa,Xb,Xc] :
( ~ s_col(Xa,Xb,Xc)
| s_col(Xc,Xb,Xa) ) ).
fof(aSatz4_11d,axiom,
! [Xa,Xb,Xc] :
( ~ s_col(Xa,Xb,Xc)
| s_col(Xb,Xa,Xc) ) ).
fof(aSatz4_11e,axiom,
! [Xa,Xb,Xc] :
( ~ s_col(Xa,Xb,Xc)
| s_col(Xa,Xc,Xb) ) ).
fof(aSatz4_12,axiom,
! [Xa,Xb] : s_col(Xa,Xa,Xb) ).
fof(aSatz4_12b,axiom,
! [Xa,Xb] : s_col(Xa,Xb,Xa) ).
fof(aSatz4_13,axiom,
! [Xa,Xb,Xc,Xa1,Xb1,Xc1] :
( ~ s_col(Xa,Xb,Xc)
| ~ s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1)
| s_col(Xa1,Xb1,Xc1) ) ).
fof(aSatz4_14,axiom,
! [Xa,Xb,Xc,Xa1,Xb1] :
( ~ s_col(Xa,Xb,Xc)
| ~ s_e(Xa,Xb,Xa1,Xb1)
| s_e3(Xa,Xb,Xc,Xa1,Xb1,insert5(Xa,Xb,Xc,Xa1,Xb1)) ) ).
fof(aSatz4_16,axiom,
! [Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1] :
( ~ s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)
| Xa = Xb
| s_e(Xc,Xd,Xc1,Xd1) ) ).
fof(aSatz4_17,axiom,
! [Xa,Xb,Xc,Xp,Xq] :
( Xa = Xb
| ~ s_col(Xa,Xb,Xc)
| ~ s_e(Xa,Xp,Xa,Xq)
| ~ s_e(Xb,Xp,Xb,Xq)
| s_e(Xc,Xp,Xc,Xq) ) ).
fof(aSatz4_18,axiom,
! [Xa,Xb,Xc,Xc1] :
( Xa = Xb
| ~ s_col(Xa,Xb,Xc)
| ~ s_e(Xa,Xc,Xa,Xc1)
| ~ s_e(Xb,Xc,Xb,Xc1)
| Xc = Xc1 ) ).
fof(aSatz4_19,axiom,
! [Xa,Xc,Xb,Xc1] :
( ~ s_t(Xa,Xc,Xb)
| ~ s_e(Xa,Xc,Xa,Xc1)
| ~ s_e(Xb,Xc,Xb,Xc1)
| Xc = Xc1 ) ).
fof(aSatz5_1,axiom,
! [Xa,Xb,Xc,Xd] :
( Xa = Xb
| ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xa,Xb,Xd)
| s_t(Xa,Xc,Xd)
| s_t(Xa,Xd,Xc) ) ).
fof(aSatz5_2,axiom,
! [Xa,Xb,Xc,Xd] :
( Xa = Xb
| ~ s_t(Xa,Xb,Xc)
| ~ s_t(Xa,Xb,Xd)
| s_t(Xb,Xc,Xd)
| s_t(Xb,Xd,Xc) ) ).
fof(aSatz5_3,axiom,
! [Xa,Xb,Xd,Xc] :
( ~ s_t(Xa,Xb,Xd)
| ~ s_t(Xa,Xc,Xd)
| s_t(Xa,Xb,Xc)
| s_t(Xa,Xc,Xb) ) ).
fof(aSatz5_5a,axiom,
! [Xa,Xb,Xc,Xd] :
( ( ~ le(Xa,Xb,Xc,Xd)
| s_t(Xa,Xb,ins(Xc,Xd,Xa,Xb)) )
& ( ~ le(Xa,Xb,Xc,Xd)
| s_e(Xa,ins(Xc,Xd,Xa,Xb),Xc,Xd) )
& ( ~ le(Xa,Xb,Xc,Xd)
| ins(Xc,Xd,Xa,Xb) = ext(Xa,Xb,insert(Xa,Xb,Xc,Xd),Xd) ) ) ).
fof(aSatz5_5b,axiom,
! [Xa,Xb,Xc,Xd,Xe] :
( le(Xa,Xb,Xc,Xd)
| ~ s_t(Xa,Xb,Xe)
| ~ s_e(Xa,Xe,Xc,Xd) ) ).
fof(aSatz5_6,axiom,
! [Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1] :
( ~ le(Xa,Xb,Xc,Xd)
| ~ s_e(Xa,Xb,Xa1,Xb1)
| ~ s_e(Xc,Xd,Xc1,Xd1)
| le(Xa1,Xb1,Xc1,Xd1) ) ).
fof(aSatz5_7,axiom,
! [Xa,Xb] : le(Xa,Xb,Xa,Xb) ).
fof(aSatz5_8,axiom,
! [Xa,Xb,Xc,Xd,Xe,Xf] :
( ~ le(Xa,Xb,Xc,Xd)
| ~ le(Xc,Xd,Xe,Xf)
| le(Xa,Xb,Xe,Xf) ) ).
fof(aSatz5_9,axiom,
! [Xa,Xb,Xc,Xd] :
( ~ le(Xa,Xb,Xc,Xd)
| ~ le(Xc,Xd,Xa,Xb)
| s_e(Xa,Xb,Xc,Xd) ) ).
fof(aSatz5_10,axiom,
! [Xa,Xb,Xc,Xd] :
( le(Xa,Xb,Xc,Xd)
| le(Xc,Xd,Xa,Xb) ) ).
fof(aSatz5_11,axiom,
! [Xa,Xc,Xd] : le(Xa,Xa,Xc,Xd) ).
fof(aSatz5_12a1,axiom,
! [Xa,Xb,Xc] :
( ~ s_col(Xa,Xb,Xc)
| ~ s_t(Xa,Xb,Xc)
| le(Xa,Xb,Xa,Xc) ) ).
fof(aSatz5_12a2,axiom,
! [Xa,Xb,Xc] :
( ~ s_col(Xa,Xb,Xc)
| ~ s_t(Xa,Xb,Xc)
| le(Xb,Xc,Xa,Xc) ) ).
fof(aNarbouxLemma1,axiom,
! [Xa,Xb,Xc] :
( ~ s_t(Xa,Xb,Xc)
| ~ s_e(Xa,Xc,Xa,Xb)
| Xc = Xb ) ).
fof(aSatz5_12b,axiom,
! [Xa,Xb,Xc] :
( ~ s_col(Xa,Xb,Xc)
| s_t(Xa,Xb,Xc)
| ~ le(Xa,Xb,Xa,Xc)
| ~ le(Xb,Xc,Xa,Xc) ) ).
fof(aSatz6_2a,axiom,
! [Xa,Xp,Xb,Xc] :
( Xa = Xp
| Xb = Xp
| Xc = Xp
| ~ s_t(Xa,Xp,Xc)
| ~ s_t(Xb,Xp,Xc)
| sameside(Xa,Xp,Xb) ) ).
fof(aSatz6_2b,axiom,
! [Xa,Xp,Xb,Xc] :
( Xa = Xp
| Xb = Xp
| Xc = Xp
| ~ s_t(Xa,Xp,Xc)
| s_t(Xb,Xp,Xc)
| ~ sameside(Xa,Xp,Xb) ) ).
fof(aSatz6_3a,axiom,
! [Xa,Xp,Xb] :
( ( ~ sameside(Xa,Xp,Xb)
| Xa != Xp )
& ( ~ sameside(Xa,Xp,Xb)
| Xb != Xp )
& ( ~ sameside(Xa,Xp,Xb)
| c63(Xa,Xp,Xb) != Xp )
& ( ~ sameside(Xa,Xp,Xb)
| s_t(Xa,Xp,c63(Xa,Xp,Xb)) )
& ( ~ sameside(Xa,Xp,Xb)
| s_t(Xb,Xp,c63(Xa,Xp,Xb)) ) ) ).
fof(aSatz6_3b,axiom,
! [Xa,Xp,Xb,Xc] :
( sameside(Xa,Xp,Xb)
| Xa = Xp
| Xb = Xp
| Xc = Xp
| ~ s_t(Xa,Xp,Xc)
| ~ s_t(Xb,Xp,Xc) ) ).
fof(aSatz6_4a,axiom,
! [Xa,Xp,Xb] :
( ( ~ sameside(Xa,Xp,Xb)
| s_col(Xa,Xp,Xb) )
& ( ~ sameside(Xa,Xp,Xb)
| ~ s_t(Xa,Xp,Xb) ) ) ).
fof(aSatz6_4b,axiom,
! [Xa,Xp,Xb] :
( sameside(Xa,Xp,Xb)
| ~ s_col(Xa,Xp,Xb)
| s_t(Xa,Xp,Xb) ) ).
fof(aSatz6_5,axiom,
! [Xa,Xp] :
( Xa = Xp
| sameside(Xa,Xp,Xa) ) ).
fof(aSatz6_6,axiom,
! [Xa,Xp,Xb] :
( ~ sameside(Xa,Xp,Xb)
| sameside(Xb,Xp,Xa) ) ).
fof(aSatz6_7,axiom,
! [Xa,Xp,Xb,Xc] :
( ~ sameside(Xa,Xp,Xb)
| ~ sameside(Xb,Xp,Xc)
| sameside(Xa,Xp,Xc) ) ).
fof(aSatz6_11a,conjecture,
! [Xr,Xa,Xb,Xc] :
( ( Xr = Xa
| Xb = Xc
| sameside(insert(Xb,Xc,Xa,Xr),Xa,Xr) )
& ( Xr = Xa
| Xb = Xc
| s_e(Xa,insert(Xb,Xc,Xa,Xr),Xb,Xc) ) ) ).
fof(d_insert,axiom,
! [Xa,Xb,Xa1,Xc1] : insert(Xa,Xb,Xa1,Xc1) = ext(ext(Xc1,Xa1,alpha,gamma),Xa1,Xa,Xb) ).
fof(d_Defn2_10,axiom,
! [Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd] :
( ( ~ s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_t(Xa,Xb,Xc) )
& ( ~ s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_t(Za,Zb,Zc) )
& ( ~ s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_e(Xa,Xb,Za,Zb) )
& ( ~ s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_e(Xb,Xc,Zb,Zc) )
& ( ~ s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_e(Xa,Xd,Za,Zd) )
& ( ~ s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_e(Xb,Xd,Zb,Zd) )
& ( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Za,Zb,Zc)
| ~ s_e(Xa,Xb,Za,Zb)
| ~ s_e(Xb,Xc,Zb,Zc)
| ~ s_e(Xa,Xd,Za,Zd)
| ~ s_e(Xb,Xd,Zb,Zd)
| s_afs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) ) ) ).
fof(d_Defn4_1,axiom,
! [Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd] :
( ( ~ s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_t(Xa,Xb,Xc) )
& ( ~ s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_t(Za,Zb,Zc) )
& ( ~ s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_e(Xa,Xc,Za,Zc) )
& ( ~ s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_e(Xb,Xc,Zb,Zc) )
& ( ~ s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_e(Xa,Xd,Za,Zd) )
& ( ~ s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd)
| s_e(Xc,Xd,Zc,Zd) )
& ( ~ s_t(Xa,Xb,Xc)
| ~ s_t(Za,Zb,Zc)
| ~ s_e(Xa,Xc,Za,Zc)
| ~ s_e(Xb,Xc,Zb,Zc)
| ~ s_e(Xa,Xd,Za,Zd)
| ~ s_e(Xc,Xd,Zc,Zd)
| s_ifs(Xa,Xb,Xc,Xd,Za,Zb,Zc,Zd) ) ) ).
fof(d_Defn4_4,axiom,
! [Xa1,Xa2,Xa3,Xb1,Xb2,Xb3] :
( ( ~ s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)
| s_e(Xa1,Xa2,Xb1,Xb2) )
& ( ~ s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)
| s_e(Xa1,Xa3,Xb1,Xb3) )
& ( ~ s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3)
| s_e(Xa2,Xa3,Xb2,Xb3) )
& ( ~ s_e(Xa1,Xa2,Xb1,Xb2)
| ~ s_e(Xa1,Xa3,Xb1,Xb3)
| ~ s_e(Xa2,Xa3,Xb2,Xb3)
| s_e3(Xa1,Xa2,Xa3,Xb1,Xb2,Xb3) ) ) ).
fof(d_Defn4_10,axiom,
! [Xa,Xb,Xc] :
( ( ~ s_col(Xa,Xb,Xc)
| s_t(Xa,Xb,Xc)
| s_t(Xb,Xc,Xa)
| s_t(Xc,Xa,Xb) )
& ( s_col(Xa,Xb,Xc)
| ~ s_t(Xa,Xb,Xc) )
& ( s_col(Xa,Xb,Xc)
| ~ s_t(Xb,Xc,Xa) )
& ( s_col(Xa,Xb,Xc)
| ~ s_t(Xc,Xa,Xb) ) ) ).
fof(d_Defn4_15,axiom,
! [Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1] :
( ( ~ s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)
| s_col(Xa,Xb,Xc) )
& ( ~ s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)
| s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1) )
& ( ~ s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)
| s_e(Xa,Xd,Xa1,Xd1) )
& ( ~ s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1)
| s_e(Xb,Xd,Xb1,Xd1) )
& ( ~ s_col(Xa,Xb,Xc)
| ~ s_e3(Xa,Xb,Xc,Xa1,Xb1,Xc1)
| ~ s_e(Xa,Xd,Xa1,Xd1)
| ~ s_e(Xb,Xd,Xb1,Xd1)
| s_fs(Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1) ) ) ).
fof(d_Defn5_4,axiom,
! [Xa,Xb,Xc,Xd,Y] :
( ( ~ le(Xa,Xb,Xc,Xd)
| s_t(Xc,insert(Xa,Xb,Xc,Xd),Xd) )
& ( ~ le(Xa,Xb,Xc,Xd)
| s_e(Xa,Xb,Xc,insert(Xa,Xb,Xc,Xd)) )
& ( ~ s_t(Xc,Y,Xd)
| ~ s_e(Xa,Xb,Xc,Y)
| le(Xa,Xb,Xc,Xd) ) ) ).
fof(d_Defn6_1,axiom,
! [Xa,Xp,Xb] :
( ( ~ sameside(Xa,Xp,Xb)
| Xa != Xp )
& ( ~ sameside(Xa,Xp,Xb)
| Xb != Xp )
& ( ~ sameside(Xa,Xp,Xb)
| s_t(Xp,Xa,Xb)
| s_t(Xp,Xb,Xa) )
& ( ~ s_t(Xp,Xa,Xb)
| Xa = Xp
| xb = Xp
| sameside(Xa,Xp,Xb) )
& ( ~ s_t(Xp,Xb,Xa)
| Xa = Xp
| Xb = Xp
| sameside(Xa,Xp,Xb) ) ) ).
%------------------------------------------------------------------------------