TPTP Problem File: SWV118+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV118+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Domain : Software Verification
% Problem : Unsimplified proof obligation quaternion_ds1_symm_0011
% Version : [DFS04] axioms : Especial.
% English : Proof obligation emerging from the symm-safety verification for
% the quaternion_ds1 program. symmetry-safety ensures that certain
% two-dimensional arrays remain symmetric.
% Refs : [Fis04] Fischer (2004), Email to G. Sutcliffe
% : [DFS04] Denney et al. (2004), Using Automated Theorem Provers
% Source : [Fis04]
% Names : quaternion_ds1_symm_0011 [Fis04]
% Status : Theorem
% Rating : 0.97 v8.1.0, 0.94 v7.5.0, 0.97 v7.1.0, 0.96 v7.0.0, 1.00 v6.2.0, 0.96 v6.1.0, 1.00 v4.1.0, 0.96 v4.0.1, 1.00 v3.3.0
% Syntax : Number of formulae : 111 ( 74 unt; 0 def)
% Number of atoms : 419 ( 112 equ)
% Maximal formula atoms : 136 ( 3 avg)
% Number of connectives : 316 ( 8 ~; 23 |; 192 &)
% ( 5 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 42 ( 42 usr; 22 con; 0-4 aty)
% Number of variables : 217 ( 217 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixes : v3.3.0 - Bugfix in SWV003+0
%------------------------------------------------------------------------------
%----Include NASA software certification axioms
include('Axioms/SWV003+0.ax').
%------------------------------------------------------------------------------
%----Proof obligation generated by the AutoBayes/AutoFilter system
fof(quaternion_ds1_symm_0011,conjecture,
( ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [A,B] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,minus(n6,n1))
& leq(B,minus(n6,n1)) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
& ! [C,D] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,minus(n3,n1))
& leq(D,minus(n3,n1)) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [E,F] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,minus(n6,n1))
& leq(F,minus(n6,n1)) )
=> a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) )
& ! [G] :
( ( leq(n0,G)
& leq(G,minus(n6,n1)) )
=> ! [H] :
( ( leq(n0,H)
& leq(H,minus(n6,n1)) )
=> a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G) ) ) )
=> ( ( ~ gt(pv5,n0)
=> ( ( ~ gt(pv5,n0)
=> ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [I,J] :
( ( leq(n0,I)
& leq(n0,J)
& leq(I,minus(n6,n1))
& leq(J,minus(n6,n1)) )
=> a_select3(q_ds1_filter,I,J) = a_select3(q_ds1_filter,J,I) )
& ! [K,L] :
( ( leq(n0,K)
& leq(n0,L)
& leq(K,minus(n3,n1))
& leq(L,minus(n3,n1)) )
=> a_select3(r_ds1_filter,K,L) = a_select3(r_ds1_filter,L,K) )
& ! [M,N] :
( ( leq(n0,M)
& leq(n0,N)
& leq(M,minus(n6,n1))
& leq(N,minus(n6,n1)) )
=> a_select3(tptp_madd(q_ds1_filter,tptp_mmul(phi_ds1_filter,tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(phi_ds1_filter)))),M,N) = a_select3(tptp_madd(q_ds1_filter,tptp_mmul(phi_ds1_filter,tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(phi_ds1_filter)))),N,M) )
& ! [O,P] :
( ( leq(n0,O)
& leq(n0,P)
& leq(O,minus(n6,n1))
& leq(P,minus(n6,n1)) )
=> a_select3(tptp_madd(q_ds1_filter,tptp_mmul(phi_ds1_filter,tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(phi_ds1_filter)))),O,P) = a_select3(tptp_madd(q_ds1_filter,tptp_mmul(phi_ds1_filter,tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(phi_ds1_filter)))),P,O) )
& ! [Q] :
( ( leq(n0,Q)
& leq(Q,minus(n6,n1)) )
=> ! [R] :
( ( leq(n0,R)
& leq(R,minus(n6,n1)) )
=> a_select3(id_ds1_filter,Q,R) = a_select3(id_ds1_filter,R,Q) ) ) ) )
& ( gt(pv5,n0)
=> ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [S,T] :
( ( leq(n0,S)
& leq(n0,T)
& leq(S,minus(n6,n1))
& leq(T,minus(n6,n1)) )
=> a_select3(q_ds1_filter,S,T) = a_select3(q_ds1_filter,T,S) )
& ! [U,V] :
( ( leq(n0,U)
& leq(n0,V)
& leq(U,minus(n3,n1))
& leq(V,minus(n3,n1)) )
=> a_select3(r_ds1_filter,U,V) = a_select3(r_ds1_filter,V,U) )
& ! [W,X] :
( ( leq(n0,W)
& leq(n0,X)
& leq(W,minus(n6,n1))
& leq(X,minus(n6,n1)) )
=> a_select3(tptp_madd(q_ds1_filter,tptp_mmul(phi_ds1_filter,tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(phi_ds1_filter)))),W,X) = a_select3(tptp_madd(q_ds1_filter,tptp_mmul(phi_ds1_filter,tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(phi_ds1_filter)))),X,W) )
& ! [Y,Z] :
( ( leq(n0,Y)
& leq(n0,Z)
& leq(Y,minus(n6,n1))
& leq(Z,minus(n6,n1)) )
=> a_select3(tptp_madd(q_ds1_filter,tptp_mmul(phi_ds1_filter,tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(phi_ds1_filter)))),Y,Z) = a_select3(tptp_madd(q_ds1_filter,tptp_mmul(phi_ds1_filter,tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(phi_ds1_filter)))),Z,Y) )
& ! [A1] :
( ( leq(n0,A1)
& leq(A1,minus(n6,n1)) )
=> ! [B1] :
( ( leq(n0,B1)
& leq(B1,minus(n6,n1)) )
=> a_select3(id_ds1_filter,A1,B1) = a_select3(id_ds1_filter,B1,A1) ) ) ) ) ) )
& ( gt(pv5,n0)
=> ( ( ~ gt(pv5,n0)
=> ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [C1,D1] :
( ( leq(n0,C1)
& leq(n0,D1)
& leq(C1,minus(n6,n1))
& leq(D1,minus(n6,n1)) )
=> a_select3(q_ds1_filter,C1,D1) = a_select3(q_ds1_filter,D1,C1) )
& ! [E1,F1] :
( ( leq(n0,E1)
& leq(n0,F1)
& leq(E1,minus(n3,n1))
& leq(F1,minus(n3,n1)) )
=> a_select3(r_ds1_filter,E1,F1) = a_select3(r_ds1_filter,F1,E1) )
& ! [G1,H1] :
( ( leq(n0,G1)
& leq(n0,H1)
& leq(G1,minus(n6,n1))
& leq(H1,minus(n6,n1)) )
=> a_select3(tptp_madd(q_ds1_filter,tptp_mmul(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))),tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))))))),G1,H1) = a_select3(tptp_madd(q_ds1_filter,tptp_mmul(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))),tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))))))),H1,G1) )
& ! [I1,J1] :
( ( leq(n0,I1)
& leq(n0,J1)
& leq(I1,minus(n6,n1))
& leq(J1,minus(n6,n1)) )
=> a_select3(tptp_madd(q_ds1_filter,tptp_mmul(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))),tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))))))),I1,J1) = a_select3(tptp_madd(q_ds1_filter,tptp_mmul(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))),tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))))))),J1,I1) )
& ! [K1] :
( ( leq(n0,K1)
& leq(K1,minus(n6,n1)) )
=> ! [L1] :
( ( leq(n0,L1)
& leq(L1,minus(n6,n1)) )
=> a_select3(id_ds1_filter,K1,L1) = a_select3(id_ds1_filter,L1,K1) ) ) ) )
& ( gt(pv5,n0)
=> ( leq(n0,pv5)
& leq(pv5,minus(n999,n1))
& ! [M1,N1] :
( ( leq(n0,M1)
& leq(n0,N1)
& leq(M1,minus(n6,n1))
& leq(N1,minus(n6,n1)) )
=> a_select3(q_ds1_filter,M1,N1) = a_select3(q_ds1_filter,N1,M1) )
& ! [O1,P1] :
( ( leq(n0,O1)
& leq(n0,P1)
& leq(O1,minus(n3,n1))
& leq(P1,minus(n3,n1)) )
=> a_select3(r_ds1_filter,O1,P1) = a_select3(r_ds1_filter,P1,O1) )
& ! [Q1,R1] :
( ( leq(n0,Q1)
& leq(n0,R1)
& leq(Q1,minus(n6,n1))
& leq(R1,minus(n6,n1)) )
=> a_select3(tptp_madd(q_ds1_filter,tptp_mmul(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))),tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))))))),Q1,R1) = a_select3(tptp_madd(q_ds1_filter,tptp_mmul(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))),tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))))))),R1,Q1) )
& ! [S1,T1] :
( ( leq(n0,S1)
& leq(n0,T1)
& leq(S1,minus(n6,n1))
& leq(T1,minus(n6,n1)) )
=> a_select3(tptp_madd(q_ds1_filter,tptp_mmul(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))),tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))))))),S1,T1) = a_select3(tptp_madd(q_ds1_filter,tptp_mmul(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))),tptp_mmul(tptp_madd(tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),tptp_mmul(r_ds1_filter,trans(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter)))))))))),tptp_mmul(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)),tptp_mmul(pminus_ds1_filter,trans(tptp_msub(id_ds1_filter,tptp_mmul(tptp_mmul(pminus_ds1_filter,tptp_mmul(trans(h_ds1_filter),inv(tptp_madd(r_ds1_filter,tptp_mmul(h_ds1_filter,tptp_mmul(pminus_ds1_filter,trans(h_ds1_filter))))))),h_ds1_filter)))))),trans(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(tptp_update3(phi_ds1_filter,n2,n1,times(minus(a_select3(xhatmin_ds1_filter,n3,n0),a_select3(u,n0,pv5)),divide(n1,n400))),n2,n0,times(minus(a_select3(u,n1,pv5),a_select3(xhatmin_ds1_filter,n4,n0)),divide(n1,n400))),n1,n2,times(minus(a_select3(u,n0,pv5),a_select3(xhatmin_ds1_filter,n3,n0)),divide(n1,n400))),n1,n0,times(minus(a_select3(xhatmin_ds1_filter,n5,n0),a_select3(u,n2,pv5)),divide(n1,n400))),n0,n2,times(minus(a_select3(xhatmin_ds1_filter,n4,n0),a_select3(u,n1,pv5)),divide(n1,n400))),n0,n1,times(minus(a_select3(u,n2,pv5),a_select3(xhatmin_ds1_filter,n5,n0)),divide(n1,n400))))))),T1,S1) )
& ! [U1] :
( ( leq(n0,U1)
& leq(U1,minus(n6,n1)) )
=> ! [V1] :
( ( leq(n0,V1)
& leq(V1,minus(n6,n1)) )
=> a_select3(id_ds1_filter,U1,V1) = a_select3(id_ds1_filter,V1,U1) ) ) ) ) ) ) ) ) ).
%----Automatically generated axioms
fof(gt_5_4,axiom,
gt(n5,n4) ).
fof(gt_6_4,axiom,
gt(n6,n4) ).
fof(gt_400_4,axiom,
gt(n400,n4) ).
fof(gt_999_4,axiom,
gt(n999,n4) ).
fof(gt_6_5,axiom,
gt(n6,n5) ).
fof(gt_400_5,axiom,
gt(n400,n5) ).
fof(gt_999_5,axiom,
gt(n999,n5) ).
fof(gt_400_6,axiom,
gt(n400,n6) ).
fof(gt_999_6,axiom,
gt(n999,n6) ).
fof(gt_4_tptp_minus_1,axiom,
gt(n4,tptp_minus_1) ).
fof(gt_5_tptp_minus_1,axiom,
gt(n5,tptp_minus_1) ).
fof(gt_6_tptp_minus_1,axiom,
gt(n6,tptp_minus_1) ).
fof(gt_400_tptp_minus_1,axiom,
gt(n400,tptp_minus_1) ).
fof(gt_999_tptp_minus_1,axiom,
gt(n999,tptp_minus_1) ).
fof(gt_0_tptp_minus_1,axiom,
gt(n0,tptp_minus_1) ).
fof(gt_1_tptp_minus_1,axiom,
gt(n1,tptp_minus_1) ).
fof(gt_2_tptp_minus_1,axiom,
gt(n2,tptp_minus_1) ).
fof(gt_3_tptp_minus_1,axiom,
gt(n3,tptp_minus_1) ).
fof(gt_999_400,axiom,
gt(n999,n400) ).
fof(gt_4_0,axiom,
gt(n4,n0) ).
fof(gt_5_0,axiom,
gt(n5,n0) ).
fof(gt_6_0,axiom,
gt(n6,n0) ).
fof(gt_400_0,axiom,
gt(n400,n0) ).
fof(gt_999_0,axiom,
gt(n999,n0) ).
fof(gt_1_0,axiom,
gt(n1,n0) ).
fof(gt_2_0,axiom,
gt(n2,n0) ).
fof(gt_3_0,axiom,
gt(n3,n0) ).
fof(gt_4_1,axiom,
gt(n4,n1) ).
fof(gt_5_1,axiom,
gt(n5,n1) ).
fof(gt_6_1,axiom,
gt(n6,n1) ).
fof(gt_400_1,axiom,
gt(n400,n1) ).
fof(gt_999_1,axiom,
gt(n999,n1) ).
fof(gt_2_1,axiom,
gt(n2,n1) ).
fof(gt_3_1,axiom,
gt(n3,n1) ).
fof(gt_4_2,axiom,
gt(n4,n2) ).
fof(gt_5_2,axiom,
gt(n5,n2) ).
fof(gt_6_2,axiom,
gt(n6,n2) ).
fof(gt_400_2,axiom,
gt(n400,n2) ).
fof(gt_999_2,axiom,
gt(n999,n2) ).
fof(gt_3_2,axiom,
gt(n3,n2) ).
fof(gt_4_3,axiom,
gt(n4,n3) ).
fof(gt_5_3,axiom,
gt(n5,n3) ).
fof(gt_6_3,axiom,
gt(n6,n3) ).
fof(gt_400_3,axiom,
gt(n400,n3) ).
fof(gt_999_3,axiom,
gt(n999,n3) ).
fof(finite_domain_4,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n4) )
=> ( X = n0
| X = n1
| X = n2
| X = n3
| X = n4 ) ) ).
fof(finite_domain_5,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n5) )
=> ( X = n0
| X = n1
| X = n2
| X = n3
| X = n4
| X = n5 ) ) ).
fof(finite_domain_6,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n6) )
=> ( X = n0
| X = n1
| X = n2
| X = n3
| X = n4
| X = n5
| X = n6 ) ) ).
fof(finite_domain_0,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n0) )
=> X = n0 ) ).
fof(finite_domain_1,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n1) )
=> ( X = n0
| X = n1 ) ) ).
fof(finite_domain_2,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n2) )
=> ( X = n0
| X = n1
| X = n2 ) ) ).
fof(finite_domain_3,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n3) )
=> ( X = n0
| X = n1
| X = n2
| X = n3 ) ) ).
fof(successor_4,axiom,
succ(succ(succ(succ(n0)))) = n4 ).
fof(successor_5,axiom,
succ(succ(succ(succ(succ(n0))))) = n5 ).
fof(successor_6,axiom,
succ(succ(succ(succ(succ(succ(n0)))))) = n6 ).
fof(successor_1,axiom,
succ(n0) = n1 ).
fof(successor_2,axiom,
succ(succ(n0)) = n2 ).
fof(successor_3,axiom,
succ(succ(succ(n0))) = n3 ).
%------------------------------------------------------------------------------