theorem :: GATE_3:2

for s0, s1, s2, s3, ns0, ns1, ns2, ns3, q1, q2, nq1, nq2, R being set holds
not ( ( not s0 is empty implies not AND2 ((NOT1 q2),(NOT1 q1)) is empty ) & ( not AND2 ((NOT1 q2),(NOT1 q1)) is empty implies not s0 is empty ) & ( not s1 is empty implies not AND2 ((NOT1 q2),q1) is empty ) & ( not AND2 ((NOT1 q2),q1) is empty implies not s1 is empty ) & ( not s2 is empty implies not AND2 (q2,(NOT1 q1)) is empty ) & ( not AND2 (q2,(NOT1 q1)) is empty implies not s2 is empty ) & ( not s3 is empty implies not AND2 (q2,q1) is empty ) & ( not AND2 (q2,q1) is empty implies not s3 is empty ) & ( not ns0 is empty implies not AND2 ((NOT1 nq2),(NOT1 nq1)) is empty ) & ( not AND2 ((NOT1 nq2),(NOT1 nq1)) is empty implies not ns0 is empty ) & ( not ns1 is empty implies not AND2 ((NOT1 nq2),nq1) is empty ) & ( not AND2 ((NOT1 nq2),nq1) is empty implies not ns1 is empty ) & ( not ns2 is empty implies not AND2 (nq2,(NOT1 nq1)) is empty ) & ( not AND2 (nq2,(NOT1 nq1)) is empty implies not ns2 is empty ) & ( not ns3 is empty implies not AND2 (nq2,nq1) is empty ) & ( not AND2 (nq2,nq1) is empty implies not ns3 is empty ) & ( not nq1 is empty implies not AND2 ((NOT1 q2),R) is empty ) & ( not AND2 ((NOT1 q2),R) is empty implies not nq1 is empty ) & ( not nq2 is empty implies not AND2 (q1,R) is empty ) & ( not AND2 (q1,R) is empty implies not nq2 is empty ) & not ( ( not ns1 is empty implies not AND2 (s0,R) is empty ) & ( not AND2 (s0,R) is empty implies not ns1 is empty ) & ( not ns3 is empty implies not AND2 (s1,R) is empty ) & ( not AND2 (s1,R) is empty implies not ns3 is empty ) & ( not ns2 is empty implies not AND2 (s3,R) is empty ) & ( not AND2 (s3,R) is empty implies not ns2 is empty ) & ( not ns0 is empty implies not OR2 ((AND2 (s2,R)),(NOT1 R)) is empty ) & ( not OR2 ((AND2 (s2,R)),(NOT1 R)) is empty implies not ns0 is empty ) ) )