fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq2_2Ec_2Emartingale_2Efcp__sigma_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,![A_27a, A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emartingale_2Efcp__sigma_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),c_2Emartingale_2Efcp__sigma_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0))))).
fof(arityeq3_2Ec_2Emartingale_2Egeneral__sigma_2E3_2Emono_2Etyop_2Efcp_2Ecart_28A_27a_2CA_27b_29_20mono_2Etyop_2Efcp_2Ecart_28A_27a_2CA_27c_29_20mono_2Etyop_2Efcp_2Ecart_28A_27a_2Ctyop_2Esum_2Esum_28A_27b_2CA_27c_29_29,axiom,![A_27a, A_27b, A_27c]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emartingale_2Egeneral__sigma_2E3(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)))),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))),c_2Emartingale_2Egeneral__sigma_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)))),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X2_2E0))))).
fof(martingaleTheory_2Efcp__sigma__alt,axiom,![A_27a, A_27b, A_27c]: ![V0A_2E0, V1B_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emartingale_2Efcp__sigma_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0A_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1B_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emartingale_2Egeneral__sigma_2E3(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)))),c_2Efcp_2EFCP__CONCAT_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0A_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V1B_2E0))))).
