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(arityeq1_2Ec_2Efcp_2EBIT0A_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,X0_2E0))) = s(tyop_2Efcp_2Ebit0(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),c_2Efcp_2EBIT0A_2E0),s(A_27a,X0_2E0))))).
fof(arityeq1_2Ec_2Efcp_2EBIT0B_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,X0_2E0))) = s(tyop_2Efcp_2Ebit0(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),c_2Efcp_2EBIT0B_2E0),s(A_27a,X0_2E0))))).
fof(arityeq3_2Ec_2Efcp_2Ebit0__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0, X2_2E0]: (s(A_27b,c_2Efcp_2Ebit0__CASE_2E3(s(tyop_2Efcp_2Ebit0(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))),c_2Efcp_2Ebit0__CASE_2E0),s(tyop_2Efcp_2Ebit0(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))))).
fof(fcpTheory_2Ebit0__case__cong,axiom,![A_27a, A_27b]: ![V0f1_27_2E0, V1f_27_2E0, V2M_2E0, V3M_27_2E0, V4f_2E0, V5f1_2E0]: (((s(tyop_2Efcp_2Ebit0(A_27a),V2M_2E0) = s(tyop_2Efcp_2Ebit0(A_27a),V3M_27_2E0)) & (![V6a_2E0]: ((s(tyop_2Efcp_2Ebit0(A_27a),V3M_27_2E0) = s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V6a_2E0)))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(A_27a,V6a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0),s(A_27a,V6a_2E0))))) & ![V7a_2E0]: ((s(tyop_2Efcp_2Ebit0(A_27a),V3M_27_2E0) = s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V7a_2E0)))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5f1_2E0),s(A_27a,V7a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_27_2E0),s(A_27a,V7a_2E0))))))) => (s(A_27b,c_2Efcp_2Ebit0__CASE_2E3(s(tyop_2Efcp_2Ebit0(A_27a),V2M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f1_2E0))) = s(A_27b,c_2Efcp_2Ebit0__CASE_2E3(s(tyop_2Efcp_2Ebit0(A_27a),V3M_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_27_2E0)))))).
