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_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ewellorder_2Eorderiso_2E2(s(tyop_2Ewellorder_2Ewellorder(A_27a),X0_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Ebool)),c_2Ewellorder_2Eorderiso_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27a),X0_2E0))),s(tyop_2Ewellorder_2Ewellorder(A_27b),X1_2E0))))).
fof(arityeq2_2Ec_2Ewellorder_2Eorderiso_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,![A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ewellorder_2Eorderiso_2E2(s(tyop_2Ewellorder_2Ewellorder(A_27c),X0_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27d),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27d),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27d),tyop_2Emin_2Ebool)),c_2Ewellorder_2Eorderiso_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27c),X0_2E0))),s(tyop_2Ewellorder_2Ewellorder(A_27d),X1_2E0))))).
fof(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,![A_27a, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ewellorder_2Eorderlt_2E2(s(tyop_2Ewellorder_2Ewellorder(A_27a),X0_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27c),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27a),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27c),tyop_2Emin_2Ebool)),c_2Ewellorder_2Eorderlt_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27a),X0_2E0))),s(tyop_2Ewellorder_2Ewellorder(A_27c),X1_2E0))))).
fof(arityeq2_2Ec_2Ewellorder_2Eorderlt_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,![A_27b, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ewellorder_2Eorderlt_2E2(s(tyop_2Ewellorder_2Ewellorder(A_27b),X0_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27d),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27d),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27b),tyop_2Emin_2Efun(tyop_2Ewellorder_2Ewellorder(A_27d),tyop_2Emin_2Ebool)),c_2Ewellorder_2Eorderlt_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27b),X0_2E0))),s(tyop_2Ewellorder_2Ewellorder(A_27d),X1_2E0))))).
fof(wellorderTheory_2Eorderlt__orderiso,axiom,![A_27a, A_27b, A_27c, A_27d]: ![V0b0_2E0, V1a0_2E0, V2y0_2E0, V3x0_2E0]: ((p(s(tyop_2Emin_2Ebool,c_2Ewellorder_2Eorderiso_2E2(s(tyop_2Ewellorder_2Ewellorder(A_27a),V3x0_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27b),V2y0_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ewellorder_2Eorderiso_2E2(s(tyop_2Ewellorder_2Ewellorder(A_27c),V1a0_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27d),V0b0_2E0))))) => (s(tyop_2Emin_2Ebool,c_2Ewellorder_2Eorderlt_2E2(s(tyop_2Ewellorder_2Ewellorder(A_27a),V3x0_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27c),V1a0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ewellorder_2Eorderlt_2E2(s(tyop_2Ewellorder_2Ewellorder(A_27b),V2y0_2E0),s(tyop_2Ewellorder_2Ewellorder(A_27d),V0b0_2E0)))))).
