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_2Einftree_2Einftree__rec_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,![A_27a, A_27b, A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a),c_2Einftree_2Einftree__rec_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a))),c_2Einftree_2Einftree__rec_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27a_20mono_2Etyop_2Einftree_2Einftree_28A_27b_2CA_27c_2CA_27d_29,axiom,![A_27a, A_27b, A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27d,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),tyop_2Emin_2Efun(A_27d,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),tyop_2Emin_2Efun(A_27d,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),X1_2E0))))).
fof(arityeq1_2Ec_2Einftree_2EiLf_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,![A_27b, A_27c, A_27d]: ![X0_2E0]: (s(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),c_2Einftree_2EiLf_2E1(s(A_27b,X0_2E0))) = s(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),c_2Einftree_2EiLf_2E0),s(A_27b,X0_2E0))))).
fof(arityeq3_2Ec_2Einftree_2Einftree__rec_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,![A_27a, A_27b, A_27c, A_27d]: ![X0_2E0, X1_2E0, X2_2E0]: (s(A_27a,c_2Einftree_2Einftree__rec_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),X1_2E0),s(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a))),c_2Einftree_2Einftree__rec_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),X1_2E0))),s(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),X2_2E0))))).
fof(arityeq2_2Ec_2Einftree_2EiNd_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,![A_27b, A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),c_2Einftree_2EiNd_2E2(s(A_27c,X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),X1_2E0))) = s(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d))),c_2Einftree_2EiNd_2E0),s(A_27c,X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),X1_2E0))))).
fof(namespace__tagTheory_2Einftree__rec__thm,axiom,![A_27a, A_27b, A_27c, A_27d]: ![V0d_2E0, V1b_2E0, V2a_2E0, V3nd_2E0, V4lf_2E0]: ((s(A_27a,c_2Einftree_2Einftree__rec_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V4lf_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),V3nd_2E0),s(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),c_2Einftree_2EiLf_2E1(s(A_27b,V2a_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V4lf_2E0),s(A_27b,V2a_2E0)))) & (s(A_27a,c_2Einftree_2Einftree__rec_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V4lf_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),V3nd_2E0),s(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),c_2Einftree_2EiNd_2E2(s(A_27c,V1b_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),V0d_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),V3nd_2E0),s(A_27c,V1b_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d),A_27a),c_2Einftree_2Einftree__rec_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V4lf_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),A_27a)),V3nd_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27b,A_27c,A_27d)),V0d_2E0)))))))).
