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_2Einftree_2EiLf_2E1_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,![A_27a, A_27c, A_27d]: ![X0_2E0]: (s(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),c_2Einftree_2EiLf_2E1(s(A_27a,X0_2E0))) = s(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d)),c_2Einftree_2EiLf_2E0),s(A_27a,X0_2E0))))).
fof(arityeq4_2Ec_2Einftree_2Erelrec_2E4_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, X3_2E0]: (s(tyop_2Emin_2Ebool,c_2Einftree_2Erelrec_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),A_27b)),X1_2E0),s(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),A_27b)),tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),A_27b)),tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Einftree_2Erelrec_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),A_27b)),X1_2E0))),s(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),X2_2E0))),s(A_27b,X3_2E0))))).
fof(arityeq2_2Ec_2Einftree_2EiNd_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,![A_27a, A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),c_2Einftree_2EiNd_2E2(s(A_27c,X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d)),X1_2E0))) = s(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d)),tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d)),tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d))),c_2Einftree_2EiNd_2E0),s(A_27c,X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d)),X1_2E0))))).
fof(inftreeTheory_2Erelrec__rules,axiom,![A_27a, A_27b, A_27c, A_27d]: (![V0lf_2E0, V1nd_2E0, V2a_2E0]: p(s(tyop_2Emin_2Ebool,c_2Einftree_2Erelrec_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0lf_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),A_27b)),V1nd_2E0),s(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),c_2Einftree_2EiLf_2E1(s(A_27a,V2a_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0lf_2E0),s(A_27a,V2a_2E0)))))) & ![V3lf_2E0, V4nd_2E0, V5b_2E0, V6df_2E0, V7g_2E0]: (![V8d_2E0]: p(s(tyop_2Emin_2Ebool,c_2Einftree_2Erelrec_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V3lf_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),A_27b)),V4nd_2E0),s(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d)),V6df_2E0),s(A_27d,V8d_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V7g_2E0),s(A_27d,V8d_2E0)))))) => p(s(tyop_2Emin_2Ebool,c_2Einftree_2Erelrec_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V3lf_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),A_27b)),V4nd_2E0),s(tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d),c_2Einftree_2EiNd_2E2(s(A_27c,V5b_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Einftree_2Einftree(A_27a,A_27c,A_27d)),V6df_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),A_27b)),V4nd_2E0),s(A_27c,V5b_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),V7g_2E0))))))))).
