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(arityeq3_2Ec_2Epair_2E_23_23_2E3_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27c_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27d_2CA_27c_29_29,axiom,![A_27a, A_27b, A_27c, A_27d]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),X2_2E0))) = s(tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c)))))),c_2Epair_2E_23_23_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),X2_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_23_23_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c,axiom,![A_27a, A_27b, A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c)),c_2Epair_2E_23_23_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c)))),c_2Epair_2E_23_23_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))))).
fof(arityeq1_2Ec_2Ellist_2ELMAP_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27c_29,axiom,![A_27a, A_27b, A_27c, A_27d]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),c_2Ellist_2ELMAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c)))),c_2Ellist_2ELMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c)),X0_2E0))))).
fof(arityeq1_2Ec_2Epath_2EfromPath_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epath_2EfromPath_2E1(s(tyop_2Epath_2Epath(A_27a,A_27b),X0_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Epath_2EfromPath_2E0),s(tyop_2Epath_2Epath(A_27a,A_27b),X0_2E0))))).
fof(arityeq1_2Ec_2Epath_2EtoPath_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,![A_27c, A_27d]: ![X0_2E0]: (s(tyop_2Epath_2Epath(A_27c,A_27d),c_2Epath_2EtoPath_2E1(s(tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),X0_2E0))) = s(tyop_2Epath_2Epath(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),tyop_2Epath_2Epath(A_27c,A_27d)),c_2Epath_2EtoPath_2E0),s(tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),X0_2E0))))).
fof(arityeq3_2Ec_2Epath_2Epmap_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(tyop_2Epath_2Epath(A_27c,A_27d),c_2Epath_2Epmap_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Epath_2Epath(A_27a,A_27b),X2_2E0))) = s(tyop_2Epath_2Epath(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27c,A_27d)))),c_2Epath_2Epmap_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Epath_2Epath(A_27a,A_27b),X2_2E0))))).
fof(pathTheory_2Epmap__def,axiom,![A_27a, A_27b, A_27c, A_27d]: ![V0f_2E0, V1g_2E0, V2p_2E0]: (s(tyop_2Epath_2Epath(A_27c,A_27d),c_2Epath_2Epmap_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Epath_2Epath(A_27a,A_27b),V2p_2E0))) = s(tyop_2Epath_2Epath(A_27c,A_27d),c_2Epath_2EtoPath_2E1(s(tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),c_2Ellist_2ELMAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c)),c_2Epair_2E_23_23_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0))))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epath_2EfromPath_2E1(s(tyop_2Epath_2Epath(A_27a,A_27b),V2p_2E0))))))))).
