0.11/0.32 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.33 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.53 % Computer : n027.cluster.edu 0.11/0.53 % Model : x86_64 x86_64 0.11/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.53 % Memory : 8042.1875MB 0.11/0.53 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.54 % CPULimit : 960 0.11/0.54 % DateTime : Thu Jul 2 14:21:32 EDT 2020 0.11/0.54 % CPUTime : 107.43/107.50 ============================== Prover9 =============================== 107.43/107.50 Prover9 (32) version 2009-11A, November 2009. 107.43/107.50 Process 27666 was started by sandbox on n027.cluster.edu, 107.43/107.50 Thu Jul 2 14:22:00 2020 107.43/107.50 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_27461_n027.cluster.edu". 107.43/107.50 ============================== end of head =========================== 107.43/107.50 107.43/107.50 ============================== INPUT ================================= 107.43/107.50 107.43/107.50 % Reading from file /tmp/Prover9_27461_n027.cluster.edu 107.43/107.50 107.43/107.50 set(prolog_style_variables). 107.43/107.50 set(auto2). 107.43/107.50 % set(auto2) -> set(auto). 107.43/107.50 % set(auto) -> set(auto_inference). 107.43/107.50 % set(auto) -> set(auto_setup). 107.43/107.50 % set(auto_setup) -> set(predicate_elim). 107.43/107.50 % set(auto_setup) -> assign(eq_defs, unfold). 107.43/107.50 % set(auto) -> set(auto_limits). 107.43/107.50 % set(auto_limits) -> assign(max_weight, "100.000"). 107.43/107.50 % set(auto_limits) -> assign(sos_limit, 20000). 107.43/107.50 % set(auto) -> set(auto_denials). 107.43/107.50 % set(auto) -> set(auto_process). 107.43/107.50 % set(auto2) -> assign(new_constants, 1). 107.43/107.50 % set(auto2) -> assign(fold_denial_max, 3). 107.43/107.50 % set(auto2) -> assign(max_weight, "200.000"). 107.43/107.50 % set(auto2) -> assign(max_hours, 1). 107.43/107.50 % assign(max_hours, 1) -> assign(max_seconds, 3600). 107.43/107.50 % set(auto2) -> assign(max_seconds, 0). 107.43/107.50 % set(auto2) -> assign(max_minutes, 5). 107.43/107.50 % assign(max_minutes, 5) -> assign(max_seconds, 300). 107.43/107.50 % set(auto2) -> set(sort_initial_sos). 107.43/107.50 % set(auto2) -> assign(sos_limit, -1). 107.43/107.50 % set(auto2) -> assign(lrs_ticks, 3000). 107.43/107.50 % set(auto2) -> assign(max_megs, 400). 107.43/107.50 % set(auto2) -> assign(stats, some). 107.43/107.50 % set(auto2) -> clear(echo_input). 107.43/107.50 % set(auto2) -> set(quiet). 107.43/107.50 % set(auto2) -> clear(print_initial_clauses). 107.43/107.50 % set(auto2) -> clear(print_given). 107.43/107.50 assign(lrs_ticks,-1). 107.43/107.50 assign(sos_limit,10000). 107.43/107.50 assign(order,kbo). 107.43/107.50 set(lex_order_vars). 107.43/107.50 clear(print_given). 107.43/107.50 107.43/107.50 % formulas(sos). % not echoed (12193 formulas) 107.43/107.50 107.43/107.50 ============================== end of input ========================== 107.43/107.50 107.43/107.50 % From the command line: assign(max_seconds, 960). 107.43/107.50 107.43/107.50 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 107.43/107.50 107.43/107.50 % Formulas that are not ordinary clauses: 107.43/107.50 1 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 2 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 3 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 4 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 5 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 6 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 7 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 8 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 9 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 10 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 11 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 12 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 13 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 14 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 15 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 16 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 17 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 18 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 19 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 20 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 21 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ebool_2ERES__ABSTRACT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__ABSTRACT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 22 (all A_27a all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,f160_0_2E1(s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Ebool_2ERES__FORALL__TRUE) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 23 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),f165_1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),f165_1_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef165_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 24 (all V0y_2E0 all V1x_2E0 ((p(s(tyop_2Emin_2Ebool,V0y_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0))) -> (-p(s(tyop_2Emin_2Ebool,V1x_2E0)) -> -p(s(tyop_2Emin_2Ebool,V0y_2E0))))) # label(thm_2Ebool_2EMONO__NOT) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 25 (all A_27a all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f144_0_2E1(s(A_27a,V0a_2E0))))))) # label(thm_2Ebool_2EEXISTS__UNIQUE__REFL) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 26 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 27 (all A_27a all V0P_2E0 all V1Q_2E0 (((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) <-> (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))))) & ((all V5x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5x_2E0)))) & p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))))) & ((all V7x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V7x_2E0)))))) <-> (all V6x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V6x_2E0))))) & p(s(tyop_2Emin_2Ebool,V1Q_2E0))))) # label(thm_2Ebool_2EPULL__FORALL) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 28 (all A_27a all V0x_2E0 all V1x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))))))) # label(thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 29 (all A_27a all V0x_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f71_0_2E1(s(A_27a,V0x_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Ebool_2ESELECT__REFL) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 30 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 31 (all A_27a all V0P_2E0 all V1Q_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f154_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 32 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 33 (all V0P_2E0 all V1P_27_2E0 all V2Q_2E0 all V3Q_27_2E0 ((p(s(tyop_2Emin_2Ebool,V2Q_2E0)) -> s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1P_27_2E0)) & (p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) -> s(tyop_2Emin_2Ebool,V3Q_27_2E0) = s(tyop_2Emin_2Ebool,V2Q_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0P_2E0)) & p(s(tyop_2Emin_2Ebool,V2Q_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) & p(s(tyop_2Emin_2Ebool,V3Q_27_2E0))))) # label(thm_2Ebool_2EAND__CONG) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 34 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Ebool_2Eliteral__case__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 35 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f29_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef29_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 36 (all A_27a all A_27b all A_27c all V0b_2E0 all V1N_2E0 all V2M_2E0 s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),f122_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27b,V0b_2E0))),s(A_27a,V2M_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f122_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0))),s(A_27a,V2M_2E0))),s(A_27b,V0b_2E0)))) # label(thm_2Ebool_2ELET__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 37 (all A_27a all V0P_2E0 all V1f_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,f158_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0)))))) # label(def1_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 38 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ebool_2Eitself_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 39 (all A_27a all V0x_2E0 ((all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))))) # label(thm_2Ebool_2EFORALL__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 40 (all A_27a all V0t_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,f155_0_2E2(s(tyop_2Emin_2Ebool,V0t_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Ebool_2EUEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 41 (all V0A_2E0 all V1B_2E0 all V2C_2E0 (p(s(tyop_2Emin_2Ebool,V2C_2E0)) & p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0))) & p(s(tyop_2Emin_2Ebool,V0A_2E0)))) # label(thm_2Ebool_2ERIGHT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 42 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,f168_0_2E4(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0),s(A_27a,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)))),f168_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef168_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 43 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,X0_2E0))) = 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)))) # label(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 44 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f154_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f154_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef154_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 45 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EEXCLUDED__MIDDLE) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 46 (all V0b_2E0 all V1t1_2E0 all V2t2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1t1_2E0),s(tyop_2Emin_2Ebool,V2t2_2E0)))) <-> (-p(s(tyop_2Emin_2Ebool,V0b_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t2_2E0))) & (p(s(tyop_2Emin_2Ebool,V0b_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t1_2E0))))) # label(thm_2Ebool_2ECOND__EXPAND__IMP) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 47 (all A_27a all V0P_2E0 all V1Q_2E0 all V2x_2E0 all V3x_27_2E0 all V4y_2E0 all V5y_27_2E0 (s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1Q_2E0) & (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> s(A_27a,V2x_2E0) = s(A_27a,V3x_27_2E0)) & (-p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> s(A_27a,V5y_27_2E0) = s(A_27a,V4y_2E0)) -> s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V1Q_2E0),s(A_27a,V3x_27_2E0),s(A_27a,V5y_27_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(A_27a,V2x_2E0),s(A_27a,V4y_2E0))))) # label(thm_2Ebool_2Ebool__case__CONG) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 48 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 49 (all A_27a all V0x_2E0 all V1x_27_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))))) # label(thm_2Ebool_2ERES__EXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 50 (all V0t_2E0 p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Ebool_2EF__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 51 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f121_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),f121_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ef121_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 52 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> -p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EIMP__F) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 53 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 54 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(thm_2Ebool_2EIMP__F__EQ__F) # label(axiom) # label(non_clause). [assumption]. 107.43/107.50 55 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> ((all V3x_2E0 p(s(tyop_2Emin_2Ebool,V0P_2E0))) -> (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2EBOTH__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 56 (all A_27a all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,f71_0_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0)))) <-> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) # label(def0_2Ethm_2Ebool_2ESELECT__REFL) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 57 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) | p(s(tyop_2Emin_2Ebool,V1Q_2E0)) <-> (exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) | p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2ELEFT__OR__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 58 (all A_27a all V0P_2E0 all V1Q_2E0 (((exists V5x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5x_2E0)))) & p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))))) & ((exists V7x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V7x_2E0)))))) <-> (exists V6x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V6x_2E0))))) & p(s(tyop_2Emin_2Ebool,V1Q_2E0))) & (((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0))))))) # label(thm_2Ebool_2EPULL__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 59 (all A_27a all A_27b all V0b_2E0 all V1f_2E0 all V2g_2E0 all V3x_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0),s(A_27a,V3x_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0))),s(A_27a,V3x_2E0)))) # label(thm_2Ebool_2ECOND__ABS) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 60 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 ((all V2x_27_2E0 all V3x_27_27_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1x_27_2E0),s(A_27b,V2x_27_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1x_27_2E0),s(A_27b,V3x_27_27_2E0))) -> s(A_27b,V2x_27_2E0) = s(A_27b,V3x_27_27_2E0))) & (all V4x_2E0 ((exists V5x_27_2E0 s(A_27a,V4x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1x_27_2E0),s(A_27b,V5x_27_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V4x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1x_27_2E0)))))) # label(thm_2Ebool_2ETYPE__DEFINITION) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 61 (all A_27a all V0P_2E0 all V1f_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) # label(thm_2Ebool_2ERES__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 62 (all V0t_2E0 (((p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) & ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))) & ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))))) # label(thm_2Ebool_2EIMP__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 63 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2M_2E0 all V3N_2E0 ((all V4x_2E0 (s(A_27a,V4x_2E0) = s(A_27a,V3N_2E0) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V4x_2E0))))) & s(A_27a,V3N_2E0) = s(A_27a,V2M_2E0) -> s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2M_2E0))) = s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V3N_2E0))))) # label(thm_2Ebool_2ELET__CONG) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 64 (all A_27a all A_27b all V1N_2E0 all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V3x_2E0))) = s(A_27b,f121_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Ebool_2ELET__RAND) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 65 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) <-> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4x_2E0))))) & (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))))) # label(thm_2Ebool_2EFORALL__AND__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 66 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f70_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f70_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef70_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 67 (all V0A_2E0 all V1B_2E0 all V2C_2E0 (p(s(tyop_2Emin_2Ebool,V1B_2E0)) & p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0))) & (p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V2C_2E0))))) # label(thm_2Ebool_2ELEFT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 68 (all A_27a all V0Q_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,V0Q_2E0)) | (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) | p(s(tyop_2Emin_2Ebool,V0Q_2E0)))))) # label(thm_2Ebool_2ELEFT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 69 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 70 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f71_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = 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)),f71_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef71_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 71 (all A_27a all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,f161_0_2E1(s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Ebool_2ERES__EXISTS__FALSE) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 72 (all A_27a all V0x_2E0 all V1y_2E0 all V2z_2E0 (s(A_27a,V2z_2E0) = s(A_27a,V1y_2E0) & s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) -> s(A_27a,V0x_2E0) = s(A_27a,V2z_2E0))) # label(thm_2Ebool_2EEQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 73 (all A_27a all V0g_2E0 all V1f_2E0 all V2Q_2E0 all V3P_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0) -> ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0)))))) # label(thm_2Ebool_2ERES__EXISTS__CONG) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 74 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebool_2Eitself__case_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))),s(A_27b,X1_2E0))) = s(A_27b,c_2Ebool_2Eitself__case_2E2(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eitself__case_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 75 (all V0A_2E0 all V1B_2E0 all V2C_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V2C_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0))) & (p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0))))) # label(thm_2Ebool_2ERIGHT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 76 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f121_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27b,f121_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef121_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 77 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))) | p(s(tyop_2Emin_2Ebool,V0P_2E0)))) <-> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))))) | p(s(tyop_2Emin_2Ebool,V0P_2E0)))) # label(thm_2Ebool_2ERIGHT__OR__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 78 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f154_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef154_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 79 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 80 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (all V0x_2E0 s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0)) # label(thm_2Ebool_2ET__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 81 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 82 (all X0_2E0 s(tyop_2Emin_2Ebool,f163_3_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_3_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef163_3_2E1) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 83 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 84 (all A_27a all A_27b all V0P_2E0 all V1rep_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) <-> (exists V5x_27_2E0 s(A_27a,V4x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1rep_2E0),s(A_27b,V5x_27_2E0)))))) & (all V2x_27_2E0 all V3x_27_27_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1rep_2E0),s(A_27b,V2x_27_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1rep_2E0),s(A_27b,V3x_27_27_2E0))) -> s(A_27b,V2x_27_2E0) = s(A_27b,V3x_27_27_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1rep_2E0)))))) # label(thm_2Ebool_2ETYPE__DEFINITION__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 85 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2x_2E0)))))) -> ((exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))) -> (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Ebool_2EMONO__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 86 (all A_27a all V0x_2E0 all V1x_27_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))) # label(thm_2Ebool_2EIN__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 87 (all A_27a all V0P_2E0 (-(all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))) <-> (exists V2x_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Ebool_2ENOT__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 88 (all A_27a all A_27b all A_27c all V0P_2E0 all V1N_2E0 all V2M_2E0 s(A_27c,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),f165_1_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V2M_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0P_2E0),s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),f165_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V2M_2E0)))))) # label(thm_2Ebool_2Eliteral__case__RAND) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 89 (all V1b_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,f163_0_2E1(s(tyop_2Emin_2Ebool,V1b_2E0)))) # label(def1_2Ethm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 90 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f121_1_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f121_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef121_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 91 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))))) # label(thm_2Ebool_2EEXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 92 (all A_27a all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 all V3x_2E0 ((s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0) -> s(A_27a,V3x_2E0) = s(A_27a,V1x_27_2E0)) & (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0) -> s(A_27a,V2x_27_27_2E0) = s(A_27a,V3x_2E0)) <-> p(s(tyop_2Emin_2Ebool,f21_0_2E4(s(tyop_2Emin_2Ebool,V0x_2E0),s(A_27a,V1x_27_2E0),s(A_27a,V2x_27_27_2E0),s(A_27a,V3x_2E0)))))) # label(def0_2Ethm_2Ebool_2ECOND__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 93 (all A_27a all V0g_2E0 all V1f_2E0 all V2Q_2E0 all V3P_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0) -> ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) # label(thm_2Ebool_2ERES__FORALL__CONG) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 94 (all A_27a all A_27b all V0t_2E0 all V1x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0t_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0t_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Ebool_2EETA__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 95 (all A_27a all V0P_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Ebool_2ERES__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 96 (all A_27a all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f160_0_2E0)))) # label(thm_2Ebool_2ERES__FORALL__TRUE) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 97 (all V0z_2E0 all V1y_2E0 all V2x_2E0 all V3w_2E0 ((p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0))) & (p(s(tyop_2Emin_2Ebool,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1y_2E0))) -> (p(s(tyop_2Emin_2Ebool,V2x_2E0)) & p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V1y_2E0)) & p(s(tyop_2Emin_2Ebool,V3w_2E0))))) # label(thm_2Ebool_2EMONO__AND) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 98 (all V0A_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)))) # label(thm_2Ebool_2EDISJ__COMM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 99 (all A_27a all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f161_0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Ebool_2ERES__EXISTS__FALSE) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 100 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) <-> (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))))) # label(thm_2Ebool_2ERIGHT__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 101 (all A_27a all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) | (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Ebool_2ERIGHT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 102 (all A_27a all V0i_2E0 s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0) = s(tyop_2Ebool_2Eitself(A_27a),V0i_2E0)) # label(thm_2Ebool_2EITSELF__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 103 (all A_27a all A_27b all V0f_2E0 all V1b_2E0 all V2x_2E0 all V3y_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V1b_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0)))))) # label(thm_2Ebool_2ECOND__RAND) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 104 (all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 105 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ebool_2ERES__ABSTRACT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ebool_2ERES__ABSTRACT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ERES__ABSTRACT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 106 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) <-> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) # label(thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 107 (all A_27a all V1Q_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,f154_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4x_2E0)))) # label(def1_2Ethm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 108 (all A_27a all A_27b all V0u_2E0 all V1t_2E0 all V2a_2E0 s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),f168_0_2E3(s(A_27a,V2a_2E0),s(A_27b,V1t_2E0),s(A_27b,V0u_2E0))),s(A_27a,V2a_2E0))) = s(A_27b,V1t_2E0)) # label(thm_2Ebool_2Eliteral__case__id) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 109 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f121_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f121_1_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef121_1_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 110 (all A_27a all V0t1_2E0 all V1t2_2E0 exists V2fn_2E0 (s(A_27a,V1t2_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V2fn_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,A_27a),V2fn_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) = s(A_27a,V0t1_2E0))) # label(thm_2Ebool_2EboolAxiom) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 111 (all A_27a all V0a_2E0 exists V1x_2E0 s(A_27a,V0a_2E0) = s(A_27a,V1x_2E0)) # label(thm_2Ebool_2EEXISTS__REFL) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 112 (all A_27a all A_27b all V0f_2E0 ((all V1x1_2E0 all V2x2_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x1_2E0))) -> s(A_27a,V1x1_2E0) = s(A_27a,V2x2_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))))) # label(thm_2Ebool_2EONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 113 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f166_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f166_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0)))) # label(arityeq1_2Ef166_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 114 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f21_0_2E4(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f21_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef21_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 115 (all A_27a all A_27b all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))) <-> (all V1y_2E0 exists V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,V1y_2E0)))) # label(thm_2Ebool_2EONTO__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 116 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f160_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,f160_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef160_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 117 (all A_27a all V0x_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 118 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))))) # label(thm_2Ebool_2ELEFT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 119 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),f122_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))) = s(A_27c,f122_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef122_1_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 120 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(thm_2Ebool_2EFUN__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 121 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0)))) # label(thm_2Ebool_2EAND2__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 122 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 123 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 124 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 125 (all V0t_2E0 (--p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 126 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 127 (all V0bool_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(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)),V0bool_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))))) # label(thm_2Ebool_2EDATATYPE__BOOL) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 128 (all A_27a all V0x_2E0 all V1x_27_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f30_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0))))) = s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))) # label(thm_2Ebool_2ERES__SELECT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 129 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f155_0_2E1(s(tyop_2Emin_2Ebool,V0t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & (all V2x_2E0 all V3y_2E0 s(A_27a,V2x_2E0) = s(A_27a,V3y_2E0)))) # label(thm_2Ebool_2EUEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 130 (all V3b_2E0 s(tyop_2Emin_2Ebool,f163_2_2E1(s(tyop_2Emin_2Ebool,V3b_2E0))) = s(tyop_2Emin_2Ebool,V3b_2E0)) # label(def3_2Ethm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 131 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 132 (all V0A_2E0 all V1B_2E0 all V2C_2E0 (p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)))) # label(thm_2Ebool_2EDISJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 133 (all V0A_2E0 all V1B_2E0 (-p(s(tyop_2Emin_2Ebool,V1B_2E0)) & p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> -(p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,V1B_2E0))))) # label(thm_2Ebool_2ENOT__IMP) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 134 (all A_27a all V0P_2E0 all V1a_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) & s(A_27a,V2x_2E0) = s(A_27a,V1a_2E0))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1a_2E0)))))) # label(thm_2Ebool_2EUNWIND__THM2) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 135 (all V2b_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,f163_1_2E1(s(tyop_2Emin_2Ebool,V2b_2E0)))) # label(def2_2Ethm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 136 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f158_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f158_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef158_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 137 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f154_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef154_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 138 (all A_27a all A_27b all V0b_2E0 s(A_27b,c_2Ebool_2Eitself__case_2E2(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0),s(A_27b,V0b_2E0))) = s(A_27b,V0b_2E0)) # label(thm_2Ebool_2Eitself__case__thm) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 139 (all A_27a all A_27b all A_27c all V1N_2E0 all V0b_2E0 all V4x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V4x_2E0))),s(A_27b,V0b_2E0))) = s(A_27c,f122_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27b,V0b_2E0),s(A_27a,V4x_2E0)))) # label(def0_2Ethm_2Ebool_2ELET__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 140 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f161_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f161_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef161_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 141 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EBOUNDED_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EBOUNDED_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EBOUNDED_2E1) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 142 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) | -p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & -p(s(tyop_2Emin_2Ebool,V1t2_2E0)) <-> s(tyop_2Emin_2Ebool,V1t2_2E0) = s(tyop_2Emin_2Ebool,V0t1_2E0))) # label(thm_2Ebool_2EEQ__EXPAND) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 143 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebool_2EONTO_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONTO_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 144 (all A_27a all A_27b all V2a_2E0 all V1t_2E0 all V0u_2E0 all V3x_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f168_1_2E2(s(A_27a,V3x_2E0),s(A_27a,V2a_2E0))),s(A_27b,V1t_2E0),s(A_27b,V0u_2E0))) = s(A_27b,f168_0_2E4(s(A_27a,V2a_2E0),s(A_27b,V1t_2E0),s(A_27b,V0u_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Ebool_2Eliteral__case__id) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 145 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2EAND1__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 146 (all V0x_2E0 (-p(s(tyop_2Emin_2Ebool,V0x_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Ebool_2ENOT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 147 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 148 (all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EBOUNDED_2E1(s(tyop_2Emin_2Ebool,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2EBOUNDED__DEF) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 149 (all A_27a all V3x_2E0 all V2a_2E0 (s(A_27a,V3x_2E0) = s(A_27a,V2a_2E0) <-> p(s(tyop_2Emin_2Ebool,f168_1_2E2(s(A_27a,V3x_2E0),s(A_27a,V2a_2E0)))))) # label(def0_2Ethm_2Ebool_2Eliteral__case__id) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 150 (all A_27a all A_27b all A_27c all V1N_2E0 all V3x_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),f122_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Ebool_2ELET__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 151 (all V0z_2E0 all V1y_2E0 all V2x_2E0 all V3w_2E0 ((p(s(tyop_2Emin_2Ebool,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1y_2E0))) & (p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0))) -> (p(s(tyop_2Emin_2Ebool,V2x_2E0)) | p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0)) | p(s(tyop_2Emin_2Ebool,V1y_2E0))))) # label(thm_2Ebool_2EMONO__OR) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 152 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f125_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) <-> (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) -> s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0))) & (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Ebool_2EEXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 153 (all V0t1_2E0 all V1t2_2E0 all V2t3_2E0 ((p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t3_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t3_2E0)))))) # label(thm_2Ebool_2EAND__IMP__INTRO) # label(axiom) # label(non_clause). [assumption]. 107.43/107.51 154 (all A_27a all V0P_2E0 all V1Q_2E0 all V2x_2E0 all V3x_27_2E0 all V4y_2E0 all V5y_27_2E0 (s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1Q_2E0) & (-p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> s(A_27a,V5y_27_2E0) = s(A_27a,V4y_2E0)) & (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> s(A_27a,V2x_2E0) = s(A_27a,V3x_27_2E0)) -> s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V1Q_2E0),s(A_27a,V3x_27_2E0),s(A_27a,V5y_27_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(A_27a,V2x_2E0),s(A_27a,V4y_2E0))))) # label(thm_2Ebool_2ECOND__CONG) # label(axiom) # label(non_clause). [assumption]. 107.43/107.52 155 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f29_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f29_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef29_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.52 156 (all V0P_2E0 ((all V1b_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,V1b_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))))) # label(thm_2Ebool_2EFORALL__BOOL) # label(axiom) # label(non_clause). [assumption]. 107.43/107.52 157 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f29_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef29_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.52 158 (all A_27a all A_27b all A_27c all V0P_2E0 all V1N_2E0 all V4x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V4x_2E0))))) = s(A_27c,f165_1_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V4x_2E0)))) # label(def0_2Ethm_2Ebool_2Eliteral__case__RAND) # label(axiom) # label(non_clause). [assumption]. 107.43/107.52 159 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Ebool_2EDATATYPE__TAG__THM) # label(axiom) # label(non_clause). [assumption]. 107.43/107.52 160 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f154_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f154_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef154_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.43/107.52 161 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,f163_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef163_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.43/107.52 162 (all A_27a all X0_2E0 all X1_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f29_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef29_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 163 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f30_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f30_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef30_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 164 (all V0x_2E0 all V1x_27_2E0 ((all V2t_2E0 ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t_2E0))) -> p(s(tyop_2Emin_2Ebool,V2t_2E0))))) <-> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) | p(s(tyop_2Emin_2Ebool,V0x_2E0)))) # label(thm_2Ebool_2EOR__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 165 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 166 (all A_27a all V0b_2E0 all V1t_2E0 s(A_27a,V1t_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27a,V1t_2E0),s(A_27a,V1t_2E0)))) # label(thm_2Ebool_2ECOND__ID) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 167 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),f165_1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) = s(A_27c,f165_1_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef165_1_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 168 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef158_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 169 (all V0b_2E0 all V1t1_2E0 all V2t2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1t1_2E0),s(tyop_2Emin_2Ebool,V2t2_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1t1_2E0)) & p(s(tyop_2Emin_2Ebool,V0b_2E0)) | -p(s(tyop_2Emin_2Ebool,V0b_2E0)) & p(s(tyop_2Emin_2Ebool,V2t2_2E0)))) # label(thm_2Ebool_2ECOND__EXPAND__OR) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 170 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 171 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V0t1_2E0))))) # label(thm_2Ebool_2EAND__INTRO__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 172 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,V0x_2E0)) # label(thm_2Ebool_2EEQ__REFL) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 173 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 174 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 175 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0)) | p(s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2EOR__INTRO__THM1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 176 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V3x_2E0 p(s(tyop_2Emin_2Ebool,V0P_2E0))) | (all V4x_2E0 p(s(tyop_2Emin_2Ebool,V1Q_2E0))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) | p(s(tyop_2Emin_2Ebool,V0P_2E0)))))) # label(thm_2Ebool_2EBOTH__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 177 (all A_27a all A_27b all V0t_2E0 all V1x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0t_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0t_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Ebool_2EETA__AX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 178 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EFORALL__SIMP) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 179 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(A_27a,X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 180 (all A_27a all A_27b all A_27c all V1N_2E0 all V3x_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),f166_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Ebool_2Eliteral__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 181 (all A_27a all V0P_2E0 all V1f_2E0 s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))) = s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f159_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) # label(thm_2Ebool_2ERES__SELECT__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 182 (all V0x_2E0 all V1x_27_2E0 (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) & p(s(tyop_2Emin_2Ebool,V0x_2E0)) <-> (all V2t_2E0 ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,V2t_2E0)))))) # label(thm_2Ebool_2EAND__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 183 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f154_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f154_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef154_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 184 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0)))) <-> (all V1y_2E0 exists V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V2x_2E0))) = s(A_27b,V1y_2E0)))) # label(thm_2Ebool_2EONTO__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 185 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f29_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f29_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef29_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 186 (all A_27a all A_27b all V0P_2E0 ((all V1x_2E0 all V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))) <-> (all V3y_2E0 all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V4x_2E0))),s(A_27b,V3y_2E0))))))) # label(thm_2Ebool_2ESWAP__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 187 (all V0A_2E0 all V1B_2E0 (-p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,V1B_2E0))))) # label(thm_2Ebool_2EIMP__DISJ__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 188 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Ebool_2EF__IMP) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 189 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f159_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f159_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef159_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 190 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2EDATATYPE__TAG__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 191 (all A_27a all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) & (all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V1x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V2y_2E0)))) -> s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0))))) # label(thm_2Ebool_2EEXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 192 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))) & (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Ebool_2ESELECT__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 193 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) & p(s(tyop_2Emin_2Ebool,V1Q_2E0)) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))))) # label(thm_2Ebool_2ELEFT__AND__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 194 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(thm_2Ebool_2EFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 195 (all V0t1_2E0 all V1t2_2E0 ((p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t1_2E0))) -> s(tyop_2Emin_2Ebool,V0t1_2E0) = s(tyop_2Emin_2Ebool,V1t2_2E0)))) # label(thm_2Ebool_2EIMP__ANTISYM__AX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 196 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) -> (all V1b_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Ebool,V1b_2E0))))))) # label(thm_2Ebool_2Ebool__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 197 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f155_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f155_0_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef155_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 198 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f144_0_2E1(s(A_27a,X0_2E0))) = 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)),f144_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef144_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 199 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f158_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef158_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 200 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f70_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) <-> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Ebool_2ESELECT__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 201 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f154_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef154_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 202 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),tyop_2Emin_2Ebool),c_2Ebool_2EONE__ONE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 203 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),f168_0_2E3(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)))),f168_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef168_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 204 (all A_27a all V0f_2E0 all V1v_2E0 ((all V2x_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V1v_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1v_2E0)))))) # label(thm_2Ebool_2EUNWIND__FORALL__THM1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 205 (all A_27a all A_27b all V0f_2E0 all V1y_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1y_2E0)))) # label(thm_2Ebool_2EBETA__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 206 (all V0A_2E0 all V1B_2E0 ((p(s(tyop_2Emin_2Ebool,V1B_2E0)) -> p(s(tyop_2Emin_2Ebool,V0A_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0A_2E0))))) # label(thm_2Ebool_2EOR__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 207 (all A_27a all V0P_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Ebool,f154_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) # label(def2_2Ethm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 208 (all A_27a all V0P_2E0 all V1f_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f159_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Ebool_2ERES__SELECT__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 209 (all A_27a all V0P_2E0 all V1Q_2E0 (((all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0))) <-> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2ELEFT__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 210 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Ebool_2ELET__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 211 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f122_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f122_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0)))) # label(arityeq1_2Ef122_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 212 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f125_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f125_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef125_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 213 (all V0A_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,V1B_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)))) # label(thm_2Ebool_2EDISJ__SYM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 214 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 215 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,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),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 216 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> ((exists V3x_2E0 p(s(tyop_2Emin_2Ebool,V0P_2E0))) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2EBOTH__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 217 (all A_27a all V1f_2E0 all V3x_2E0 all V4y_2E0 ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0)))) -> s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0)) <-> p(s(tyop_2Emin_2Ebool,f158_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))))) # label(def0_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 218 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))))) # label(thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 219 (all A_27a all V0x_2E0 all V1x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Ebool_2ERES__FORALL__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 220 (all A_27a all A_27b all V0P_2E0 ((exists V1x_2E0 exists V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))) <-> (exists V3y_2E0 exists V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V4x_2E0))),s(A_27b,V3y_2E0))))))) # label(thm_2Ebool_2ESWAP__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 221 (all A_27a all V0P_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) # label(thm_2Ebool_2EEXISTS__itself) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 222 (all A_27a all A_27b all V1N_2E0 all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V3x_2E0))) = s(A_27b,f165_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Ebool_2Eliteral__case__RAND) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 223 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 224 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 225 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f71_0_2E1(s(A_27a,X0_2E0))) = 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)),f71_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef71_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 226 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 227 (all V0f_2E0 ((all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V2x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) | (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V4x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V4x_2E0)))) | (all V3x_2E0 s(tyop_2Emin_2Ebool,V3x_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V3x_2E0)))) | (all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0f_2E0),s(tyop_2Emin_2Ebool,V1x_2E0)))))) # label(thm_2Ebool_2EBOOL__FUN__CASES__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 228 (all A_27a all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) & (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))))) # label(thm_2Ebool_2ERIGHT__AND__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 229 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 230 (all A_27a all V0P_2E0 all V1Q_2E0 (((exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)))))) # label(thm_2Ebool_2ELEFT__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 231 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) <-> (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))))) # label(thm_2Ebool_2ERIGHT__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 232 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 233 (all V0P_2E0 all V1P_27_2E0 all V2Q_2E0 all V3Q_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) -> s(tyop_2Emin_2Ebool,V3Q_27_2E0) = s(tyop_2Emin_2Ebool,V2Q_2E0)) & s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1P_27_2E0) -> (p(s(tyop_2Emin_2Ebool,V3Q_27_2E0)) | p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2Q_2E0)) | p(s(tyop_2Emin_2Ebool,V0P_2E0))))) # label(thm_2Ebool_2ELEFT__OR__CONG) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 234 (all A_27a all A_27b all V0e_2E0 exists V1f_2E0 s(A_27b,V0e_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27b),V1f_2E0),s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))) # label(thm_2Ebool_2Eitself__Axiom) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 235 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),f122_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),f122_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef122_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 236 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),f166_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f166_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef166_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 237 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f144_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = 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)),f144_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef144_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 238 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f155_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f155_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef155_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 239 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 240 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),f165_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f165_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ef165_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 241 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_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_3F_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 242 (all A_27a all A_27b all V0t1_2E0 all V1t2_2E0 s(A_27a,V0t1_2E0) = s(A_27a,V0t1_2E0)) # label(thm_2Ebool_2EABS__SIMP) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 243 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2M_2E0 all V3N_2E0 (s(A_27a,V3N_2E0) = s(A_27a,V2M_2E0) & (all V4x_2E0 (s(A_27a,V4x_2E0) = s(A_27a,V3N_2E0) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))))) -> s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2M_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V3N_2E0))))) # label(thm_2Ebool_2Eliteral__case__CONG) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 244 (all A_27a all V0f_2E0 all V1v_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1v_2E0)))) <-> (all V2x_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V1v_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Ebool_2EUNWIND__FORALL__THM2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 245 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 246 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0)) & (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 247 (all A_27a all X0_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 248 (all V0t1_2E0 all V1t2_2E0 ((p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t1_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0))) <-> s(tyop_2Emin_2Ebool,V0t1_2E0) = s(tyop_2Emin_2Ebool,V1t2_2E0))) # label(thm_2Ebool_2EEQ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 249 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(thm_2Ebool_2EEQ__EXT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.52 250 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),f166_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),f166_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef166_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 251 (all A_27a all V0P_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,f70_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Ebool_2ESELECT__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 252 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0)))) <-> (all V1x1_2E0 all V2x2_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V1x1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V2x2_2E0))) -> s(A_27a,V2x2_2E0) = s(A_27a,V1x1_2E0))))) # label(thm_2Ebool_2EONE__ONE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 253 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 254 (all A_27a all A_27b all V0P_2E0 ((exists V1rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1rep_2E0))))) -> (exists V2rep_2E0 exists V3abs_2E0 ((all V5r_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5r_2E0)))) <-> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3abs_2E0),s(A_27a,V5r_2E0))))) = s(A_27a,V5r_2E0))) & (all V4a_2E0 s(A_27b,V4a_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3abs_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V4a_2E0)))))))))) # label(thm_2Ebool_2EABS__REP__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 255 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 256 (all A_27a all V1x_27_2E0 all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,f29_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V4y_2E0)))) -> s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 257 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f21_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f21_0_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef21_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 258 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2x_2E0)))))) -> ((all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Ebool_2EMONO__ALL) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 259 (all X0_2E0 s(tyop_2Emin_2Ebool,f163_2_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_2_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef163_2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 260 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)))) # label(thm_2Ebool_2ECONJ__SYM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 261 (all A_27a all V0t_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2EEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 262 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS__UNIQUE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS__UNIQUE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 263 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 264 (all A_27a all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0x_2E0),s(A_27a,V1x_27_2E0),s(A_27a,V2x_27_27_2E0))) = s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f21_0_2E3(s(tyop_2Emin_2Ebool,V0x_2E0),s(A_27a,V1x_27_2E0),s(A_27a,V2x_27_27_2E0)))))) # label(thm_2Ebool_2ECOND__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 265 (all A_27a all V0P_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) # label(thm_2Ebool_2EFORALL__itself) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 266 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a)),c_2Ebool_2ERES__SELECT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__SELECT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 267 (all A_27a all V0P_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Ebool_2ESELECT__AX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 268 (all A_27a exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,c_2Ebool_2EARB_2E0))),s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),A_27a),V0rep_2E0))))) # label(thm_2Ebool_2Eitself__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 269 (all A_27a all V0x_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f72_0_2E1(s(A_27a,V0x_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Ebool_2ESELECT__REFL__2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 270 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V1x_27_2E0))) = s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V1x_27_2E0)))) # label(thm_2Ebool_2ELET__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 271 (all V4b_2E0 (p(s(tyop_2Emin_2Ebool,f163_3_2E1(s(tyop_2Emin_2Ebool,V4b_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V4b_2E0)))) # label(def0_2Ethm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 272 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f125_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f125_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef125_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 273 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 274 (all V0t_2E0 all V1t1_2E0 all V2t2_2E0 (p(s(tyop_2Emin_2Ebool,V2t2_2E0)) | p(s(tyop_2Emin_2Ebool,V1t1_2E0)) -> ((p(s(tyop_2Emin_2Ebool,V1t1_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V2t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))))) # label(thm_2Ebool_2EOR__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 275 (all A_27a all V0P_2E0 all V1t_2E0 ((all V2x_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V1t_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Ebool_2EJRH__INDUCT__UTIL) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 276 (all A_27a all V0f_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))),s(A_27a,V3z_2E0)))) -> ((all V4x_2E0 all V5y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V5y_2E0))),s(A_27a,V4x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> (all V6x_2E0 all V7y_2E0 all V8z_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V7y_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V6x_2E0))),s(A_27a,V8z_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V6x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V7y_2E0))),s(A_27a,V8z_2E0))))))))) # label(thm_2Ebool_2ELCOMM__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 277 (all A_27a all V0P_2E0 (-(exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))) <-> (all V2x_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Ebool_2ENOT__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 278 (all V0t1_2E0 all V1t2_2E0 all V2t3_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V2t3_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V2t3_2E0)))) # label(thm_2Ebool_2ECONJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 279 (all V0z_2E0 all V1y_2E0 all V2x_2E0 all V3w_2E0 ((p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0))) & (p(s(tyop_2Emin_2Ebool,V1y_2E0)) -> p(s(tyop_2Emin_2Ebool,V2x_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,V0z_2E0))) -> (p(s(tyop_2Emin_2Ebool,V1y_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0)))))) # label(thm_2Ebool_2EMONO__IMP) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 280 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f158_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef158_2_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 281 (all V0P_2E0 all V1Q_2E0 all V2R_2E0 ((p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V2R_2E0))) & (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) -> p(s(tyop_2Emin_2Ebool,V2R_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1Q_2E0)) | p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V2R_2E0))))) # label(thm_2Ebool_2EDISJ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 282 (all V0b_2E0 all V1t1_2E0 all V2t2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Ebool,V1t1_2E0),s(tyop_2Emin_2Ebool,V2t2_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V1t1_2E0)) | -p(s(tyop_2Emin_2Ebool,V0b_2E0))) & (p(s(tyop_2Emin_2Ebool,V2t2_2E0)) | p(s(tyop_2Emin_2Ebool,V0b_2E0))))) # label(thm_2Ebool_2ECOND__EXPAND) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 283 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 284 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,f166_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),f166_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef166_1_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 285 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Ebool_2EONE__ONE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 286 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f29_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f29_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef29_2_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 287 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,f72_0_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0)))))) # label(def0_2Ethm_2Ebool_2ESELECT__REFL__2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 288 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f158_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef158_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 289 (all A_27a all V0t1_2E0 all V1t2_2E0 (s(A_27a,V1t2_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) & s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = s(A_27a,V0t1_2E0))) # label(thm_2Ebool_2ECOND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 290 (all A_27a all X0_2E0 all X1_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef158_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 291 (all A_27a all A_27b all A_27c all V0b_2E0 all V1N_2E0 all V2M_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f166_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0))),s(A_27a,V2M_2E0))),s(A_27b,V0b_2E0))) = s(A_27c,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),f166_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27b,V0b_2E0))),s(A_27a,V2M_2E0)))) # label(thm_2Ebool_2Eliteral__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 292 (all V0A_2E0 all V1B_2E0 ((-p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,V1B_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0)))) # label(thm_2Ebool_2EDISJ__EQ__IMP) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 293 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0))) & (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 294 (all A_27a all A_27b all V0P_2E0 all V1N_2E0 all V2M_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f121_1_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V2M_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),f121_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0))),s(A_27a,V2M_2E0)))))) # label(thm_2Ebool_2ELET__RAND) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 295 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 296 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f159_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f159_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef159_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 297 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,V0P_2E0)) & p(s(tyop_2Emin_2Ebool,V1Q_2E0)))) <-> (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,V1Q_2E0))) & (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,V0P_2E0))))) # label(thm_2Ebool_2EBOTH__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 298 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__FORALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 299 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 (s(tyop_2Emin_2Ebool,V1x_27_2E0) = s(tyop_2Emin_2Ebool,V0x_2E0) & (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> s(tyop_2Emin_2Ebool,V3y_27_2E0) = s(tyop_2Emin_2Ebool,V2y_2E0)) -> ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))))) # label(thm_2Ebool_2EIMP__CONG) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 300 (all A_27a all V0P_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,f125_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Ebool_2EEXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 301 (all A_27a all V0x_2E0 all V1x_27_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f30_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))))) # label(def0_2Ethm_2Ebool_2ERES__SELECT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 302 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27c,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(A_27a,X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 303 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) -> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) # label(thm_2Ebool_2EEQ__SYM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 304 (all V0z_2E0 all V1y_2E0 all V2x_2E0 all V3w_2E0 all V4b_2E0 ((p(s(tyop_2Emin_2Ebool,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1y_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V0z_2E0)) -> p(s(tyop_2Emin_2Ebool,V3w_2E0))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V4b_2E0),s(tyop_2Emin_2Ebool,V2x_2E0),s(tyop_2Emin_2Ebool,V0z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V4b_2E0),s(tyop_2Emin_2Ebool,V1y_2E0),s(tyop_2Emin_2Ebool,V3w_2E0)))))))) # label(thm_2Ebool_2EMONO__COND) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 305 (all A_27a all V1f_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f158_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))) # label(def2_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 306 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) & p(s(tyop_2Emin_2Ebool,V0P_2E0)) <-> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,V0P_2E0)))))) # label(thm_2Ebool_2ERIGHT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 307 (all V0P_2E0 all V1P_27_2E0 all V2Q_2E0 all V3Q_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) -> s(tyop_2Emin_2Ebool,V2Q_2E0) = s(tyop_2Emin_2Ebool,V3Q_27_2E0)) & (-p(s(tyop_2Emin_2Ebool,V2Q_2E0)) -> s(tyop_2Emin_2Ebool,V1P_27_2E0) = s(tyop_2Emin_2Ebool,V0P_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0P_2E0)) | p(s(tyop_2Emin_2Ebool,V2Q_2E0)) <-> p(s(tyop_2Emin_2Ebool,V3Q_27_2E0)) | p(s(tyop_2Emin_2Ebool,V1P_27_2E0))))) # label(thm_2Ebool_2EOR__CONG) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 308 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V0t1_2E0)) & p(s(tyop_2Emin_2Ebool,V1t2_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1t2_2E0)) & p(s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2ECONJ__COMM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 309 (all A_27a all V0P_2E0 all V1x_2E0 ((all V2y_2E0 (s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2y_2E0)))))) -> s(A_27a,V1x_2E0) = s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) # label(thm_2Ebool_2ESELECT__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 310 (all V0A_2E0 all V1B_2E0 all V2C_2E0 ((p(s(tyop_2Emin_2Ebool,V2C_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0))) & p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2C_2E0)) & p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V0A_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)))) # label(thm_2Ebool_2ELEFT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 311 (all A_27a all A_27b ((all V0p_2E0 all V1m_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) -> s(A_27b,c_2Ebool_2ERES__ABSTRACT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0),s(A_27a,V2x_2E0))))) & (all V3p_2E0 all V4m1_2E0 all V5m2_2E0 ((all V6x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3p_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4m1_2E0),s(A_27a,V6x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5m2_2E0),s(A_27a,V6x_2E0))))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5m2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4m1_2E0))))))) # label(thm_2Ebool_2ERES__ABSTRACT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 312 (all A_27a all V0x_2E0 all V1x_27_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,f29_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f29_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V3x_2E0)))))) # label(def1_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 313 (all A_27a all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f154_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 314 (all A_27a all A_27b all V0P_2E0 ((all V1x_2E0 exists V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))) <-> (exists V3f_2E0 all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V4x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V4x_2E0))))))))) # label(thm_2Ebool_2ESKOLEM__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 315 (all V0y_2E0 all V1x_2E0 ((-p(s(tyop_2Emin_2Ebool,V1x_2E0)) -> -p(s(tyop_2Emin_2Ebool,V0y_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V0y_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0))))) # label(thm_2Ebool_2EMONO__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 316 (all V0v_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EBOUNDED_2E1(s(tyop_2Emin_2Ebool,V0v_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Ebool_2EBOUNDED__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 317 (all A_27a all A_27b all V0b_2E0 all V1f_2E0 all V2g_2E0 all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0))),s(A_27a,V3x_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2g_2E0),s(A_27a,V3x_2E0)))))) # label(thm_2Ebool_2ECOND__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 318 (exists V0f_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),V0f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),V0f_2E0)))))) # label(thm_2Ebool_2EINFINITY__AX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 319 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f165_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27b,f165_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef165_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 320 (all A_27a all X0_2E0 all X1_2E0 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)),f72_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f72_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef72_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 321 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f70_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f70_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef70_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 322 (all A_27a ((all V0t1_2E0 all V1t2_2E0 s(A_27a,V0t1_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0)))) & (all V2t1_2E0 all V3t2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V2t1_2E0),s(A_27a,V3t2_2E0))) = s(A_27a,V3t2_2E0)))) # label(thm_2Ebool_2Ebool__case__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 323 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),f122_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f122_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef122_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 324 (all A_27a all A_27b all A_27c all V1N_2E0 all V0b_2E0 all V4x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27a,V4x_2E0))),s(A_27b,V0b_2E0))) = s(A_27c,f166_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1N_2E0),s(A_27b,V0b_2E0),s(A_27a,V4x_2E0)))) # label(def0_2Ethm_2Ebool_2Eliteral__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 325 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V1x_27_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0x_2E0),s(A_27a,V1x_27_2E0)))) # label(thm_2Ebool_2Eliteral__case__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 326 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(thm_2Ebool_2EBOOL__CASES__AX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 327 (all A_27a all V1x_27_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,f29_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))) # label(def2_2Ethm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 328 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 329 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_0_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_1_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_3_2E0)))) -> (all V5f_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V5f_2E0))))))) # label(thm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 330 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(thm_2Ebool_2EEXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 331 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))) -> (all V1i_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ebool_2Eitself(A_27a),V1i_2E0))))))) # label(thm_2Ebool_2Eitself__induction) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 332 (all V0P_2E0 all V1Q_2E0 all V2R_2E0 ((p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0)) & p(s(tyop_2Emin_2Ebool,V2R_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V2R_2E0))) & (p(s(tyop_2Emin_2Ebool,V0P_2E0)) -> p(s(tyop_2Emin_2Ebool,V1Q_2E0))))) # label(thm_2Ebool_2EIMP__CONJ__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 333 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f168_1_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = 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)),f168_1_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef168_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 334 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f30_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f30_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef30_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 335 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),tyop_2Emin_2Ebool),c_2Ebool_2EONTO_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONTO_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 336 (all A_27a all V0b_2E0 all V1t_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27a,V1t_2E0),s(A_27a,V1t_2E0))) = s(A_27a,V1t_2E0)) # label(thm_2Ebool_2Ebool__case__ID) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 337 (all A_27a all A_27b all V0P_2E0 all V1N_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,f121_1_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1N_2E0),s(A_27a,V4x_2E0)))))) # label(def0_2Ethm_2Ebool_2ELET__RAND) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 338 (all A_27a all V0P_2E0 all V1Q_2E0 ((exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) <-> (exists V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4x_2E0))))) | (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))))) # label(thm_2Ebool_2EEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 339 (all V0t_2E0 -(-p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Ebool_2ENOT__AND) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 340 (all A_27a all V0P_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))))) # label(thm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 341 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(thm_2Ebool_2ENOT__F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 342 (all A_27a all V0P_2E0 all V1a_2E0 ((exists V2x_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V1a_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1a_2E0)))))) # label(thm_2Ebool_2EUNWIND__THM1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 343 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 344 (all A_27a all X0_2E0 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)),f72_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f72_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef72_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 345 (all A_27a all V0a_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,f144_0_2E2(s(A_27a,V0a_2E0),s(A_27a,V1x_2E0)))) <-> s(A_27a,V1x_2E0) = s(A_27a,V0a_2E0))) # label(def0_2Ethm_2Ebool_2EEXISTS__UNIQUE__REFL) # label(axiom) # label(non_clause). [assumption]. 107.51/107.53 346 (all V0Q_2E0 all V1P_2E0 (((p(s(tyop_2Emin_2Ebool,V1P_2E0)) -> p(s(tyop_2Emin_2Ebool,V0Q_2E0))) -> p(s(tyop_2Emin_2Ebool,V1P_2E0))) -> p(s(tyop_2Emin_2Ebool,V1P_2E0)))) # label(thm_2Ebool_2EPEIRCE) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 347 (all V0P_2E0 all V1P_27_2E0 all V2Q_2E0 all V3Q_27_2E0 (s(tyop_2Emin_2Ebool,V0P_2E0) = s(tyop_2Emin_2Ebool,V1P_27_2E0) & (p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) -> s(tyop_2Emin_2Ebool,V2Q_2E0) = s(tyop_2Emin_2Ebool,V3Q_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V3Q_27_2E0)) & p(s(tyop_2Emin_2Ebool,V1P_27_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2Q_2E0)) & p(s(tyop_2Emin_2Ebool,V0P_2E0))))) # label(thm_2Ebool_2ELEFT__AND__CONG) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 348 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f163_1_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,f163_1_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef163_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 349 (all V0A_2E0 all V1B_2E0 ((-p(s(tyop_2Emin_2Ebool,V0A_2E0)) | -p(s(tyop_2Emin_2Ebool,V1B_2E0)) <-> -(p(s(tyop_2Emin_2Ebool,V0A_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)))) & (-(p(s(tyop_2Emin_2Ebool,V0A_2E0)) | p(s(tyop_2Emin_2Ebool,V1B_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0A_2E0)) & -p(s(tyop_2Emin_2Ebool,V1B_2E0))))) # label(thm_2Ebool_2EDE__MORGAN__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 350 (all V0t1_2E0 all V1t2_2E0 (p(s(tyop_2Emin_2Ebool,V1t2_2E0)) -> p(s(tyop_2Emin_2Ebool,V1t2_2E0)) | p(s(tyop_2Emin_2Ebool,V0t1_2E0)))) # label(thm_2Ebool_2EOR__INTRO__THM2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 351 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2EConseqConv_2EOR__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 352 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EAND__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 353 (all V0c_2E0 all V1x_2E0 all V2x_27_2E0 all V3y_2E0 all V4y_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V0c_2E0)) -> (p(s(tyop_2Emin_2Ebool,V4y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_2E0)))) & (p(s(tyop_2Emin_2Ebool,V0c_2E0)) -> (p(s(tyop_2Emin_2Ebool,V2x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V2x_27_2E0),s(tyop_2Emin_2Ebool,V4y_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,V3y_2E0))))))) # label(thm_2EConseqConv_2EIMP__CONG__cond) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 354 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 355 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 356 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))) & (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V0x_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0))) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))))) # label(thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 357 (all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 358 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)))) & (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))) -> (p(s(tyop_2Emin_2Ebool,V2y_2E0)) & p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) & p(s(tyop_2Emin_2Ebool,V1x_27_2E0))))) # label(thm_2EConseqConv_2EIMP__CONG__conj__weaken) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 359 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 360 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2EConseqConv_2EAND__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 361 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EAND__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 362 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EOR__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 363 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2EConseqConv_2Etrue__imp) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 364 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EOR__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 365 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 366 (all V0c_2E0 all V1x_2E0 all V2x_27_2E0 all V3y_2E0 all V4y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V2x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0))) & (p(s(tyop_2Emin_2Ebool,V4y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_2E0))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V2x_27_2E0),s(tyop_2Emin_2Ebool,V4y_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,V3y_2E0))))))) # label(thm_2EConseqConv_2EIMP__CONG__cond__simple) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 367 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2EConseqConv_2ENOT__CLAUSES__T) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 368 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2s_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2s_2E0)))) -> ((all V4s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4s_2E0))))) <-> (all V3s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3s_2E0)))))))) # label(thm_2EConseqConv_2Eforall__eq__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 369 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EIMP__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 370 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 371 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 372 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 373 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 374 (all X0_2E0 all X1_2E0 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_2EConseqConv_2EASM__MARKER_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2EConseqConv_2EASM__MARKER_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 375 (all V0t_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EIMP__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 376 (all V0x_2E0 all V1x_27_2E0 s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,V0x_2E0),s(tyop_2Emin_2Ebool,V1x_27_2E0))) = s(tyop_2Emin_2Ebool,V1x_27_2E0)) # label(thm_2EConseqConv_2EASM__MARKER__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 377 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2EConseqConv_2EAND__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 378 (all V0c_2E0 all V1x_2E0 ((-p(s(tyop_2Emin_2Ebool,V0c_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,V1x_2E0)))))) # label(thm_2EConseqConv_2ECOND__CLAUSES__TT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 379 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 380 (all A_27a all V0b_2E0 all V1t_2E0 s(A_27a,V1t_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(A_27a,V1t_2E0),s(A_27a,V1t_2E0)))) # label(thm_2EConseqConv_2ECOND__CLAUSES__ID) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 381 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))) & (-p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V0x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) | p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V0x_2E0)) | p(s(tyop_2Emin_2Ebool,V2y_2E0))))) # label(thm_2EConseqConv_2EIMP__CONG__disj__strengthen) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 382 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)))) & (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> (p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))) -> ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0))) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))))) # label(thm_2EConseqConv_2EIMP__CONG__imp__strengthen) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 383 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))) & (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_27_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0))) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))))) # label(thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 384 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2EConseqConv_2ENOT__CLAUSES__F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 385 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> (p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))) & (-p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V0x_2E0)))) -> ((p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0))) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))))) # label(thm_2EConseqConv_2EIMP__CONG__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 386 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2EConseqConv_2EAND__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 387 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 388 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 389 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2EConseqConv_2EIMP__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 390 (all V0y_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,V1x_2E0) = s(tyop_2Emin_2Ebool,c_2EConseqConv_2EASM__MARKER_2E2(s(tyop_2Emin_2Ebool,V0y_2E0),s(tyop_2Emin_2Ebool,V1x_2E0)))) # label(thm_2EConseqConv_2EASM__MARKER__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 391 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 392 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0))))) # label(thm_2EConseqConv_2EIMP__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 393 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 394 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 395 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) -> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2Efalse__imp) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 396 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2s_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2s_2E0)))) -> ((exists V4s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0Q_2E0),s(A_27a,V4s_2E0))))) <-> (exists V3s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3s_2E0)))))))) # label(thm_2EConseqConv_2Eexists__eq__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 397 (all V0c_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0c_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_2E0))))) # label(thm_2EConseqConv_2ECOND__CLAUSES__FT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 398 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((-p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)))) & (-p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> p(s(tyop_2Emin_2Ebool,V3y_27_2E0)))) -> (p(s(tyop_2Emin_2Ebool,V0x_2E0)) | p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) | p(s(tyop_2Emin_2Ebool,V3y_27_2E0))))) # label(thm_2EConseqConv_2EIMP__CONG__disj__weaken) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 399 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> (p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))))) # label(thm_2EConseqConv_2EIMP__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 400 (all V0c_2E0 all V1x_2E0 (-p(s(tyop_2Emin_2Ebool,V0c_2E0)) & p(s(tyop_2Emin_2Ebool,V1x_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Ebool,V1x_2E0)))))) # label(thm_2EConseqConv_2ECOND__CLAUSES__TF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 401 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 402 (all A_27a all V0t1_2E0 all V1t2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0))) = s(A_27a,V1t2_2E0)) # label(thm_2EConseqConv_2ECOND__CLAUSES__CF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 403 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EOR__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 404 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 405 (all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) | p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2EOR__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 406 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 407 (all V0c_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0c_2E0),s(tyop_2Emin_2Ebool,V1x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0c_2E0)) & p(s(tyop_2Emin_2Ebool,V1x_2E0)))) # label(thm_2EConseqConv_2ECOND__CLAUSES__FF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 408 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 409 (all A_27a all V0t1_2E0 all V1t2_2E0 s(A_27a,V0t1_2E0) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(A_27a,V0t1_2E0),s(A_27a,V1t2_2E0)))) # label(thm_2EConseqConv_2ECOND__CLAUSES__CT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 410 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 411 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 412 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 413 (all V0x_2E0 all V1x_27_2E0 all V2y_2E0 all V3y_27_2E0 ((p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> (p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)))) & (p(s(tyop_2Emin_2Ebool,V2y_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V0x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,V1x_27_2E0)) & p(s(tyop_2Emin_2Ebool,V3y_27_2E0)) -> p(s(tyop_2Emin_2Ebool,V2y_2E0)) & p(s(tyop_2Emin_2Ebool,V0x_2E0))))) # label(thm_2EConseqConv_2EIMP__CONG__conj__strengthen) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 414 (all V0t_2E0 (--p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2EConseqConv_2ENOT__CLAUSES__X) # label(axiom) # label(non_clause). [assumption]. 107.51/107.54 415 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 416 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 417 (all V0lab_2E0 all V1argument_2E0 s(tyop_2Emin_2Ebool,c_2Emarker_2E_3A_2D_2E2(s(tyop_2Emin_2Eind,V0lab_2E0),s(tyop_2Emin_2Ebool,V1argument_2E0))) = s(tyop_2Emin_2Ebool,V1argument_2E0)) # label(thm_2Emarker_2Elabel__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 418 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 419 (all A_27a all V0x_2E0 s(A_27a,c_2Emarker_2Eunint_2E1(s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(thm_2Emarker_2Eunint__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 420 (all V0b1_2E0 all V1b2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emarker_2EAC_2E2(s(tyop_2Emin_2Ebool,V0b1_2E0),s(tyop_2Emin_2Ebool,V1b2_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1b2_2E0)) & p(s(tyop_2Emin_2Ebool,V0b1_2E0)))) # label(thm_2Emarker_2EAC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 421 (all X0_2E0 all X1_2E0 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_2Emarker_2EAC_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Emarker_2EAC_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Emarker_2EAC_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 422 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 423 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emarker_2E_3A_2D_2E0),s(tyop_2Emin_2Eind,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Emarker_2E_3A_2D_2E2(s(tyop_2Emin_2Eind,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Emarker_2E_3A_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 424 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2EAbbrev_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Emarker_2EAbbrev_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2EAbbrev_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 425 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 426 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 427 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 428 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 429 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 430 (all V0p_2E0 all V1q_2E0 all V2m_2E0 ((p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,V0p_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V0p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))))) # label(thm_2Emarker_2Emove__left__conj) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 431 (all V0p_2E0 all V1q_2E0 all V2m_2E0 ((p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) | p(s(tyop_2Emin_2Ebool,V1q_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))) & (p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))))) # label(thm_2Emarker_2Emove__right__disj) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 432 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 433 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 434 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2Estmarker_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2Estmarker_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 435 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 436 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Emarker_2Estmarker_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Emarker_2Estmarker__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 437 (all V0x_2E0 s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,c_2Emarker_2EAbbrev_2E1(s(tyop_2Emin_2Ebool,V0x_2E0)))) # label(thm_2Emarker_2EAbbrev__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 438 (all V0p_2E0 all V1q_2E0 all V2m_2E0 ((p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V0p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V0p_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V1q_2E0)) & p(s(tyop_2Emin_2Ebool,V0p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) & p(s(tyop_2Emin_2Ebool,V1q_2E0))))) # label(thm_2Emarker_2Emove__right__conj) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 439 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 440 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Emarker_2Eunint_2E0),s(A_27a,X0_2E0))) = s(A_27a,c_2Emarker_2Eunint_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2Eunint_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 441 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 442 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 443 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 444 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 445 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 446 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 447 (all V0p_2E0 all V1q_2E0 all V2m_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0p_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0p_2E0))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))) & (p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0p_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Emarker_2Estmarker_2E1(s(tyop_2Emin_2Ebool,V2m_2E0))))))) # label(thm_2Emarker_2Emove__left__disj) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 448 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Emarker_2ECong_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2ECong_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2ECong_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 449 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 450 (all V0x_2E0 s(tyop_2Emin_2Ebool,V0x_2E0) = s(tyop_2Emin_2Ebool,c_2Emarker_2ECong_2E1(s(tyop_2Emin_2Ebool,V0x_2E0)))) # label(thm_2Emarker_2ECong__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 451 (all A_27a all X0_2E0 s(A_27a,c_2Emarker_2Estmarker_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Emarker_2Estmarker_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Emarker_2Estmarker_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 452 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,c_2EnormalForms_2EEXT__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2EnormalForms_2EEXT__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(thm_2EnormalForms_2EEXT__POINT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 453 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27a)),c_2EnormalForms_2EEXT__POINT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(A_27a,c_2EnormalForms_2EEXT__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2EnormalForms_2EEXT__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 454 (all A_27a all V0p_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(A_27a,c_2EnormalForms_2EUNIV__POINT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))))))) # label(thm_2EnormalForms_2EUNIV__POINT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 455 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 456 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 457 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 458 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 459 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 460 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 461 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 462 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 463 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 464 (all A_27a all V0p_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(A_27a,c_2EnormalForms_2EUNIV__POINT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))))) -> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(A_27a,V1x_2E0))))))) # label(thm_2EnormalForms_2EUNIV__POINT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 465 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 466 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 467 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 468 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 469 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 470 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,c_2EnormalForms_2EEXT__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2EnormalForms_2EEXT__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(thm_2EnormalForms_2EEXT__POINT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 471 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 472 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 473 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2EnormalForms_2EUNIV__POINT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,c_2EnormalForms_2EUNIV__POINT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2EnormalForms_2EUNIV__POINT_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 474 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 475 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 476 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 477 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 478 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 479 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 480 (all V0s_2E0 all V1r_2E0 all V2q_2E0 all V3p_2E0 (s(tyop_2Emin_2Ebool,V3p_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2q_2E0),s(tyop_2Emin_2Ebool,V1r_2E0),s(tyop_2Emin_2Ebool,V0s_2E0))) <-> (-p(s(tyop_2Emin_2Ebool,V2q_2E0)) | -p(s(tyop_2Emin_2Ebool,V1r_2E0)) | p(s(tyop_2Emin_2Ebool,V3p_2E0))) & (-p(s(tyop_2Emin_2Ebool,V3p_2E0)) | p(s(tyop_2Emin_2Ebool,V0s_2E0)) | p(s(tyop_2Emin_2Ebool,V2q_2E0))) & (-p(s(tyop_2Emin_2Ebool,V2q_2E0)) | p(s(tyop_2Emin_2Ebool,V1r_2E0)) | -p(s(tyop_2Emin_2Ebool,V3p_2E0))) & (p(s(tyop_2Emin_2Ebool,V3p_2E0)) | -p(s(tyop_2Emin_2Ebool,V1r_2E0)) | -p(s(tyop_2Emin_2Ebool,V0s_2E0))) & (p(s(tyop_2Emin_2Ebool,V3p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0s_2E0)) | p(s(tyop_2Emin_2Ebool,V2q_2E0))))) # label(thm_2Esat_2Edc__cond) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 481 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 482 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 483 (all V0A_2E0 all V1B_2E0 all V2C_2E0 ((p(s(tyop_2Emin_2Ebool,V0A_2E0)) & p(s(tyop_2Emin_2Ebool,V1B_2E0)) -> p(s(tyop_2Emin_2Ebool,V2C_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> (p(s(tyop_2Emin_2Ebool,V1B_2E0)) -> p(s(tyop_2Emin_2Ebool,V2C_2E0)))))) # label(thm_2Esat_2EAND__IMP) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 484 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 485 (all V0A_2E0 ((-p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> ((p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 486 (all V0B_2E0 all V1A_2E0 (((p(s(tyop_2Emin_2Ebool,V1A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) -> (-p(s(tyop_2Emin_2Ebool,V0B_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) <-> (-(p(s(tyop_2Emin_2Ebool,V0B_2E0)) | p(s(tyop_2Emin_2Ebool,V1A_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EOR__DUAL2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 487 (all V0q_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,V1p_2E0)) & p(s(tyop_2Emin_2Ebool,V0q_2E0)) -> p(s(tyop_2Emin_2Ebool,V0q_2E0)))) # label(thm_2Esat_2Epth__an2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 488 (all V0q_2E0 all V1p_2E0 ((-p(s(tyop_2Emin_2Ebool,V0q_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1p_2E0))) <-> (-p(s(tyop_2Emin_2Ebool,V1p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0q_2E0))) & (p(s(tyop_2Emin_2Ebool,V1p_2E0)) | p(s(tyop_2Emin_2Ebool,V0q_2E0))))) # label(thm_2Esat_2Edc__neg) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 489 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 490 (all V0q_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,V0q_2E0)) & p(s(tyop_2Emin_2Ebool,V1p_2E0)) -> p(s(tyop_2Emin_2Ebool,V1p_2E0)))) # label(thm_2Esat_2Epth__an1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 491 (all V0A_2E0 ((-p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0A_2E0)))) # label(thm_2Esat_2ENOT__ELIM2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 492 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 493 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 494 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 495 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 496 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 497 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 498 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 499 (all V0t_2E0 (-p(s(tyop_2Emin_2Ebool,V0t_2E0)) -> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(thm_2Esat_2EEQF__Imp1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 500 (all V0q_2E0 all V1p_2E0 (-(p(s(tyop_2Emin_2Ebool,V1p_2E0)) -> p(s(tyop_2Emin_2Ebool,V0q_2E0))) -> -p(s(tyop_2Emin_2Ebool,V0q_2E0)))) # label(thm_2Esat_2Epth__ni2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 501 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 502 (all V0q_2E0 all V1p_2E0 (-(p(s(tyop_2Emin_2Ebool,V1p_2E0)) | p(s(tyop_2Emin_2Ebool,V0q_2E0))) -> -p(s(tyop_2Emin_2Ebool,V0q_2E0)))) # label(thm_2Esat_2Epth__no2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 503 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0)) <-> p(s(tyop_2Emin_2Ebool,V2p_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0)) | -p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (p(s(tyop_2Emin_2Ebool,V2p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))))) # label(thm_2Esat_2Edc__disj) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 504 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V2p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0))) <-> (s(tyop_2Emin_2Ebool,V0r_2E0) = s(tyop_2Emin_2Ebool,V1q_2E0) <-> p(s(tyop_2Emin_2Ebool,V2p_2E0))))) # label(thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 505 (all V0q_2E0 all V1p_2E0 (-(p(s(tyop_2Emin_2Ebool,V0q_2E0)) | p(s(tyop_2Emin_2Ebool,V1p_2E0))) -> -p(s(tyop_2Emin_2Ebool,V1p_2E0)))) # label(thm_2Esat_2Epth__no1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 506 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 507 (all V0t_2E0 (--p(s(tyop_2Emin_2Ebool,V0t_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0t_2E0)))) # label(thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 508 (all V0p_2E0 (--p(s(tyop_2Emin_2Ebool,V0p_2E0)) -> p(s(tyop_2Emin_2Ebool,V0p_2E0)))) # label(thm_2Esat_2Epth__nn) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 509 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 510 (all V0q_2E0 all V1p_2E0 (-(p(s(tyop_2Emin_2Ebool,V1p_2E0)) -> p(s(tyop_2Emin_2Ebool,V0q_2E0))) -> p(s(tyop_2Emin_2Ebool,V1p_2E0)))) # label(thm_2Esat_2Epth__ni1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 511 (all V0A_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) & -p(s(tyop_2Emin_2Ebool,V0A_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2Esat_2EAND__INV) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 512 (all V0b_2E0 (p(s(tyop_2Emin_2Ebool,V0b_2E0)) -> s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0b_2E0))) # label(thm_2Esat_2EEQT__Imp1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 513 (all V0B_2E0 all V1A_2E0 ((-p(s(tyop_2Emin_2Ebool,V1A_2E0)) -> (-p(s(tyop_2Emin_2Ebool,V0B_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) <-> (-(p(s(tyop_2Emin_2Ebool,V0B_2E0)) | p(s(tyop_2Emin_2Ebool,V1A_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EOR__DUAL) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 514 (all V0B_2E0 all V1A_2E0 ((-(p(s(tyop_2Emin_2Ebool,V0B_2E0)) | -p(s(tyop_2Emin_2Ebool,V1A_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V1A_2E0)) -> (-p(s(tyop_2Emin_2Ebool,V0B_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))))) # label(thm_2Esat_2EOR__DUAL3) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 515 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 516 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 517 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0)) | -p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (p(s(tyop_2Emin_2Ebool,V2p_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (p(s(tyop_2Emin_2Ebool,V1q_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))) <-> ((p(s(tyop_2Emin_2Ebool,V1q_2E0)) -> p(s(tyop_2Emin_2Ebool,V0r_2E0))) <-> p(s(tyop_2Emin_2Ebool,V2p_2E0))))) # label(thm_2Esat_2Edc__imp) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 518 (all V0r_2E0 all V1q_2E0 all V2p_2E0 ((-p(s(tyop_2Emin_2Ebool,V1q_2E0)) | -p(s(tyop_2Emin_2Ebool,V0r_2E0)) | p(s(tyop_2Emin_2Ebool,V2p_2E0))) & (-p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V0r_2E0))) & (-p(s(tyop_2Emin_2Ebool,V2p_2E0)) | p(s(tyop_2Emin_2Ebool,V1q_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V2p_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0r_2E0)) & p(s(tyop_2Emin_2Ebool,V1q_2E0))))) # label(thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 519 (all V0A_2E0 (p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> (-p(s(tyop_2Emin_2Ebool,V0A_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) # label(thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 520 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 521 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 522 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 523 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(A_27a,V2x_2E0)))) # label(thm_2Ecombin_2Eo__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 524 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool)),c_2Ecombin_2EFCOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 525 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2EUPDATE_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,X0_2E0),s(A_27d,X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 526 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(A_27a,X0_2E0))) = s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 527 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ELEFT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 528 (all A_27a all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27d,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 529 (all A_27a all A_27b all V0f_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0))) & s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(thm_2Ecombin_2EI__o__ID) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 530 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V1e_2E0)))) <-> (all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V1e_2E0))),s(A_27b,V2x_2E0))) = s(A_27b,V2x_2E0)))) # label(thm_2Ecombin_2ELEFT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 531 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 532 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),f278_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),f278_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef278_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 533 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(A_27c,X1_2E0))) = s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 534 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 535 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 536 (all A_27d all A_27e all A_27f all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27f,A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27d),tyop_2Emin_2Efun(A_27f,A_27e))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27f,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27f,A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27f_20mono_2EA_27e_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 537 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 538 (all A_27a all A_27c all V1f_2E0 all V3x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,V3x_2E0))) = s(A_27c,f276_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ecombin_2Eo__ABS__L) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 539 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1a_2E0))) = s(A_27b,V2b_2E0) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(thm_2Ecombin_2EUPDATE__APPLY__ID) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 540 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))) <-> (all V1x_2E0 all V2y_2E0 all V3z_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))),s(A_27a,V3z_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0)))))))) # label(thm_2Ecombin_2EASSOC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 541 (all A_27a all A_27b all V0f_2E0 all V1b_2E0 all V2a_2E0 (s(A_27b,V1b_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2a_2E0))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) # label(thm_2Ecombin_2EUPDATE__APPLY__IMP__ID) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 542 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 543 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27d,c_2Ecombin_2EUPDATE_2E4(s(A_27c,X0_2E0),s(A_27d,X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0),s(A_27c,X3_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2EUPDATE_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))),s(A_27c,X3_2E0)))) # label(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 544 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 545 (all A_27a all A_27b all V0f1_2E0 all V1f2_2E0 all V2a_2E0 all V3b_2E0 all V4c_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V4c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V3b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0))) -> (all V5v_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V5v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2a_2E0),s(A_27b,V5v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0)))) & s(A_27b,V4c_2E0) = s(A_27b,V3b_2E0))) # label(thm_2Ecombin_2EUPD__SAME__KEY__UNWIND) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 546 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 all V4d_2E0 (s(A_27a,V1a_2E0) != s(A_27a,V2b_2E0) & s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) & s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) | s(A_27a,V1a_2E0) = s(A_27a,V2b_2E0) & s(A_27b,V4d_2E0) = s(A_27b,V3c_2E0) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) # label(thm_2Ecombin_2EUPD11__SAME__BASE) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 547 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V0x_2E0))) = s(A_27a,c_2Ecombin_2E_3A_3E_2E2(s(A_27b,V0x_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0)))) # label(thm_2Ecombin_2EAPP__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 548 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),f279_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f279_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0)))) # label(arityeq1_2Ef279_0_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 549 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 all V4d_2E0 (s(A_27a,V2b_2E0) != s(A_27a,V1a_2E0) -> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V2b_2E0),s(A_27b,V4d_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))))) # label(thm_2Ecombin_2EUPDATE__COMMUTES) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 550 (all A_27a all V1a_2E0 all V3c_2E0 (p(s(tyop_2Emin_2Ebool,f286_0_2E2(s(A_27a,V1a_2E0),s(A_27a,V3c_2E0)))) <-> s(A_27a,V1a_2E0) = s(A_27a,V3c_2E0))) # label(def0_2Ethm_2Ecombin_2EAPPLY__UPDATE__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 551 (all A_27a all A_27b all A_27c all V1f_2E0 all V3x_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),f278_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ecombin_2ES__ABS__L) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 552 (all A_27a s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0)) # label(thm_2Ecombin_2EI__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 553 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 554 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2EFAIL_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) = s(A_27a,c_2Ecombin_2EFAIL_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 555 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(A_27b,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 556 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 557 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 558 (all A_27a all A_27b all V0f_2E0 ((all V1x_2E0 all V2y_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0)))))) # label(thm_2Ecombin_2ECOMM__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 559 (all A_27a all V0v_2E0 all V1f_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V0v_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_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_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2EAbbrev_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,V0v_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) # label(thm_2Ecombin_2ELET__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 560 (all A_27a all A_27b all A_27c all A_27d ((all V3a_2E0 all V4b_2E0 all V5x_2E0 all V6f_2E0 (s(A_27c,V4b_2E0) != s(A_27c,V3a_2E0) -> s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V4b_2E0))) = s(A_27d,c_2Ecombin_2EUPDATE_2E4(s(A_27c,V3a_2E0),s(A_27d,V5x_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V4b_2E0))))) & (all V0a_2E0 all V1x_2E0 all V2f_2E0 s(A_27b,V1x_2E0) = s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V0a_2E0),s(A_27b,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V0a_2E0)))))) # label(thm_2Ecombin_2EUPDATE__APPLY) # label(axiom) # label(non_clause). [assumption]. 107.51/107.55 561 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2x_2E0 s(A_27b,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),f279_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0))),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V2x_2E0))),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Ecombin_2ES__ABS__R) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 562 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Ecombin_2ECOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 563 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1a_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)) # label(thm_2Ecombin_2EAPPLY__UPDATE__ID) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 564 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 565 (all A_27a all A_27c all V0g_2E0 all V3x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V3x_2E0))) = s(A_27c,f279_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ecombin_2ES__ABS__R) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 566 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 567 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2x_2E0 s(A_27b,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),f278_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V2x_2E0))),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Ecombin_2ES__ABS__L) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 568 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),f278_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),f278_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0)))) # label(arityeq1_2Ef278_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 569 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 570 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f279_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27c,f279_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef279_0_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 571 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 all V2h_2E0 s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),V2h_2E0)))) # label(thm_2Ecombin_2Eo__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 572 (all A_27a all V0f_2E0 all V1e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1e_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1e_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1e_2E0)))))) # label(thm_2Ecombin_2EMONOID__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 573 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 574 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 (s(A_27b,V2b_2E0) = s(A_27b,V3c_2E0) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) # label(thm_2Ecombin_2EUPD11__SAME__KEY__AND__BASE) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 575 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 576 (all A_27a all A_27b all A_27c all V0x_2E0 all V1v_2E0 all V2f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1v_2E0))),s(A_27c,V0x_2E0))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27c,V0x_2E0))),s(A_27b,V1v_2E0)))) # label(thm_2Ecombin_2EGEN__LET__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 577 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 578 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 579 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 580 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 s(A_27a,c_2Ecombin_2EFAIL_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))) = s(A_27a,V1x_2E0)) # label(thm_2Ecombin_2EFAIL__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 581 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),V1g_2E0)))) <-> (all V2x_2E0 all V3y_2E0 all V4z_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),V1g_2E0),s(A_27c,V2x_2E0))),s(A_27a,V3y_2E0))))),s(A_27b,V4z_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27a)),V1g_2E0),s(A_27c,V2x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(A_27a,V3y_2E0))),s(A_27b,V4z_2E0)))))))) # label(thm_2Ecombin_2EFCOMM__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 582 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(A_27c,X1_2E0))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 583 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 584 (all A_27a all V0f_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))) # label(thm_2Ecombin_2EFCOMM__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 585 (all A_27a all V0f_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))),s(A_27a,V3z_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))))) # label(thm_2Ecombin_2EASSOC__SYM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 586 (all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2EK_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 587 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))),s(A_27b,X2_2E0))) = s(A_27c,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 588 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 589 (all A_27a all A_27b all A_27c all V0v_2E0 all V1f_2E0 all V2P_2E0 s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0))),s(A_27c,V0v_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,V0v_2E0)))))) # label(thm_2Ecombin_2EGEN__literal__case__RAND) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 590 (all A_27d all A_27f all X0_2E0 s(tyop_2Emin_2Efun(A_27f,A_27d),c_2Ecombin_2EK_2E1(s(A_27d,X0_2E0))) = s(tyop_2Emin_2Efun(A_27f,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27f,A_27d)),c_2Ecombin_2EK_2E0),s(A_27d,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27d_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 591 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 592 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Ecombin_2EFAIL_2E2(s(A_27a,V0x_2E0),s(A_27b,V1x_27_2E0)))) # label(thm_2Ecombin_2EFAIL__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 593 (all A_27a all X0_2E0 all X1_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 594 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(A_27c,X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(A_27c,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 595 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(A_27a,X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EW_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 596 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3c_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f286_0_2E2(s(A_27a,V1a_2E0),s(A_27a,V3c_2E0))),s(A_27b,V2b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3c_2E0)))))) # label(thm_2Ecombin_2EAPPLY__UPDATE__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 597 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2ERIGHT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 598 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 599 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EMONOID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 600 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),f281_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),f281_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef281_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 601 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),f281_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b))),f281_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0)))) # label(arityeq1_2Ef281_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 602 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V1_2E0) = s(A_27a,V0_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 603 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 604 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 605 (all A_27a all A_27b all A_27c all V0x_2E0 all V1v_2E0 all V2f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1v_2E0))),s(A_27c,V0x_2E0))) = s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27c,V0x_2E0))),s(A_27b,V1v_2E0)))) # label(thm_2Ecombin_2EGEN__literal__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 606 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V2x_2E0))))) = s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),f277_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0))),s(A_27a,V2x_2E0)))) # label(thm_2Ecombin_2Eo__ABS__R) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 607 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 608 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 609 (all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 610 (all A_27a all A_27c all V0g_2E0 all V3x_2E0 s(A_27c,f277_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V3x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0g_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ecombin_2Eo__ABS__R) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 611 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0),s(A_27c,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))),s(A_27c,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 612 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1f1_2E0 all V2f2_2E0 all V3a_2E0 all V4b_2E0 all V5c_2E0 (s(A_27d,V5c_2E0) != s(A_27d,V4b_2E0) -> s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,V3a_2E0),s(A_27d,V4b_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V0f_2E0))) != s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Ecombin_2EUPDATE_2E3(s(A_27c,V3a_2E0),s(A_27d,V5c_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V0f_2E0))))) # label(thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 613 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 614 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0)))) # label(thm_2Ecombin_2EW__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 615 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2EK_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 616 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 all V2y_2E0 s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27b,V1x_2E0),s(A_27a,V2y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2y_2E0))),s(A_27b,V1x_2E0)))) # label(thm_2Ecombin_2EC__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 617 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0)))) # label(thm_2Ecombin_2EK__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 618 (all A_27a all A_27b all A_27c all V0v_2E0 all V1f_2E0 all V2P_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,V0v_2E0))))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2P_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0))),s(A_27c,V0v_2E0)))) # label(thm_2Ecombin_2EGEN__LET__RAND) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 619 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 620 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2EK_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 621 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,V0x_2E0),s(A_27b,V1x_27_2E0)))) # label(thm_2Ecombin_2EK__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 622 (all A_27a all A_27b all A_27c all V0y_2E0 all V1f_2E0 all V2x_2E0 s(A_27b,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),f281_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0))),s(A_27c,V0y_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V2x_2E0))),s(A_27c,V0y_2E0)))) # label(thm_2Ecombin_2EC__ABS__L) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 623 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f266_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = 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)),f266_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef266_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 624 (all A_27e all A_27f all X0_2E0 s(tyop_2Emin_2Efun(A_27f,A_27e),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,A_27e)),c_2Ecombin_2EK_2E0),s(A_27e,X0_2E0))) = s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2EK_2E1(s(A_27e,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27e_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 625 (all A_27a all A_27b all V0f_2E0 all V1a_2E0 all V2b_2E0 all V3c_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1a_2E0),s(A_27b,V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))) # label(thm_2Ecombin_2EUPDATE__EQ) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 626 (all A_27a all V0a_2E0 all V3x_27_2E0 (p(s(tyop_2Emin_2Ebool,f266_0_2E2(s(A_27a,V0a_2E0),s(A_27a,V3x_27_2E0)))) <-> s(A_27a,V0a_2E0) = s(A_27a,V3x_27_2E0))) # label(def0_2Ethm_2Ecombin_2EUPDATE__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 627 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27a)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(A_27c,X1_2E0))) = s(A_27a,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 628 (all A_27a all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 629 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0x_2E0),s(A_27a,V1x_27_2E0))),s(A_27a,V1x_27_2E0))) = s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0x_2E0),s(A_27a,V1x_27_2E0)))) # label(thm_2Ecombin_2EW__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 630 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f276_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),f276_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0)))) # label(arityeq1_2Ef276_0_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 631 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(A_27c,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 632 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 633 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(A_27b,X1_2E0))) = s(A_27a,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 634 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 635 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27c,f276_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(A_27a,X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f276_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef276_0_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 636 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Ecombin_2EI__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 637 (all A_27a all A_27b all A_27c all A_27d all A_27e all A_27f ((all V0f_2E0 all V1v_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,V1v_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2EK_2E1(s(A_27c,V1v_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))) & (all V2f_2E0 all V3v_2E0 s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V2f_2E0),s(tyop_2Emin_2Efun(A_27f,A_27d),c_2Ecombin_2EK_2E1(s(A_27d,V3v_2E0))))) = s(tyop_2Emin_2Efun(A_27f,A_27e),c_2Ecombin_2EK_2E1(s(A_27e,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27e),V2f_2E0),s(A_27d,V3v_2E0)))))))) # label(thm_2Ecombin_2EK__o__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 638 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 639 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 640 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 641 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 642 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27d,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(A_27d,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(A_27d,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 643 (all A_27a all A_27b all A_27c all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 s(A_27c,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1x_27_2E0),s(A_27a,V2x_27_27_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(A_27a,V2x_27_27_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1x_27_2E0),s(A_27a,V2x_27_27_2E0)))))) # label(thm_2Ecombin_2ES__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 644 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 645 (all A_27a all A_27b all V0a_2E0 all V1b_2E0 all V2x_2E0 all V3x_27_2E0 s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,V0a_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_27_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f266_0_2E2(s(A_27a,V0a_2E0),s(A_27a,V3x_27_2E0))),s(A_27b,V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_27_2E0)))))) # label(thm_2Ecombin_2EUPDATE__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 646 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 647 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f277_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),f277_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0)))) # label(arityeq1_2Ef277_0_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 648 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Ecombin_2E_3A_3E_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(A_27a,c_2Ecombin_2E_3A_3E_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2E_3A_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 649 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ERIGHT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ERIGHT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 650 (all A_27a all A_27b all A_27c all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(A_27b,V1x_27_2E0),s(A_27a,V2x_27_27_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(A_27a,V2x_27_27_2E0))),s(A_27b,V1x_27_2E0)))) # label(thm_2Ecombin_2EC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 651 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2EMONOID_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2EMONOID_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EMONOID_2E2_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 652 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 653 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,c_2Ecombin_2EUPDATE_2E4(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(A_27a,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Ecombin_2EUPDATE_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 654 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 ((all V2x_2E0 s(A_27a,V2x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,V1e_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ERIGHT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(A_27b,V1e_2E0)))))) # label(thm_2Ecombin_2ERIGHT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 655 (all A_27a all A_27b all A_27c all V1f_2E0 all V3x_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),f281_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,A_27b)),V1f_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Ecombin_2EC__ABS__L) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 656 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 657 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27c)),f277_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27c,f277_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef277_0_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 658 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V2x_2E0))))) = s(A_27c,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),f276_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V2x_2E0)))) # label(thm_2Ecombin_2Eo__ABS__L) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 659 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2ELEFT__ID_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2ELEFT__ID_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ELEFT__ID_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 660 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(A_27c,X1_2E0))) = s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 661 (all A_27a all X0_2E0 all X1_2E0 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)),f286_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f286_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef286_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 662 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 663 (all A_27a all V0v_2E0 all V1f_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_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_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emarker_2EAbbrev_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,V0v_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V0v_2E0)))) # label(thm_2Ecombin_2Eliteral__case__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 664 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 665 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Ecombin_2ES__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 666 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(A_27c,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(A_27c,V2x_2E0)))))) # label(thm_2Ecombin_2Eo__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 667 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ecombin_2EFCOMM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool)),c_2Ecombin_2EFCOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EFCOMM_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 668 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 669 (all X0_2E0 s(tyop_2Emin_2Eind,c_2Enum_2ESUC__REP_2E1(s(tyop_2Emin_2Eind,X0_2E0))) = s(tyop_2Emin_2Eind,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),c_2Enum_2ESUC__REP_2E0),s(tyop_2Emin_2Eind,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC__REP_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 670 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.51/107.56 671 (all V0m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Enum_2EIS__NUM__REP_2E1(s(tyop_2Emin_2Eind,V0m_2E0)))) <-> (all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Eind,c_2Enum_2EZERO__REP_2E0)))) & (all V2n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Eind,V2n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Eind,c_2Enum_2ESUC__REP_2E1(s(tyop_2Emin_2Eind,V2n_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Eind,V0m_2E0)))))))) # label(thm_2Enum_2EIS__NUM__REP) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 672 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 673 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),tyop_2Emin_2Ebool),c_2Ebool_2EONE__ONE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 674 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 675 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 676 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 677 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 678 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 679 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) -> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Enum_2EINV__SUC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 680 (all X0_2E0 s(tyop_2Emin_2Eind,c_2Enum_2EREP__num_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Eind,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),c_2Enum_2EREP__num_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2EREP__num_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 681 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 682 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) & (all V1n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) -> (all V2n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) # label(thm_2Enum_2EINDUCTION) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 683 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 684 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 685 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 686 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 687 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 688 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Enum_2EIS__NUM__REP_2E1(s(tyop_2Emin_2Eind,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),c_2Enum_2EIS__NUM__REP_2E0),s(tyop_2Emin_2Eind,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2EIS__NUM__REP_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 689 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enum_2ENOT__SUC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 690 (all V0y_2E0 s(tyop_2Emin_2Eind,c_2Enum_2ESUC__REP_2E1(s(tyop_2Emin_2Eind,V0y_2E0))) != s(tyop_2Emin_2Eind,c_2Enum_2EZERO__REP_2E0)) # label(thm_2Enum_2EZERO__REP__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 691 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 692 (all V0a_2E0 s(tyop_2Enum_2Enum,c_2Enum_2EABS__num_2E1(s(tyop_2Emin_2Eind,c_2Enum_2EREP__num_2E1(s(tyop_2Enum_2Enum,V0a_2E0))))) = s(tyop_2Enum_2Enum,V0a_2E0)) # label(thm_2Enum_2Enum__ISO__DEF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 693 (all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Enum_2EIS__NUM__REP_2E1(s(tyop_2Emin_2Eind,V1r_2E0)))) <-> s(tyop_2Emin_2Eind,c_2Enum_2EREP__num_2E1(s(tyop_2Enum_2Enum,c_2Enum_2EABS__num_2E1(s(tyop_2Emin_2Eind,V1r_2E0))))) = s(tyop_2Emin_2Eind,V1r_2E0))) # label(thm_2Enum_2Enum__ISO__DEF_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 694 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 695 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 696 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 697 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2EABS__num_2E1(s(tyop_2Emin_2Eind,c_2Enum_2ESUC__REP_2E1(s(tyop_2Emin_2Eind,c_2Enum_2EREP__num_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) # label(thm_2Enum_2ESUC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 698 (exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Ebool),c_2Enum_2EIS__NUM__REP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Eind),V0rep_2E0))))) # label(thm_2Enum_2Enum__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 699 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Enum_2Enum),c_2Enum_2EABS__num_2E0),s(tyop_2Emin_2Eind,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2EABS__num_2E1(s(tyop_2Emin_2Eind,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2EABS__num_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 700 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 701 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 702 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),tyop_2Emin_2Ebool),c_2Ebool_2EONTO_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONTO_2E1_2Emono_2Etyop_2Emin_2Eind_20mono_2Etyop_2Emin_2Eind) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 703 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 704 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 705 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 706 (all A_27a all V0x_2E0 s(A_27a,c_2Eone_2Eone__CASE_2E2(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(thm_2Eone_2Eone__case__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 707 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 708 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 709 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 710 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 711 (all V0x_2E0 s(tyop_2Emin_2Ebool,f320_0_2E1(s(tyop_2Eone_2Eone,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(def0_2Ethm_2Eone_2Eone__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 712 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,c_2Eone_2Eone__CASE_2E2(s(tyop_2Eone_2Eone,X0_2E0),s(A_27a,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Eone_2Eone__CASE_2E0),s(tyop_2Eone_2Eone,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Eone_2Eone__CASE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 713 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 714 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 715 (all X0_2E0 s(tyop_2Emin_2Ebool,f320_0_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),f320_0_2E0),s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ef320_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 716 (all X0_2E0 s(tyop_2Emin_2Ebool,f319_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f319_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef319_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 717 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool)),f324_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,f324_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),X1_2E0)))) # label(arityeq2_2Ef324_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 718 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 719 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 720 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),f324_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool)),f324_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef324_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 721 (all A_27a all V0e_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),tyop_2Emin_2Ebool),f324_0_2E1(s(A_27a,V0e_2E0))))))) # label(thm_2Eone_2Eone__Axiom) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 722 (all V1b_2E0 s(tyop_2Emin_2Ebool,V1b_2E0) = s(tyop_2Emin_2Ebool,f319_0_2E1(s(tyop_2Emin_2Ebool,V1b_2E0)))) # label(def0_2Ethm_2Eone_2Eone__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 723 (all X0_2E0 s(tyop_2Eone_2Eone,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eone_2Eone,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Eone_2Eone),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 724 (all V0P_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eone_2Eone,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))))) # label(thm_2Eone_2EFORALL__ONE) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 725 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 726 (all A_27a all V0f_2E0 all V1g_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V0f_2E0)) # label(thm_2Eone_2Eone__axiom) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 727 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 728 (all V0v_2E0 s(tyop_2Eone_2Eone,V0v_2E0) = s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)) # label(thm_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 729 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 730 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 731 (exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),f319_0_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0rep_2E0))))) # label(thm_2Eone_2Eone__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 732 (all A_27a all V0u_2E0 all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,c_2Eone_2Eone__CASE_2E2(s(tyop_2Eone_2Eone,V0u_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Eone_2Eone__case__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 733 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 734 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 735 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V1_2E0) = s(A_27a,V0_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 736 (all A_27a all V0e_2E0 all V1fn_2E0 (p(s(tyop_2Emin_2Ebool,f324_0_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),V1fn_2E0)))) <-> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),V1fn_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))) = s(A_27a,V0e_2E0))) # label(def0_2Ethm_2Eone_2Eone__Axiom) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 737 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 738 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 739 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 740 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 741 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 742 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 743 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))) -> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eone_2Eone,V1x_2E0))))))) # label(thm_2Eone_2Eone__induction) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 744 (all A_27a all V0e_2E0 exists V1fn_2E0 s(A_27a,V0e_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27a),V1fn_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))) # label(thm_2Eone_2Eone__prim__rec) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 745 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0)))))))) # label(thm_2Erelation_2Etotal__inv__image) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 746 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERDOM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0)))) <-> (exists V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))))) # label(thm_2Erelation_2ERDOM__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 747 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Ediag_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Ediag_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ediag_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 748 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 749 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) <-> (exists V3u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3u_2E0),s(A_27a,V2y_2E0)))))))) # label(thm_2Erelation_2ERTC__CASES__RTC__TWICE) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 750 (all A_27a all V0R_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWF__EQ__WFP) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 751 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Esymmetric__SC__identity) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 752 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> (all V1P_2E0 ((all V2x_2E0 ((all V3y_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)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0))))))))) # label(thm_2Erelation_2EWF__INDUCTION__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 753 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0))))) # label(thm_2Erelation_2Einv__INVOL) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 754 (all A_27a all V0R_2E0 all V1x_2E0 ((all V2y_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)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0)))))) # label(thm_2Erelation_2EWFP__RULES) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 755 (all A_27a all V0R_2E0 all V1P_2E0 ((all V3x_2E0 all V4y_2E0 all V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_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)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_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)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_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)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))))) & (all V2x_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0))))) -> (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6x_2E0),s(A_27a,V7y_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)),V1P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))))) # label(thm_2Erelation_2ERTC__STRONG__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 756 (all A_27a all A_27b all A_27c all A_27d all V0R3_2E0 all V1R2_2E0 all V2R1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V1R2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V0R3_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V0R3_2E0)))))) # label(thm_2Erelation_2EO__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 757 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Enf_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0)))) <-> (all V2y_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))))) # label(thm_2Erelation_2Enf__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 758 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 all V6z_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)),V1P_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_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)),V0R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7x_2E0),s(A_27a,V8y_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)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Erelation_2ETC__INDUCT__LEFT1) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 759 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1x_2E0 all V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) <-> 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)),V0R_2E0),s(A_27a,V1x_2E0))) = 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)),V0R_2E0),s(A_27a,V2y_2E0))))))) # label(thm_2Erelation_2EALT__equivalence) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 760 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2ETC__IDEM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 761 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Einv__EQC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 762 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 763 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) | p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__CASES__TC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 764 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_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)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))))))) # label(thm_2Erelation_2ESC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 765 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWCR_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWCR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWCR_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 766 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 767 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> (all V1y_2E0 all V2z_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)),V0R_2E0),s(A_27a,V1y_2E0))),s(A_27a,V2z_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)),V0R_2E0),s(A_27a,V2z_2E0))),s(A_27a,V1y_2E0)))) <-> s(A_27a,V2z_2E0) = s(A_27a,V1y_2E0))))) # label(thm_2Erelation_2EWeakOrder__EQ) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 768 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etrichotomous_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etrichotomous_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 769 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Einv__image_2E4(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3y_2E0)))))) # label(thm_2Erelation_2Einv__image__thm) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 770 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0)))) & (all V3x_2E0 all V4y_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)),V1R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4y_2E0)))))))) -> (all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V5x_2E0),s(A_27a,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V6y_2E0)))))))))) # label(thm_2Erelation_2ETC__lifts__transitive__relations) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 771 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 772 (all A_27a all A_27b all V0R3_2E0 all V1R2_2E0 all V2R1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R3_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R3_2E0)))))) # label(thm_2Erelation_2ERINTER__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 773 (all A_27g all V0Z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))))) # label(thm_2Erelation_2EWeakOrder) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 774 (all A_27a all V0R_2E0 all V1P_2E0 ((all V3x_2E0 all V4y_2E0 all V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0),s(A_27a,V5z_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)),V1P_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_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)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_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)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))))) & (all V2x_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0))))) -> (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6x_2E0),s(A_27a,V7y_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)),V1P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))))) # label(thm_2Erelation_2ERTC__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 775 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EWFP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFP_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 776 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 777 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Ereflexive__Id__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 778 (all A_27a all V0R_2E0 all V1Q_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2a_2E0)))) & (all V3y_2E0 all V4z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3y_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)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V4z_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4z_2E0)))))) -> (all V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2a_2E0),s(A_27a,V5z_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V5z_2E0)))))))) # label(thm_2Erelation_2ERTC__ALT__RIGHT__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 779 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ercdiamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1x_2E0 all V2y_2E0 all V3z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))) -> (exists V4u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V4u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3z_2E0),s(A_27a,V4u_2E0)))))))))) # label(thm_2Erelation_2Ercdiamond__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 780 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 ((all V3y_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)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Erelation_2EWFP__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 781 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERCOMPL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2ERCOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERCOMPL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 782 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) # label(thm_2Erelation_2ESTRORD__RC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 783 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 all V6z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5y_2E0),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_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)),V1P_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) -> (all V7u_2E0 all V8v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7u_2E0),s(A_27a,V8v_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)),V1P_2E0),s(A_27a,V7u_2E0))),s(A_27a,V8v_2E0)))))))) # label(thm_2Erelation_2ETC__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 784 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ESN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ESN__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 785 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESTRORD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ESTRORD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 786 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0)))) # label(thm_2Erelation_2ERUNION__COMM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 787 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ETC__RC__EQNS) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 788 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Erelation_2EWFREC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2EWFREC_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 789 (all A_27a all A_27b all V0x_2E0 all V1k_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERDOM__DELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1k_2E0)))))))) <-> s(A_27a,V1k_2E0) != s(A_27a,V0x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0)))))))) # label(thm_2Erelation_2EIN__RDOM__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 790 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ediamond_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ediamond_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 791 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2Ethe__fun_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Erelation_2Ethe__fun_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2Ethe__fun_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 792 (all A_27g all A_27h all A_27k all V0R1_2E0 all V1R2_2E0 all V2x_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EO_2E4(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27g,V2x_2E0),s(A_27k,V3z_2E0)))) <-> (exists V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27g,V2x_2E0))),s(A_27h,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27h,V4y_2E0))),s(A_27k,V3z_2E0)))))))) # label(thm_2Erelation_2EO__DEF) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 793 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> (all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V3z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3z_2E0)))))))) # label(thm_2Erelation_2ERTC__RTC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 794 (all A_27a all A_27b all V0R_2E0 all V1M_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> (all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))))),s(A_27a,V2x_2E0))) = s(A_27b,c_2Erelation_2EWFREC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Erelation_2EWFREC__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 795 (all A_27a all A_27b all V1M_2E0 all V3f_2E0 all V0R_2E0 all V4y_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0))))),s(A_27a,V4y_2E0))) = s(A_27b,f346_0_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0)))) # label(def0_2Ethm_2Erelation_2Eapprox__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 796 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0)))) # label(thm_2Erelation_2ERC__OR__Id) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 797 (all A_27a all V0R_2E0 all V1a_2E0 all V2b_2E0 (s(A_27a,V2b_2E0) != s(A_27a,V1a_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)),V0R_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESTRORD_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_2E0)))))) # label(thm_2Erelation_2ESTRORD) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 798 (all A_27a all A_27b all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> (all V1M_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),f489_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))))) # label(thm_2Erelation_2EWF__RECURSION__THM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 799 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),f347_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),f347_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef347_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 800 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERUNIV_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Erelation_2ERUNIV) # label(axiom) # label(non_clause). [assumption]. 107.51/107.57 801 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Einv__RC) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 802 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 803 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ECR__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 804 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ercdiamond_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ercdiamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ercdiamond_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 805 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 all V2x_2E0 all V3x_27_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Einv__image_2E4(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2x_2E0),s(A_27a,V3x_27_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_27_2E0)))))) # label(thm_2Erelation_2Einv__image__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 806 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 807 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))) # label(thm_2Erelation_2ERSUBSET__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 808 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))) # label(thm_2Erelation_2ERINTER__COMM) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 809 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 810 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_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)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Eantisymmetric__def) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 811 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 812 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 all V3Q_2E0 ((all V4x_2E0 all V5y_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)),V2R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V3Q_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))))))) # label(thm_2Erelation_2ERC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 107.51/107.58 813 (all A_27g all V0Z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))))) # label(thm_2Erelation_2EStrongOrder) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 814 (all A_27a all V0a_2E0 all V1R_2E0 all V2Q_2E0 ((all V3y_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)),V1R_2E0),s(A_27a,V0a_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V4x_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)),V1R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V5y_2E0)))))) -> (all V6b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V0a_2E0),s(A_27a,V6b_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V6b_2E0)))))))) # label(thm_2Erelation_2ETC__INDUCT__ALT__RIGHT) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 815 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERINTER_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2ERINTER_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 816 (all A_27a all V0R_2E0 all V1a_2E0 all V2b_2E0 ((all V3P_2E0 ((all V5x_2E0 all V6y_2E0 all V7z_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)),V3P_2E0),s(A_27a,V6y_2E0))),s(A_27a,V7z_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)),V0R_2E0),s(A_27a,V5x_2E0))),s(A_27a,V6y_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)),V3P_2E0),s(A_27a,V5x_2E0))),s(A_27a,V7z_2E0)))))) & (all V4x_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)),V3P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V4x_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)),V3P_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_2E0)))))) # label(thm_2Erelation_2ERTC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 817 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakOrder_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 818 (all A_27z all V0f_2E0 (s(tyop_2Emin_2Efun(A_27z,A_27z),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27z,A_27z),c_2Ecombin_2EI_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))))) # label(thm_2Erelation_2EINVOL__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 819 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 820 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERDOM__DELETE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERDOM__DELETE_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2ERDOM__DELETE_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 821 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Einv__SC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 822 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0) | (exists V3u_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)),V0R_2E0),s(A_27a,V3u_2E0))),s(A_27a,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3u_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__CASES2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 823 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Erelation_2ERESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERESTRICT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 824 (all A_27a all A_27b all V1M_2E0 all V0R_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,f489_0_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0)))) <-> (all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))))),s(A_27a,V3x_2E0)))))) # label(def0_2Ethm_2Erelation_2EWF__RECURSION__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 825 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2EEQC__R) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 826 (all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 827 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Eirrefl__trans__implies__antisym) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 828 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Esymmetric_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 829 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 830 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))) <-> (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))))))) # label(thm_2Erelation_2ERSUBSET) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 831 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ERTC__IDEM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 832 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERINTER_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 833 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 834 (all A_27a all V0R_2E0 all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))))) # label(thm_2Erelation_2EEQC__REFL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 835 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 836 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> (exists V4u_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)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V4u_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)),V0R_2E0),s(A_27a,V3z_2E0))),s(A_27a,V4u_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Ediamond__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 837 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 838 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__SINGLE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 839 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),f489_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),f489_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef489_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 840 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Einv__TC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 841 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERC__RTC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 842 (all A_27a all V0R_2E0 all V1a_2E0 all V2b_2E0 ((all V3P_2E0 ((all V6x_2E0 all V7y_2E0 all V8z_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)),V3P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_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)),V3P_2E0),s(A_27a,V7y_2E0))),s(A_27a,V8z_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)),V3P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V8z_2E0)))))) & (all V4x_2E0 all V5y_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)),V0R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V3P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V3P_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_2E0)))))) # label(thm_2Erelation_2ETC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 843 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 all V3Q_2E0 ((all V4x_2E0 all V5y_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)),V2R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V3Q_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))))))) # label(thm_2Erelation_2ESC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 844 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> s(A_27a,V2y_2E0) != s(A_27a,V1x_2E0)))) # label(thm_2Erelation_2EWF__NOT__REFL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 845 (all A_27a all A_27b p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0))))) # label(thm_2Erelation_2ERSUBSET__WeakOrder) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 846 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 847 (all A_27a all V0R_2E0 all V1P_2E0 ((all V4x_2E0 all V5y_2E0 all V6z_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V1P_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) & (all V2x_2E0 all V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7u_2E0 all V8v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7u_2E0),s(A_27a,V8v_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)),V1P_2E0),s(A_27a,V7u_2E0))),s(A_27a,V8v_2E0)))))))) # label(thm_2Erelation_2ETC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 848 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Ereflexive__EQC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 849 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ETC__RTC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 850 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27b,V1x_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Einv_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27b,V1x_2E0),s(A_27a,V2y_2E0)))) # label(thm_2Erelation_2Einv__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 851 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eantisymmetric_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 852 (all A_27a all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_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)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3y_2E0)))))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5y_2E0)))))))))) # label(thm_2Erelation_2ETC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 853 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 854 (all A_27a all V0R_2E0 ((all V1x_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Ereflexive__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 855 (all A_27a all V0b_2E0 all V1R_2E0 all V2Q_2E0 ((all V3x_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)),V1R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V0b_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0)))))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V5y_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)),V1R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V4x_2E0)))))) -> (all V6a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V6a_2E0),s(A_27a,V0b_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V6a_2E0)))))))) # label(thm_2Erelation_2ETC__INDUCT__ALT__LEFT) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 856 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 857 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2u_2E0 all V3v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERDOM__DELETE_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2u_2E0),s(A_27b,V3v_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2u_2E0))),s(A_27b,V3v_2E0)))) & s(A_27a,V2u_2E0) != s(A_27a,V1x_2E0))) # label(thm_2Erelation_2ERDOM__DELETE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 858 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_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)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))))))) # label(thm_2Erelation_2ERTC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 859 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 860 (all A_27a all V0z_2E0 all V1x_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0z_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)),V2R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V0z_2E0)))) | (exists V3y_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)),V2R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V0z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3y_2E0)))))))) # label(thm_2Erelation_2ETC__CASES2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 861 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2Einv__image_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Einv__image_2E4(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2Einv__image_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 862 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V3z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3z_2E0)))))) # label(thm_2Erelation_2EEQC__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 863 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 864 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Esymmetric__EQC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 865 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) | s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))) # label(thm_2Erelation_2ERC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 866 (all A_27z all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Ebool),c_2Erelation_2EIDEM_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EIDEM_2E1_2Emono_2EA_27z) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 867 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 868 (all A_27a all A_27b all V0R_2E0 all V1P_2E0 all V2M_2E0 all V3D_2E0 all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3D_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3D_2E0),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27b,c_2Erelation_2EWFREC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__WFREC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 869 (all A_27a all A_27b all V0M_2E0 all V1R_2E0 all V2f_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V0M_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0)))) -> (all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V0M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V3x_2E0))))),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))))))) # label(thm_2Erelation_2EWFREC__COROLLARY) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 870 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 871 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__TC__RC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 872 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Ereflexive__RC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 873 (all A_27a all V0R_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_2E0)))) <-> (all V3Q_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V1a_2E0)))) & (all V4y_2E0 all V5z_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)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V5z_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V2b_2E0)))))))) # label(thm_2Erelation_2ERTC__ALT__RIGHT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 874 (all A_27a all V0R_2E0 ((all V1a_2E0 all V2b_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)),V0R_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_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)),V0R_2E0),s(A_27a,V2b_2E0))),s(A_27a,V1a_2E0)))) | s(A_27a,V2b_2E0) = s(A_27a,V1a_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Etrichotomous) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 875 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ECR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ECR_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 876 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERRESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERRESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 877 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakLinearOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWeakLinearOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 878 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 879 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V5y_2E0)))))))) # label(thm_2Erelation_2ERTC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 880 (all A_27a all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 881 (all A_27a all V0R2_2E0 all V1R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0)))))))) # label(thm_2Erelation_2Etransitive__RINTER) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 882 (all A_27a all V0R_2E0 all V1x_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2z_2E0)))) <-> (exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0),s(A_27a,V2z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3y_2E0)))))))) # label(thm_2Erelation_2EEXTEND__RTC__TC__EQN) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 883 (all A_27a all V0R_2E0 all V1Q_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2b_2E0)))) & (all V3x_2E0 all V4y_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)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))) -> (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5x_2E0),s(A_27a,V2b_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V5x_2E0)))))))) # label(thm_2Erelation_2ERTC__ALT__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 884 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2Einv__image_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2Einv__image_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 885 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERTC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 886 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1P_2E0 ((all V2x_2E0 ((all V3y_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)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0))))))))) # label(thm_2Erelation_2EWF__EQ__INDUCTION__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 887 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ESC__SYMMETRIC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 888 (all A_27a all V0R_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))))) & (all V2x_2E0 all V3y_2E0 all V4z_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)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V4z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0),s(A_27a,V4z_2E0)))))))) # label(thm_2Erelation_2ERTC__RULES__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.58 889 (all A_27a all V0R_2E0 all V1P_2E0 ((all V7x_2E0 all V8y_2E0 all V9z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V8y_2E0),s(A_27a,V9z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7x_2E0),s(A_27a,V8y_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)),V1P_2E0),s(A_27a,V8y_2E0))),s(A_27a,V9z_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)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_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)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V9z_2E0)))))) & (all V5x_2E0 all V6y_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)),V1P_2E0),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5x_2E0),s(A_27a,V6y_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)),V1P_2E0),s(A_27a,V6y_2E0))),s(A_27a,V5x_2E0)))))) & (all V4x_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V4x_2E0))))) & (all V2x_2E0 all V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V10x_2E0 all V11y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V10x_2E0),s(A_27a,V11y_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)),V1P_2E0),s(A_27a,V10x_2E0))),s(A_27a,V11y_2E0)))))))) # label(thm_2Erelation_2ESTRONG__EQC__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 890 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERRANGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERRANGE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 891 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2EEQC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EEQC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 892 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b)))),f346_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),f346_0_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0)))) # label(arityeq3_2Ef346_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 893 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ESC__IDEM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 894 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 895 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))) -> (exists V4u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V4u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3z_2E0),s(A_27a,V4u_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWCR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWCR__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 896 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 897 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2D_2E0 all V3P_2E0 all V4M_2E0 all V5x_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V4M_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2D_2E0),s(A_27a,V5x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2D_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V4M_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V5x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5x_2E0)))))))) # label(thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__ON__WFREC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 898 (all A_27a all A_27b all V0R3_2E0 all V1R2_2E0 all V2R1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R3_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R3_2E0)))) # label(thm_2Erelation_2ERUNION__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 899 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Erelation_2EINVOL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EINVOL_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 900 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERCOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERCOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERCOMPL_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 901 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 902 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))) = 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)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Esymmetric__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 903 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakOrder_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 904 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 905 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 906 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) # label(thm_2Erelation_2Eequivalence__inv__identity) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 907 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2EEQC__MOVES__IN) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 908 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Etransitive__RTC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 909 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 910 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V5y_2E0)))))))) # label(thm_2Erelation_2ETC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 911 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0))))) # label(thm_2Erelation_2EWF__EMPTY__REL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 912 (all A_27a all A_27b all V0R_2E0 all V1M_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2Ethe__fun_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),f347_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Erelation_2Ethe__fun__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 913 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 all V6z_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_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)),V0R_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) -> (all V7u_2E0 all V8v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7u_2E0),s(A_27a,V8v_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)),V1P_2E0),s(A_27a,V7u_2E0))),s(A_27a,V8v_2E0)))))))) # label(thm_2Erelation_2ETC__STRONG__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 914 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 915 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0))))) & (all V3x_2E0 all V4y_2E0 all V5z_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)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_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)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_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)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))))) -> (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6x_2E0),s(A_27a,V7y_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)),V1P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))))) # label(thm_2Erelation_2ERTC__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 916 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ERTC__REFLEXIVE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 917 (all A_27g all V0Z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),V0Z_2E0)))))) # label(thm_2Erelation_2EOrder) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 918 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),f348_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f348_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef348_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 919 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2Einv__image_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2Einv__image_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 920 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 921 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2EWF__TC__EQN) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 922 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_2E0 all V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V5y_2E0)))))))) # label(thm_2Erelation_2ERC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 923 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESTRORD_2E0))))) # label(thm_2Erelation_2EIDEM__STRORD) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 924 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2EEQC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 925 (all A_27a all V0R_2E0 all V1P_2E0 ((all V2x_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0))))) & (all V3x_2E0 all V4y_2E0 all V5z_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)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_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)),V1P_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_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)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))))) -> (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6x_2E0),s(A_27a,V7y_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)),V1P_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))))) # label(thm_2Erelation_2ERTC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 926 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Esymmetric__inv__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 927 (all A_27a all A_27b all V0y_2E0 all V1z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1z_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1z_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0y_2E0))) # label(thm_2Erelation_2EEqIsBothRSUBSET) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 928 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ERC__IDEM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 929 (all A_27z all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Ebool),c_2Erelation_2EINVOL_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EINVOL_2E1_2Emono_2EA_27z) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 930 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 931 (all A_27a all V0A_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Ediag_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Ediag_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0)))) # label(thm_2Erelation_2Einv__diag) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 932 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_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)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))))))) # label(thm_2Erelation_2ETC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 933 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)))),c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 934 (all A_27a all V0R_2E0 all V1P_2E0 ((all V4x_2E0 all V5y_2E0 all V6z_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)),V1P_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5y_2E0),s(A_27a,V6z_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)),V0R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) & (all V2x_2E0 all V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7u_2E0 all V8v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7u_2E0),s(A_27a,V8v_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)),V1P_2E0),s(A_27a,V7u_2E0))),s(A_27a,V8v_2E0)))))))) # label(thm_2Erelation_2ETC__STRONG__INDUCT__LEFT1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 935 (all A_27a all A_27b all V0R_2E0 all V1M_2E0 all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2Ethe__fun_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f348_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))))),s(A_27a,V2x_2E0))) = s(A_27b,c_2Erelation_2EWFREC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0)))) # label(thm_2Erelation_2EWFREC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 936 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 937 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 938 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2P_2E0 all V3M_2E0 all V4x_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V3M_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V3M_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V4x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__WFREC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 939 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ETC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 940 (all A_27a all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_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)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3y_2E0)))))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5y_2E0)))))))))) # label(thm_2Erelation_2ERC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 941 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Ereflexive__RC__identity) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 942 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> s(A_27a,V0y_2E0) != s(A_27a,V1x_2E0)))) # label(thm_2Erelation_2EWF__noloops) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 943 (all A_27a all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_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)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3y_2E0)))))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5y_2E0)))))))))) # label(thm_2Erelation_2ERTC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 944 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Etrichotomous__RC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 945 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V3z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3z_2E0)))))) # label(thm_2Erelation_2EEXTEND__RTC__TC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 946 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2EEQC__EQUIVALENCE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 947 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 948 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Erelation_2EIDEM_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EIDEM_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 949 (all A_27a all A_27b all V0y_2E0 all V1R_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27b,V2x_2E0))),s(A_27a,V0y_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERRANGE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0)))))))) # label(thm_2Erelation_2EIN__RRANGE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 950 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2y_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERCOMPL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27b,V2y_2E0)))))) # label(thm_2Erelation_2ERCOMPL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 951 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ETC__TRANSITIVE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 952 (all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 953 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2EEQC__IDEM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 954 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERDOM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 955 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ESC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 956 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 957 (all A_27a all V0x_2E0 all V1R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V0x_2E0),s(A_27a,V0x_2E0))))) # label(thm_2Erelation_2ERTC__REFL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 958 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2Ereflexive__TC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 959 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eequivalence_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eequivalence_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 960 (all A_27a all A_27b all A_27c all V0S2_2E0 all V1S1_2E0 all V2R2_2E0 all V3R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1S1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0S2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1S1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0S2_2E0)))))))) # label(thm_2Erelation_2EO__MONO) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 961 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 962 (all A_27a all V0R_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_2E0)))) <-> (all V3Q_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V2b_2E0)))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V5y_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)),V0R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V4x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27a,V1a_2E0)))))))) # label(thm_2Erelation_2ERTC__ALT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 963 (all A_27a all A_27b all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2EId__O) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 964 (all A_27a all A_27b all V1M_2E0 all V0R_2E0 all V3f_2E0 all V4v_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4v_2E0))))),s(A_27a,V4v_2E0))) = s(A_27b,f348_0_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V4v_2E0)))) # label(def0_2Ethm_2Erelation_2EWFREC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 965 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2Q_2E0 ((all V3x_2E0 all V4y_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)),V1R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4y_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0)))) -> (all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V5x_2E0),s(A_27a,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V6y_2E0)))))))))) # label(thm_2Erelation_2ERTC__lifts__reflexive__transitive__relations) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 966 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EStrongOrd__Ord) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 967 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Ereflexive__RTC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 968 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 969 (all A_27a all V0A_2E0 all V1x_2E0 all V2y_2E0 (s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediag_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2Ediag__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 970 (all A_27a all A_27b all V0R_2E0 all V1M_2E0 all V2x_2E0 all V3f_2E0 s(tyop_2Emin_2Ebool,f347_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eapprox_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0)))) # label(def0_2Ethm_2Erelation_2Ethe__fun__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 971 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (s(A_27a,V2y_2E0) != s(A_27a,V1x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> (exists V3z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))) & s(A_27a,V1x_2E0) != s(A_27a,V3z_2E0))))) # label(thm_2Erelation_2ETC__implies__one__step) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 972 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERRESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERRESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2ERRESTRICT_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 973 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1x_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0))))))) # label(thm_2Erelation_2Eirreflexive__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 974 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ERC__REFLEXIVE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 975 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0),s(A_27a,V1x_2E0)))))) # label(thm_2Erelation_2EEQC__SYM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 976 (all A_27z all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))) -> (all V1a_2E0 all V2b_2E0 (s(A_27z,V1a_2E0) = s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V2b_2E0))) <-> s(A_27z,V2b_2E0) = s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V1a_2E0))))))) # label(thm_2Erelation_2EINVOL__ONE__ENO) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 977 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2y_2E0 all V3z_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)),V1R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))) = s(A_27b,c_2Erelation_2ERESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))))) # label(thm_2Erelation_2ERESTRICT__LEMMA) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 978 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Etransitive__TC__identity) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 979 (all A_27a all A_27b all V0R_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERRANGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27b,V1y_2E0)))) <-> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27b,V1y_2E0))))))) # label(thm_2Erelation_2ERRANGE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 980 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__EQC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 981 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EEMPTY__REL_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = 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_2Erelation_2EEMPTY__REL_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EEMPTY__REL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 982 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EStrongLinearOrder) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 983 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ERC__MOVES__OUT) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 984 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Etransitive__inv) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 985 (all A_27a all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_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)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3y_2E0)))))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5y_2E0)))))))))) # label(thm_2Erelation_2ESC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 986 (all A_27z all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))) -> (all V1a_2E0 all V2b_2E0 (s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V1a_2E0))) = s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V2b_2E0))) <-> s(A_27z,V2b_2E0) = s(A_27z,V1a_2E0))))) # label(thm_2Erelation_2EINVOL__ONE__ONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 987 (all A_27z all V0f_2E0 (s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0) = s(tyop_2Emin_2Efun(A_27z,A_27z),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))))) # label(thm_2Erelation_2EIDEM__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.59 988 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Erelation_2ERESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(A_27b,c_2Erelation_2ERESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2ERESTRICT_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 989 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERRANGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERRANGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERRANGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 990 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 991 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 all V3Q_2E0 ((all V4x_2E0 all V5y_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)),V2R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V3Q_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))))))) # label(thm_2Erelation_2ERTC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 992 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 993 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EStrongOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EStrongOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 994 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2Esymmetric__TC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 995 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERC_2E0))))) # label(thm_2Erelation_2EIDEM__RC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 996 (all A_27a all A_27b all V0R_2E0 all V1P_2E0 all V2M_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0)))) -> (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V3x_2E0))),s(A_27b,c_2Erelation_2EWFREC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0),s(A_27a,V3x_2E0))))))))) # label(thm_2Erelation_2EINDUCTIVE__INVARIANT__WFREC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 997 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eantisymmetric_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 998 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 999 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eequivalence_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Eequivalence__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1000 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,f348_0_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(A_27a,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),f348_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef348_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1001 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1002 (all A_27a all V0R_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & (all V2x_2E0 all V3y_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0)))))) # label(thm_2Erelation_2EWF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1003 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Eantisymmetric__inv) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1004 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0)))))))) # label(thm_2Erelation_2Ereflexive__inv__image) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1005 (all A_27a all V0R1_2E0 all V1R2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0)))))) # label(thm_2Erelation_2Eirreflexive__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1006 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f489_0_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),f489_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ef489_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1007 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1008 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EStrongLinearOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1009 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ercdiamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Ercdiamond__diamond) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1010 (all A_27a all A_27b all A_27c all V0R_2E0 all V1R_27_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_27_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_27_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Einv__O) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1011 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2Ediamond__TC__diamond) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1012 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1013 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Ereflexive__inv) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1014 (all A_27a all V0R_2E0 all V1P_2E0 ((all V4x_2E0 all V5y_2E0 all V6z_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)),V0R_2E0),s(A_27a,V5y_2E0))),s(A_27a,V6z_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))))) & (all V2x_2E0 all V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7x_2E0),s(A_27a,V8y_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)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Erelation_2ETC__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1015 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Enf_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Enf_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2Enf_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1016 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) # label(thm_2Erelation_2Esymmetric__inv__identity) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1017 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 all V2x_2E0 all V3x_27_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(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)),V1R_2E0),s(A_27a,V3x_27_2E0))),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_27_2E0))),s(A_27b,c_2Ebool_2EARB_2E0))) = s(A_27b,c_2Erelation_2ERESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0),s(A_27a,V3x_27_2E0)))) # label(thm_2Erelation_2ERESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1018 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EStrongOrder_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EStrongOrder_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1019 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Eantisymmetric__RC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1020 (all A_27a all A_27b all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)) # label(thm_2Erelation_2Einv__inv) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1021 (all A_27a all V0R2_2E0 all V1R1_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0))))))) & (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0))))))))) # label(thm_2Erelation_2Eantisymmetric__RINTER) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1022 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_27_2E0 all V3R_2E0 ((all V4x_2E0 all V5y_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)),V3R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V2R_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_27_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))))))) # label(thm_2Erelation_2EEQC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1023 (all A_27a all V0R_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0)))) <-> (all V2y_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)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0)))))))) # label(thm_2Erelation_2EWFP__CASES) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1024 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Einv_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2Einv_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1025 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1026 (all A_27g all A_27h all A_27k all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EO_2E4(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X1_2E0),s(A_27g,X2_2E0),s(A_27k,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(A_27k,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27g,X2_2E0))),s(A_27k,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2EO_2E4_2Emono_2EA_27g_20mono_2EA_27h_20mono_2EA_27k) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1027 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1028 (all A_27a all V0z_2E0 all V1x_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0z_2E0)))) <-> (exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3y_2E0),s(A_27a,V0z_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)),V2R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3y_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)),V2R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V0z_2E0)))))) # label(thm_2Erelation_2ETC__CASES1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1029 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0))))) # label(thm_2Erelation_2EIDEM__RTC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1030 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2Ediamond__RC__diamond) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1031 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWCR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2ENewmans__lemma) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1032 (all A_27a all V0R_2E0 ((all V1P_2E0 ((all V2x_2E0 ((all V3y_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)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V4x_2E0))))))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EINDUCTION__WF__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1033 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Erelation_2Eapprox_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eapprox_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2Eapprox_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1034 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ERC__STRORD) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1035 (all A_27a all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EEMPTY__REL_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Erelation_2EEMPTY__REL__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1036 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERDOM_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERDOM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERDOM_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1037 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1038 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERUNION_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ec_2Erelation_2ERUNION_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1039 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2EEQC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2EEQC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1040 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2ERTC__TRANSITIVE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1041 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0)))))))) # label(thm_2Erelation_2EWF__inv__image) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1042 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ERC__Weak) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1043 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1044 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Esymmetric__inv) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1045 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1046 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWeakOrd__Ord) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1047 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1048 (all A_27a all A_27b all V0x_2E0 all V1R_2E0 ((exists V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V0x_2E0))),s(A_27b,V2y_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0)))))))) # label(thm_2Erelation_2EIN__RDOM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1049 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1050 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1051 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2ERDOM__DELETE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERDOM__DELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERDOM__DELETE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1052 (all A_27a all V0R_2E0 ((all V2x_2E0 all V3y_2E0 all V4z_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0),s(A_27a,V4z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0),s(A_27a,V4z_2E0)))))) & (all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))))))) # label(thm_2Erelation_2ERTC__RULES) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1053 (all A_27a all A_27b all V0R_2E0 all V1D_2E0 all V2P_2E0 all V3M_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT__ON_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1D_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V3M_2E0)))) <-> (all V4f_2E0 all V5x_2E0 ((all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1D_2E0),s(A_27a,V6y_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)),V0R_2E0),s(A_27a,V6y_2E0))),s(A_27a,V5x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V6y_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(A_27a,V6y_2E0))))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1D_2E0),s(A_27a,V5x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V5x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V3M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0))),s(A_27a,V5x_2E0)))))))))) # label(thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1054 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Esymmetric_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1055 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2EREMPTY__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1056 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWF__antisymmetric) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1057 (all A_27a all A_27b all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNIV_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNIV_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ERUNIV__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1058 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EPreOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EPreOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EPreOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1059 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2ESTRORD__Strong) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1060 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_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)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Etransitive__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1061 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Eirreflexive__inv) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1062 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1x_2E0 all V2y_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)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))))))) # label(thm_2Erelation_2Etotal__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1063 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1064 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0)))))))) # label(thm_2Erelation_2Etransitive__inv__image) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1065 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 all V3Q_2E0 ((all V4x_2E0 all V5y_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)),V2R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V3Q_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3Q_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))))))) # label(thm_2Erelation_2ETC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1066 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1067 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ESTRORD_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESTRORD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ESTRORD_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1068 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ESC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_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)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))))) # label(thm_2Erelation_2ESC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1069 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1070 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWeakLinearOrder) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1071 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ESC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1072 (all A_27a all V0R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) # label(thm_2Erelation_2Einv__MOVES__OUT) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1073 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool))),c_2Erelation_2EINDUCTIVE__INVARIANT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2EINDUCTIVE__INVARIANT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1074 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERUNION_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))))) # label(thm_2Erelation_2ERUNION) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1075 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERUNIV_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNIV_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERUNIV_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1076 (all A_27a all A_27b p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0))))) # label(thm_2Erelation_2ERSUBSET__antisymmetric) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1077 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ELinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2ELinearOrder) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1078 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etrichotomous_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Etrichotomous__STRORD) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1079 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Erelation_2EINVOL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EINVOL_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1080 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ESN_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ESN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ESN_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1081 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2Etransitive__RC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1082 (all A_27a all A_27b all V0R_2E0 all V1P_2E0 all V2M_2E0 ((all V3f_2E0 all V4x_2E0 ((all V5y_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)),V0R_2E0),s(A_27a,V5y_2E0))),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V5y_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V5y_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0))),s(A_27a,V4x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINDUCTIVE__INVARIANT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V2M_2E0)))))) # label(thm_2Erelation_2EINDUCTIVE__INVARIANT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1083 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0))))) # label(thm_2Erelation_2EIDEM__TC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1084 (all A_27z all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27z,A_27z),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),X1_2E0))) = s(tyop_2Emin_2Efun(A_27z,A_27z),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Efun(A_27z,A_27z)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,A_27z),tyop_2Emin_2Efun(A_27z,A_27z))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27z,A_27z),X0_2E0))),s(tyop_2Emin_2Efun(A_27z,A_27z),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27z_20mono_2EA_27z_20mono_2EA_27z) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1085 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2ERINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERINTER_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1086 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1087 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Erelation_2EWF__TC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.60 1088 (all A_27a all A_27b all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2Einv__image_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0)))))))) # label(thm_2Erelation_2Esymmetric__inv__image) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1089 (all A_27a all V0R_2E0 all V1P_2E0 ((all V4x_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)),V1P_2E0),s(A_27a,V4x_2E0))),s(A_27a,V4x_2E0))))) & (all V5x_2E0 all V6y_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)),V1P_2E0),s(A_27a,V5x_2E0))),s(A_27a,V6y_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)),V1P_2E0),s(A_27a,V6y_2E0))),s(A_27a,V5x_2E0)))))) & (all V7x_2E0 all V8y_2E0 all V9z_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)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_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)),V1P_2E0),s(A_27a,V8y_2E0))),s(A_27a,V9z_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)),V1P_2E0),s(A_27a,V7x_2E0))),s(A_27a,V9z_2E0)))))) & (all V2x_2E0 all V3y_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1P_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V10x_2E0 all V11y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EEQC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V10x_2E0),s(A_27a,V11y_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)),V1P_2E0),s(A_27a,V10x_2E0))),s(A_27a,V11y_2E0)))))))) # label(thm_2Erelation_2EEQC__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1090 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0)))) # label(thm_2Erelation_2Einv__Id) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1091 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eantisymmetric_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1092 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1093 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EPreOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EPreOrder) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1094 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERINTER_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))))) # label(thm_2Erelation_2ERINTER) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1095 (all A_27a all V0R_2E0 all V1x_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2z_2E0)))) -> (exists V3y_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)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V3y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2z_2E0)))))) # label(thm_2Erelation_2ETC__CASES2__E) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1096 (all A_27a all V0R_2E0 all V1x_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2z_2E0)))) -> (exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0),s(A_27a,V2z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2z_2E0)))))) # label(thm_2Erelation_2ETC__CASES1__E) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1097 (all A_27a all V0R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEQC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Etransitive__EQC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1098 (all A_27a all A_27b all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0)))) # label(thm_2Erelation_2EO__Id) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1099 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1100 (all A_27a all A_27b all V0R_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERRESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))))) # label(thm_2Erelation_2ERRESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1101 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,A_27b)))),f346_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27a,X3_2E0))) = s(A_27b,f346_0_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef346_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1102 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERCOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2ESTRORD__AND__NOT__Id) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1103 (all A_27a all V0R_2E0 ((all V1B_2E0 ((exists V2w_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V2w_2E0))))) -> (exists V3min_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V3min_2E0)))) & (all V4b_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)),V0R_2E0),s(A_27a,V4b_2E0))),s(A_27a,V3min_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V4b_2E0)))))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWF__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1104 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2Esymmetric__RC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1105 (all A_27a all A_27b all V0R_2E0 all V1M_2E0 all V2x_2E0 all V3f_2E0 (s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Erelation_2ERESTRICT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),f346_0_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eapprox_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),V1M_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0)))))) # label(thm_2Erelation_2Eapprox__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1106 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWF__irreflexive) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1107 (all A_27a all V0P_2E0 all V1R_2E0 ((all V2x_2E0 ((all V3y_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)),V1R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3y_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Erelation_2EWFP__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1108 (all A_27z all V0f_2E0 ((all V1x_2E0 s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V1x_2E0))))) = s(A_27z,V1x_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EINVOL_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))))) # label(thm_2Erelation_2EINVOL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1109 (all A_27z all V0f_2E0 ((all V1x_2E0 s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V1x_2E0))))) = s(A_27z,app_2E2(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0),s(A_27z,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(A_27z,A_27z),V0f_2E0)))))) # label(thm_2Erelation_2EIDEM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1110 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EOrder_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EOrder_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EOrder_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1111 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2ERUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1112 (all A_27a all V0R_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ediamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ercdiamond_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ECR_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))))) # label(thm_2Erelation_2Eestablish__CR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1113 (all A_27a all A_27b all V0x_2E0 all V1s_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERRESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))))) # label(thm_2Erelation_2EIN__RDOM__RRESTRICT) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1114 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1115 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1a_2E0 all V2b_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)),V0R_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_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)),V0R_2E0),s(A_27a,V2b_2E0))),s(A_27a,V1a_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Erelation_2EWeakLinearOrder__dichotomy) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1116 (all A_27a all A_27b all V0f_2E0 all V1R_2E0 ((all V2x_2E0 all V3y_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)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))))))) # label(thm_2Erelation_2ERC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1117 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f347_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(A_27a,X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),f347_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(A_27a,X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0)))) # label(arityeq4_2Ef347_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1118 (all A_27a all A_27b all V0x_2E0 all V1R2_2E0 all V2R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R1_2E0)))))))) # label(thm_2Erelation_2EIN__RDOM__RUNION) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1119 (all A_27g all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1120 (all A_27a all V0R_2E0 all V1a_2E0 ((all V2P_2E0 ((all V3x_2E0 ((all V4y_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)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V1a_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWFP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1a_2E0)))))) # label(thm_2Erelation_2EWFP__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1121 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EIDEM_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESC_2E0))))) # label(thm_2Erelation_2EIDEM__SC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1122 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Erelation_2Etransitive__O__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1123 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1124 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1125 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) & (all V3x_2E0 all V4y_2E0 all V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0),s(A_27a,V5z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V5z_2E0)))))))) # label(thm_2Erelation_2ETC__RULES) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1126 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1127 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ELinearOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ELinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ELinearOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1128 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 ((exists V3u_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3u_2E0),s(A_27a,V2y_2E0)))))) | s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Erelation_2ERTC__CASES1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1129 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Ediag_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ediag_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2Ediag_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1130 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1131 (all A_27a all A_27b all A_27c all V0sum_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),A_27c)),V0sum_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR_2E0))))))) # label(thm_2Esum_2Edatatype__sum) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1132 (all A_27a all A_27b all V0e_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EABS__sum_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f572_0_2E1(s(A_27a,V0e_2E0))))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0e_2E0)))) # label(thm_2Esum_2EINL__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1133 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1134 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29_29_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1135 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2h_2E0 (p(s(tyop_2Emin_2Ebool,f585_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),V2h_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),V2h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0))) & s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),V2h_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0))) # label(def0_2Ethm_2Esum_2Esum__axiom) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1136 (all A_27a all A_27b all A_27c all A_27d ((all V3f_2E0 all V4g_2E0 all V5b_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V4g_2E0),s(A_27b,V5b_2E0))))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2E_2B_2B_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V5b_2E0)))))) & (all V0f_2E0 all V1g_2E0 all V2a_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,V2a_2E0))))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2E_2B_2B_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2a_2E0)))))))) # label(thm_2Esum_2ESUM__MAP__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1137 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1138 (all A_27a all A_27b exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Esum_2EIS__SUM__REP_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),V0rep_2E0))))) # label(thm_2Esum_2Esum__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1139 (all A_27g all A_27h all X0_2E0 s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINR_2E1(s(A_27h,X0_2E0))) = s(tyop_2Esum_2Esum(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Esum_2Esum(A_27g,A_27h)),c_2Esum_2EINR_2E0),s(A_27h,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27g_20mono_2EA_27h) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1140 (all A_27g all A_27h all X0_2E0 s(tyop_2Esum_2Esum(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Esum_2Esum(A_27g,A_27h)),c_2Esum_2EINL_2E0),s(A_27g,X0_2E0))) = s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINL_2E1(s(A_27g,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27g_20mono_2EA_27h) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1141 (all A_27e all A_27f all X0_2E0 s(tyop_2Esum_2Esum(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Esum_2Esum(A_27e,A_27f)),c_2Esum_2EINL_2E0),s(A_27e,X0_2E0))) = s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Esum_2EINL_2E1(s(A_27e,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27e_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1142 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2E_2B_2B_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b)))),c_2Esum_2E_2B_2B_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1143 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1144 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2E_2B_2B_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(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_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Esum_2E_2B_2B_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Esum_2E_2B_2B_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1145 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1146 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1147 (all A_27c all A_27d all X0_2E0 s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Esum_2EINR_2E1(s(A_27c,X0_2E0))) = s(tyop_2Esum_2Esum(A_27d,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27d,A_27c)),c_2Esum_2EINR_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1148 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))))) # label(thm_2Esum_2ENOT__ISL__ISR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1149 (all A_27a all A_27b all V0e_2E0 all V1b_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,f572_0_2E4(s(A_27a,V0e_2E0),s(tyop_2Emin_2Ebool,V1b_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))) <-> s(A_27a,V2x_2E0) = s(A_27a,V0e_2E0) & p(s(tyop_2Emin_2Ebool,V1b_2E0)))) # label(def0_2Ethm_2Esum_2EINL__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1150 (all A_27a all A_27b all A_27c all V0f1_27_2E0 all V1f_27_2E0 all V2M_2E0 all V3M_27_2E0 all V4f_2E0 all V5f1_2E0 ((all V7y_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),V3M_27_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V7y_2E0))) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V5f1_2E0),s(A_27b,V7y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f1_27_2E0),s(A_27b,V7y_2E0))))) & (all V6x_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V6x_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V3M_27_2E0) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V4f_2E0),s(A_27a,V6x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_27_2E0),s(A_27a,V6x_2E0))))) & s(tyop_2Esum_2Esum(A_27a,A_27b),V2M_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),V3M_27_2E0) -> s(A_27c,c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),V2M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V4f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V5f1_2E0))) = s(A_27c,c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),V3M_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_27_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V0f1_27_2E0))))) # label(thm_2Esum_2Esum__case__cong) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1151 (all A_27a all A_27b all V0P_2E0 ((all V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V2y_2E0))))))) & (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1x_2E0))))))) -> (all V3s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V3s_2E0))))))) # label(thm_2Esum_2Esum__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1152 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1153 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 all V2z_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Esum_2EINL_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Esum_2EINR_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0))))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2E_2B_2B_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0)))) # label(thm_2Esum_2ESUM__MAP__CASE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1154 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f572_0_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(A_27a,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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f572_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef572_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1155 (all A_27c all A_27d all X0_2E0 s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Esum_2EINL_2E1(s(A_27d,X0_2E0))) = s(tyop_2Esum_2Esum(A_27d,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27d,A_27c)),c_2Esum_2EINL_2E0),s(A_27d,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1156 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27c,A_27d),X1_2E0))),s(tyop_2Esum_2Esum(A_27c,A_27d),X2_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27c,A_27d),X1_2E0),s(tyop_2Esum_2Esum(A_27c,A_27d),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1157 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1158 (all A_27a all A_27b ((all V2y_2E0 all V3x_2E0 (s(A_27b,V3x_2E0) = s(A_27b,V2y_2E0) <-> s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V3x_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V2y_2E0))))) & (all V0y_2E0 all V1x_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1x_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0y_2E0))) <-> s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0))))) # label(thm_2Esum_2EINR__INL__11) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1159 (all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1160 (all A_27a all A_27b all V0x_2E0 s(A_27a,c_2Esum_2EOUTL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Esum_2EOUTL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1161 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f573_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,f573_0_2E4(s(A_27b,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef573_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1162 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V1y_2E0))) != s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Esum_2Esum__distinct) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1163 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),X2_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Esum_2Esum(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Esum_2Esum__CASE_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27c,A_27d)),X2_2E0)))) # label(arityeq3_2Ec_2Esum_2Esum__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1164 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1165 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1166 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f572_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f572_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef572_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1167 (all A_27a all A_27b all V0e_2E0 all V1b_2E0 all V2x_2E0 all V3y_2E0 (-p(s(tyop_2Emin_2Ebool,V1b_2E0)) & s(A_27b,V0e_2E0) = s(A_27b,V3y_2E0) <-> p(s(tyop_2Emin_2Ebool,f573_0_2E4(s(A_27b,V0e_2E0),s(tyop_2Emin_2Ebool,V1b_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))))) # label(def0_2Ethm_2Esum_2EINR__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1168 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1169 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1170 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1171 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Esum_2ESUM__ALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Esum_2ESUM__ALL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1172 (all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(A_27c,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1173 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool))),f585_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),f585_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0)))) # label(arityeq2_2Ef585_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1174 (all A_27a all A_27b all V0v1_2E0 all V1v2_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V1v2_2E0))) != s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0v1_2E0)))) # label(thm_2Esum_2Esum__distinct1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1175 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1176 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Esum_2EISL_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EISL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1177 (all A_27a all A_27b all V0s_2E0 all V1s_27_2E0 all V2P_2E0 all V3P_27_2E0 all V4Q_2E0 all V5Q_27_2E0 ((all V6a_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V6a_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_27_2E0) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V6a_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V6a_2E0))))) & (all V7b_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V7b_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_27_2E0) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Q_27_2E0),s(A_27b,V7b_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V7b_2E0))))) & s(tyop_2Esum_2Esum(A_27a,A_27b),V0s_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_27_2E0) -> s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Q_27_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V0s_2E0))))) # label(thm_2Esum_2ESUM__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1178 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Esum_2Esum(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Esum_2Esum(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Esum_2Esum(A_27b,A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27b,A_27a),X1_2E0))),s(tyop_2Esum_2Esum(A_27b,A_27a),X2_2E0))) = s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27b,A_27a),X1_2E0),s(tyop_2Esum_2Esum(A_27b,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1179 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1180 (all A_27e all A_27f all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27e,A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27e,A_27f),tyop_2Esum_2Esum(A_27e,A_27f)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27e,A_27f),X1_2E0))),s(tyop_2Esum_2Esum(A_27e,A_27f),X2_2E0))) = s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27e,A_27f),X1_2E0),s(tyop_2Esum_2Esum(A_27e,A_27f),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27e_2CA_27f_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1181 (all A_27a all A_27b all V0e_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V0e_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EABS__sum_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f573_0_2E1(s(A_27b,V0e_2E0)))))) # label(thm_2Esum_2EINR__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1182 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27d,A_27c),X1_2E0),s(tyop_2Esum_2Esum(A_27d,A_27c),X2_2E0))) = s(tyop_2Esum_2Esum(A_27d,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27d,A_27c),tyop_2Esum_2Esum(A_27d,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27d,A_27c),tyop_2Esum_2Esum(A_27d,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27d,A_27c),tyop_2Esum_2Esum(A_27d,A_27c)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27d,A_27c),X1_2E0))),s(tyop_2Esum_2Esum(A_27d,A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27d_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1183 (all A_27a all A_27b all V0ss_2E0 ((exists V1x_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),V0ss_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1x_2E0)))) | (exists V2y_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V2y_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V0ss_2E0)))) # label(thm_2Esum_2Esum__CASES) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1184 (all A_27a all A_27b all V0x_2E0 s(A_27b,c_2Esum_2EOUTR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V0x_2E0))))) = s(A_27b,V0x_2E0)) # label(thm_2Esum_2EOUTR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1185 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1186 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1187 (all A_27a all A_27b ((all V0P_2E0 all V1Q_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2x_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) & (all V3P_2E0 all V4Q_2E0 all V5y_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V5y_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V5y_2E0)))))))) # label(thm_2Esum_2ESUM__ALL__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1188 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 all V2z_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0))),s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,c_2Esum_2EOUTL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0))))))),s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(A_27b,c_2Esum_2EOUTR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0))))))))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2E_2B_2B_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V2z_2E0)))) # label(thm_2Esum_2ESUM__MAP) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1189 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1190 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool))),f585_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X2_2E0))) = s(tyop_2Emin_2Ebool,f585_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X2_2E0)))) # label(arityeq3_2Ef585_0_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1191 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1192 (all A_27g all A_27h all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Esum_2Esum(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27g,A_27h),tyop_2Esum_2Esum(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27g,A_27h),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27g,A_27h),tyop_2Esum_2Esum(A_27g,A_27h))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27g,A_27h),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27g,A_27h),tyop_2Esum_2Esum(A_27g,A_27h)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27g,A_27h),X1_2E0))),s(tyop_2Esum_2Esum(A_27g,A_27h),X2_2E0))) = s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27g,A_27h),X1_2E0),s(tyop_2Esum_2Esum(A_27g,A_27h),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27g_2CA_27h_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1193 (all A_27a all A_27b all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27a),c_2Esum_2EOUTL_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))) = s(A_27a,c_2Esum_2EOUTL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EOUTL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1194 (all A_27a all A_27b ((all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V0x_2E0))))))) & (all V1y_2E0 -p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1y_2E0))))))))) # label(thm_2Esum_2EISR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.61 1195 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1196 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Esum_2EIS__SUM__REP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Esum_2EIS__SUM__REP_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EIS__SUM__REP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1197 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0y_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1x_2E0))) <-> s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0))) # label(thm_2Esum_2EINL__11) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1198 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),f585_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0))))))) # label(thm_2Esum_2Esum__axiom) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1199 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINL_2E1(s(A_27b,X0_2E0))) = s(tyop_2Esum_2Esum(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27b,A_27a)),c_2Esum_2EINL_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1200 (all A_27a all A_27b all V0P_2E0 ((exists V3y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V3y_2E0))))))) | (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2x_2E0))))))) <-> (exists V1s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_2E0))))))) # label(thm_2Esum_2EEXISTS__SUM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1201 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1202 (all A_27a all A_27b ((all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0))))))) & (all V1y_2E0 -p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V1y_2E0))))))))) # label(thm_2Esum_2EISL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1203 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))) -> s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,c_2Esum_2EOUTR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0))))))) # label(thm_2Esum_2EINR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1204 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2E_2B_2B_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27a,A_27b)),c_2Ecombin_2EI_2E0)) # label(thm_2Esum_2ESUM__MAP__I) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1205 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1206 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EABS__sum_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EABS__sum_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EABS__sum_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1207 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 (s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V1x_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V0y_2E0))) <-> s(A_27b,V1x_2E0) = s(A_27b,V0y_2E0))) # label(thm_2Esum_2EINR__11) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1208 (all A_27a all A_27b ((all V1r_2E0 (s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Esum_2EREP__sum_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EABS__sum_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1r_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Esum_2EIS__SUM__REP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V1r_2E0)))))) & (all V0a_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),V0a_2E0) = s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EABS__sum_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Esum_2EREP__sum_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0a_2E0)))))))) # label(thm_2Esum_2Esum__ISO__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1209 (all A_27a all A_27b all A_27c ((all V0x_2E0 all V1f_2E0 all V2f1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,V0x_2E0))) = s(A_27c,c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V2f1_2E0)))) & (all V3y_2E0 all V4f_2E0 all V5f1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V5f1_2E0),s(A_27b,V3y_2E0))) = s(A_27c,c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V4f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V5f1_2E0)))))) # label(thm_2Esum_2Esum__case__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1210 (all A_27a all A_27b all V0v1_2E0 all V1v2_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V1v2_2E0))) != s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V0v1_2E0)))) # label(thm_2Esum_2EINR__neq__INL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1211 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f573_0_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f573_0_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ef573_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1212 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))))) # label(thm_2Esum_2EISL__OR__ISR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1213 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 exists V2h_2E0 ((all V3x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,V3x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),V2h_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V3x_2E0)))))) & (all V4y_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),V2h_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V4y_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(A_27b,V4y_2E0)))))) # label(thm_2Esum_2Esum__Axiom) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1214 (all A_27a all A_27b all V0s_2E0 all V1Q_27_2E0 all V2Q_2E0 all V3P_27_2E0 all V4P_2E0 ((all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27b,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_27_2E0),s(A_27b,V6y_2E0)))))) & (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(A_27a,V5x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V5x_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Esum_2ESUM__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_27_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V0s_2E0))))))) # label(thm_2Esum_2ESUM__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1215 (all A_27a all A_27b all V0f_2E0 ((exists V1v1_2E0 exists V2v2_2E0 ((all V3x_2E0 all V4x_27_2E0 all V5x_27_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0f_2E0),s(tyop_2Emin_2Ebool,V3x_2E0))),s(A_27a,V4x_27_2E0))),s(A_27b,V5x_27_27_2E0)))) <-> s(A_27a,V4x_27_2E0) = s(A_27a,V1v1_2E0) & p(s(tyop_2Emin_2Ebool,V3x_2E0)))) | (all V6x_2E0 all V7x_27_2E0 all V8x_27_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0f_2E0),s(tyop_2Emin_2Ebool,V6x_2E0))),s(A_27a,V7x_27_2E0))),s(A_27b,V8x_27_27_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V6x_2E0)) & s(A_27b,V8x_27_27_2E0) = s(A_27b,V2v2_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Esum_2EIS__SUM__REP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0f_2E0)))))) # label(thm_2Esum_2EIS__SUM__REP) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1216 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Esum_2EREP__sum_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Esum_2EREP__sum_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EREP__sum_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1217 (all A_27a all A_27b all X0_2E0 s(A_27b,c_2Esum_2EOUTR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),A_27b),c_2Esum_2EOUTR_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EOUTR_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1218 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),c_2Esum_2EINR_2E0),s(A_27a,X0_2E0))) = s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1219 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1220 (all A_27a all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27c,A_27d)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1221 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))) -> s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,c_2Esum_2EOUTL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0))))) = s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0))) # label(thm_2Esum_2EINL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1222 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,c_2Esum_2Esum__CASE_2E3(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),A_27c))),c_2Esum_2Esum__CASE_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Esum_2Esum__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1223 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1224 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Esum_2EISR_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EISR_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1225 (all A_27c all A_27d all X0_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Esum_2EINL_2E0),s(A_27c,X0_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1226 (all A_27a all A_27b all A_27c all A_27d all A_27e all A_27f all A_27g all A_27h all V0P_2E0 ((all V10x_2E0 all V11y_2E0 all V12z_2E0 (s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINL_2E1(s(A_27g,V10x_2E0))),s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINR_2E1(s(A_27h,V11y_2E0))))) = s(tyop_2Esum_2Esum(A_27g,A_27h),c_2Esum_2EINR_2E1(s(A_27h,V12z_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0P_2E0)) & s(A_27h,V11y_2E0) = s(A_27h,V12z_2E0))) & (all V7x_2E0 all V8y_2E0 all V9z_2E0 (s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Esum_2EINL_2E1(s(A_27e,V9z_2E0))) = s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Esum_2EINL_2E1(s(A_27e,V7x_2E0))),s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Esum_2EINR_2E1(s(A_27f,V8y_2E0))))) <-> s(A_27e,V7x_2E0) = s(A_27e,V9z_2E0) & p(s(tyop_2Emin_2Ebool,V0P_2E0)))) & (all V4x_2E0 all V5y_2E0 all V6z_2E0 (s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Esum_2EINL_2E1(s(A_27d,V6z_2E0))) = s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Esum_2EINR_2E1(s(A_27c,V4x_2E0))),s(tyop_2Esum_2Esum(A_27d,A_27c),c_2Esum_2EINL_2E1(s(A_27d,V5y_2E0))))) <-> -p(s(tyop_2Emin_2Ebool,V0P_2E0)) & s(A_27d,V5y_2E0) = s(A_27d,V6z_2E0))) & (all V1x_2E0 all V2y_2E0 all V3z_2E0 (s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0P_2E0),s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(s(A_27a,V1x_2E0))),s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINL_2E1(s(A_27b,V2y_2E0))))) = s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(s(A_27a,V3z_2E0))) <-> s(A_27a,V3z_2E0) = s(A_27a,V1x_2E0) & p(s(tyop_2Emin_2Ebool,V0P_2E0)))))) # label(thm_2Esum_2Econd__sum__expand) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1227 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1228 (all A_27c all A_27d all X0_2E0 s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Esum_2EINR_2E0),s(A_27d,X0_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1229 (all A_27e all A_27f all X0_2E0 s(tyop_2Esum_2Esum(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Esum_2Esum(A_27e,A_27f)),c_2Esum_2EINR_2E0),s(A_27f,X0_2E0))) = s(tyop_2Esum_2Esum(A_27e,A_27f),c_2Esum_2EINR_2E1(s(A_27f,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27e_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1230 (all A_27a all A_27b all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)))))) # label(thm_2Esum_2ENOT__ISR__ISL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1231 (all A_27a all A_27b all V0P_2E0 ((all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2x_2E0))))))) & (all V3y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V3y_2E0))))))) <-> (all V1s_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),V1s_2E0))))))) # label(thm_2Esum_2EFORALL__SUM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1232 (all A_27c all X0_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),A_27c),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27c),X0_2E0))) = s(A_27c,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1233 (all A_27a all V0x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))) # label(thm_2Eoption_2ENOT__IS__SOME__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1234 (all A_27a all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Eoption_2ENOT__SOME__NONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1235 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0),s(tyop_2Eoption_2Eoption(A_27c),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2EOPTION__MAP2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTION__MAP2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1236 (all A_27a all A_27b all V0e_2E0 all V1f_2E0 exists V2fn_2E0 ((all V3x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27b),V2fn_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0)))) & s(A_27b,V0e_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27b),V2fn_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))) # label(thm_2Eoption_2Eoption__Axiom) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1237 (all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1238 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__CHOICE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__CHOICE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1239 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),c_2Eoption_2EOPTION__GUARD_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__GUARD_2E1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1240 (all A_27a all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1241 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__IGNORE__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__IGNORE__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1242 (all A_27a all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f623_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) # label(def1_2Ethm_2Eoption_2Esome__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1243 (all A_27a all V0P_2E0 ((all V1opt_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) & (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))))))))) # label(thm_2Eoption_2EFORALL__OPTION) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1244 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(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(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1245 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2m_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0),s(A_27c,V2m_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MCOMP_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0),s(A_27c,V2m_2E0)))) # label(thm_2Eoption_2EOPTION__MCOMP__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1246 (all A_27b all X0_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))) = s(A_27b,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1247 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1248 (all A_27a all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1249 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1250 (all A_27a s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) # label(thm_2Eoption_2ENONE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1251 (all A_27a ((all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) & (all V1P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Eoption_2EOPTION__ALL__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1252 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1253 (all A_27a all A_27b all A_27c all V0v_2E0 all V1o2_2E0 all V2o1_2E0 all V3f_2E0 (s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0v_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V3f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2o1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1o2_2E0))) <-> (exists V4x1_2E0 exists V5x2_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V2o1_2E0) & s(tyop_2Eoption_2Eoption(A_27b),V1o2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V5x2_2E0))) & s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V3f_2E0),s(A_27a,V4x1_2E0))),s(A_27b,V5x2_2E0))) = s(A_27c,V0v_2E0))))) # label(thm_2Eoption_2EOPTION__MAP2__SOME) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1254 (all A_27a all A_27b ((all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) & (all V1f_2E0 all V2x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Eoption_2Eoption(A_27b),V2x_2E0)))))) # label(thm_2Eoption_2EOPTION__APPLY__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1255 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1256 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1257 (all A_27a all A_27b all V0v_2E0 all V1sc_2E0 all V2opt_2E0 all V3nc_2E0 (s(A_27b,V0v_2E0) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V2opt_2E0),s(A_27b,V3nc_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1sc_2E0))) <-> s(A_27b,V0v_2E0) = s(A_27b,V3nc_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V2opt_2E0) | (exists V4x_2E0 (s(A_27b,V0v_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1sc_2E0),s(A_27a,V4x_2E0))) & s(tyop_2Eoption_2Eoption(A_27a),V2opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))))))) # label(thm_2Eoption_2Eoption__case__eq) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1258 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 (s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))) # label(thm_2Eoption_2EOPTION__MAP__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1259 (all A_27a all X0_2E0 all X1_2E0 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)),f674_1_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f674_1_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef674_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1260 (all A_27a all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)) # label(thm_2Eoption_2Eoption__case__ID) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1261 (all A_27a all V0Q_2E0 all V1P_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0)))))))) & ((all V3x_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Eoption_2Esome__intro) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1262 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f605_0_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),f605_0_2E0),s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),X0_2E0)))) # label(arityeq1_2Ef605_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1263 (all A_27a all V0Q_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))))) -> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0)))))))) | (all V3x_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))))) # label(thm_2Eoption_2Esome__elim) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1264 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1265 (all A_27a all X0_2E0 s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),c_2Esum_2EINR_2E0),s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1266 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),c_2Ecombin_2EK_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1267 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1268 (all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1269 (all A_27a all X0_2E0 s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),c_2Eoption_2Eoption__REP_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2Eoption__REP_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1270 (all A_27a all X0_2E0 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)),f674_1_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f674_1_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef674_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1271 (all A_27a all X0_2E0 s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),c_2Esum_2EINL_2E0),s(A_27a,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1272 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1273 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1274 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1275 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 all V2e_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))))),s(A_27b,V2e_2E0))) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0)))) # label(thm_2Eoption_2Eoption__case__compute) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1276 (all A_27a all A_27b all V0x_2E0 all V2f_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V0x_2E0))) = s(A_27b,f667_0_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0)))) # label(def0_2Ethm_2Eoption_2ESOME__APPLY__PERMUTE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1277 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1278 (all A_27a all V0opt_2E0 ((exists V1x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0)))))) # label(thm_2Eoption_2EIS__SOME__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1279 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2e_2E0 ((all V3x_2E0 all V4y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) <-> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0))) & (all V5x_2E0 s(A_27a,V5x_2E0) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5x_2E0)))))) & (all V7x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7x_2E0))) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) & (all V8x_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V8x_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) & (all V13x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V13x_2E0)) & (all V17v_2E0 all V18f_2E0 s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(A_27b,V17v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V18f_2E0))) = s(A_27b,V17v_2E0)) & (all V19x_2E0 all V20v_2E0 all V21f_2E0 s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V19x_2E0))),s(A_27b,V20v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V21f_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V21f_2E0),s(A_27a,V19x_2E0)))) & (all V24f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V24f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) & (all V25x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V25x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V25x_2E0)))))) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) & (all V22f_2E0 all V23x_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V22f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V23x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V22f_2E0),s(A_27a,V23x_2E0)))))) & (all V16x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0)))) -> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V16x_2E0))) & (all V15x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0))))) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V15x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))) & (all V14x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V14x_2E0)))) -> s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V14x_2E0),s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(A_27b,V2e_2E0))) & (all V12x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V12x_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V12x_2E0)) & (all V11x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0)))) -> s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V11x_2E0))))))) & (all V10x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V10x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> -p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V10x_2E0)))))) & (all V9x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V9x_2E0)))) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V9x_2E0))) & s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) & (all V6x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0))) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) # label(thm_2Eoption_2Eoption__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1280 (all A_27a ((all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))))) & s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(thm_2Eoption_2EIS__SOME__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1281 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1282 (all A_27a all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Eoption_2ENOT__NONE__SOME) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1283 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1284 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1285 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1286 (all A_27a all V0y_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,f674_0_2E2(s(A_27a,V0y_2E0),s(A_27a,V1x_2E0)))) <-> s(A_27a,V0y_2E0) = s(A_27a,V1x_2E0))) # label(def1_2Ethm_2Eoption_2Esome__EQ) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1287 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1288 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1289 (all A_27a all V0P_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))))))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) <-> (exists V1opt_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt_2E0))))))) # label(thm_2Eoption_2EEXISTS__OPTION) # label(axiom) # label(non_clause). [assumption]. 107.57/107.62 1290 (all A_27a all V0opt_2E0 all V1opt_27_2E0 all V2P_2E0 all V3P_27_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1opt_27_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) & (all V4x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1opt_27_2E0) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0))))) # label(thm_2Eoption_2EOPTION__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1291 (all A_27a all V0opt_2E0 all V1P_27_2E0 all V2P_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_27_2E0),s(A_27a,V3x_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_27_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0))))))) # label(thm_2Eoption_2EOPTION__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1292 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))))),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27c_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27c_29_29_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1293 (all A_27a all A_27b all X0_2E0 all X1_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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),f667_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(A_27b,f667_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef667_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1294 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2Q_2E0 all V3P_2E0 ((all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0))))))) # label(thm_2Eoption_2EOPTREL__MONO) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1295 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1296 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))))) # label(thm_2Eoption_2ESOME__11) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1297 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2Esome_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1298 (all A_27a all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,f605_0_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),V1x_2E0)))) # label(def0_2Ethm_2Eoption_2Eoption__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1299 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1300 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1301 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1302 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1303 (all A_27a all V0m1_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0m1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),V0m1_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) # label(thm_2Eoption_2EOPTION__CHOICE__NONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1304 (all A_27a all A_27b all V0v_27_2E0 all V1f_27_2E0 all V2M_2E0 all V3M_27_2E0 all V4v_2E0 all V5f_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V2M_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0) & (s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) -> s(A_27b,V0v_27_2E0) = s(A_27b,V4v_2E0)) & (all V6x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(A_27a,V6x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0),s(A_27a,V6x_2E0))))) -> s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V2M_2E0),s(A_27b,V4v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0))) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V3M_27_2E0),s(A_27b,V0v_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0))))) # label(thm_2Eoption_2Eoption__case__cong) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1305 (all A_27a ((all V1r_2E0 (s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),V1r_2E0))))) = s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),V1r_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) & (all V0a_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Eoption_2Eoption__REP_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0a_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),V0a_2E0)))) # label(thm_2Eoption_2Eoption__REP__ABS__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1306 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) & (all V1a_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1a_2E0))))))) -> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0))))))) # label(thm_2Eoption_2Eoption__Induct) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1307 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2y_2E0 ((exists V3x0_2E0 exists V4y0_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) & s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V4y0_2E0))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x0_2E0))),s(A_27b,V4y0_2E0)))))) | s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0) & s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2y_2E0)))))) # label(thm_2Eoption_2EOPTREL__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1308 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool)),f614_0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27c),X1_2E0))) = s(tyop_2Emin_2Ebool,f614_0_2E2(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27c),X1_2E0)))) # label(arityeq2_2Ef614_0_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1309 (all A_27a all X0_2E0 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)),f674_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f674_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef674_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1310 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27c),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__IGNORE__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27c),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__IGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1311 (all A_27b all A_27c all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f614_0_2E2(s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0)))))) # label(def0_2Ethm_2Eoption_2EOPTION__MAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1312 (all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27c),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1313 (all A_27a all A_27b ((all V0f_2E0 all V1x_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0)))))) & (all V2f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0)))) # label(thm_2Eoption_2EOPTION__MAP__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1314 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1315 (all A_27a all A_27b ((all V0f_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) & (all V1x_2E0 all V2f_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2f_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V2f_2E0),s(A_27b,V1x_2E0)))))) # label(thm_2Eoption_2EOPTION__BIND__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1316 (all A_27a all A_27b all A_27c all V0v_2E0 all V1m_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0v_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V1m_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1m_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1m_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) # label(thm_2Eoption_2EOPTION__IGNORE__BIND__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1317 (all A_27a all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1318 (all A_27a all A_27b all V0opt1_2E0 all V1opt2_2E0 all V2f1_2E0 all V3f2_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1opt2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0opt1_2E0) & (all V4x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1opt2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0opt1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1opt2_2E0))))) # label(thm_2Eoption_2EOPTION__MAP__CONG) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1319 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1320 (all A_27a all A_27b ((all V2x_2E0 all V3v_2E0 all V4f_2E0 s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))),s(A_27b,V3v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(A_27a,V2x_2E0)))) & (all V0v_2E0 all V1f_2E0 s(A_27b,V0v_2E0) = s(A_27b,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(A_27b,V0v_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0)))))) # label(thm_2Eoption_2Eoption__case__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1321 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1322 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1323 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1324 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2Eoption__ABS_2E0),s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2Eoption__ABS_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1325 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2Eoption_2EIS__NONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1326 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1327 (all V0b_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD_2E1(s(tyop_2Emin_2Ebool,V0b_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ENONE_2E0)))) # label(thm_2Eoption_2EOPTION__GUARD__COND) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1328 (all A_27a all V0opt_2E0 ((exists V1x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0)))) | s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0))) # label(thm_2Eoption_2Eoption__CASES) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1329 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1330 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MAP2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTION__MAP2_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1331 (all A_27a all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__ABS_2E1(s(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27a,V0x_2E0)))))) # label(thm_2Eoption_2ESOME__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1332 (all A_27a all A_27b all A_27c all V0x_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27c)),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1g_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1g_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) # label(thm_2Eoption_2EOPTION__APPLY__o) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1333 (all A_27a all A_27b all A_27c all V0x_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) # label(thm_2Eoption_2EOPTION__MAP__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1334 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f623_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f623_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef623_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1335 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1336 (all A_27a all V0y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f674_0_2E1(s(A_27a,V0y_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f674_1_2E1(s(A_27a,V0y_2E0))))))) # label(thm_2Eoption_2Esome__EQ) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1337 (all A_27a all A_27b all V0x_2E0 all V1g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1g_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) # label(thm_2Eoption_2EIS__SOME__BIND) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1338 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1339 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))))),c_2Eoption_2EOPTION__APPLY_2E0),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1340 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 ((s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0)) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V0x_2E0)))) # label(thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1341 (all A_27a all V0y_2E0 all V1x_2E0 all V2P_2E0 ((s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0) & -p(s(tyop_2Emin_2Ebool,V2P_2E0)) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0)))) & (s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0) & p(s(tyop_2Emin_2Ebool,V2P_2E0)) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,V2P_2E0))) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> -p(s(tyop_2Emin_2Ebool,V2P_2E0))))) # label(thm_2Eoption_2EIF__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1342 (all A_27a s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f673_0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)) # label(thm_2Eoption_2Esome__F) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1343 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1344 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f623_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f623_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef623_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1345 (all A_27a all A_27b all V0y_2E0 all V1p_2E0 all V2f_2E0 ((s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0))) <-> (exists V3x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) & s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0),s(A_27a,V3x_2E0))))) | s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0)) & (s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) <-> (exists V4x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1p_2E0) & s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Eoption_2EOPTION__BIND__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1346 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__JOIN_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1347 (all A_27a all V0y_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f674_1_2E2(s(A_27a,V0y_2E0),s(A_27a,V2x_2E0)))) <-> s(A_27a,V0y_2E0) = s(A_27a,V2x_2E0))) # label(def0_2Ethm_2Eoption_2Esome__EQ) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1348 (all A_27a all A_27b all V0o1_2E0 all V1o2_2E0 all V2f1_2E0 all V3f2_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0o1_2E0) & (all V4x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0) -> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f1_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3f2_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1o2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V3f2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V0o1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2f1_2E0))))) # label(thm_2Eoption_2EOPTION__BIND__cong) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1349 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool))),c_2Eoption_2EOPTREL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1350 (all A_27a all A_27b all V0m1_2E0 all V1m2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),V0m1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),V0m1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Eoption_2Eoption(A_27a),V1m2_2E0)))))) # label(thm_2Eoption_2EOPTION__IGNORE__BIND__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1351 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),f667_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),f667_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef667_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1352 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 all V2y_2E0 (s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V2y_2E0))) <-> (exists V3z_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3z_2E0))) = s(A_27b,V2y_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3z_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))))) # label(thm_2Eoption_2EOPTION__MAP__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1353 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,f623_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))))) # label(def0_2Ethm_2Eoption_2Esome__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1354 (all A_27a all V0opt_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) | (exists V1x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0opt_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0)))))) # label(thm_2Eoption_2Eoption__nchotomy) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1355 (all A_27a all V0x_2E0 all V1X_2E0 all V2P_2E0 ((s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) <-> (p(s(tyop_2Emin_2Ebool,V2P_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0)))))) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) <-> p(s(tyop_2Emin_2Ebool,V2P_2E0)) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0)) & (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0))) <-> s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0))) & -p(s(tyop_2Emin_2Ebool,V2P_2E0))) & ((p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0)))) -> p(s(tyop_2Emin_2Ebool,V2P_2E0))) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1X_2E0)))))) # label(thm_2Eoption_2EIF__NONE__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1356 (all A_27a all V0P_2E0 ((all V1a_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1a_2E0))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) -> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0))))))) # label(thm_2Eoption_2Eoption__induction) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1357 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1358 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),c_2Eoption_2EOPTREL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1359 (all A_27a ((all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) # label(thm_2Eoption_2EOPTION__JOIN__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1360 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1361 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f614_0_2E2(s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0),s(A_27b,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27b),V1x_2E0))))),s(A_27c,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27c),V2y_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) # label(thm_2Eoption_2EOPTION__MAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1362 (all A_27a all V0x_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0)))) # label(thm_2Eoption_2Eoption__case__SOME__ID) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1363 (all A_27a all A_27b all V0y_2E0 all V1m2_2E0 all V2m1_2E0 ((s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0) | s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0)) & ((exists V3x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) & s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0))) <-> s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V2m1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V1m2_2E0)))))) # label(thm_2Eoption_2EOPTION__IGNORE__BIND__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1364 (all A_27a all A_27b all A_27c all A_27d all V0h_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),V2f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0h_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0h_2E0)))))) # label(thm_2Eoption_2EOPTION__MCOMP__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1365 (all A_27a all V0P_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f623_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f623_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Eoption_2Esome__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1366 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1367 (all A_27a all A_27b all A_27c all V0x1_2E0 all V1x2_2E0 all V2y1_2E0 all V3y2_2E0 all V4f1_2E0 all V5f2_2E0 ((all V6x_2E0 all V7y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),V1x2_2E0) & s(tyop_2Eoption_2Eoption(A_27b),V3y2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V7y_2E0))) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V4f1_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f2_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))))) & s(tyop_2Eoption_2Eoption(A_27b),V3y2_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V2y1_2E0) & s(tyop_2Eoption_2Eoption(A_27a),V0x1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V1x2_2E0) -> s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f2_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x2_2E0),s(tyop_2Eoption_2Eoption(A_27b),V3y2_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V4f1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V2y1_2E0))))) # label(thm_2Eoption_2EOPTION__MAP2__cong) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1368 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27c))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1369 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f673_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f673_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef673_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1370 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f674_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = 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)),f674_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef674_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1371 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__IGNORE__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__IGNORE__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__IGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1372 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1373 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))))) # label(thm_2Eoption_2ETHE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1374 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),f667_0_2E1(s(A_27a,V0x_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1f_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27a,A_27b)),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))))) # label(thm_2Eoption_2ESOME__APPLY__PERMUTE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1375 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,f673_0_2E1(s(A_27a,V0x_2E0)))) # label(def0_2Ethm_2Eoption_2Esome__F) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1376 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1377 (all A_27a ((all V0m2_2E0 s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0)))) & (all V1x_2E0 all V2m2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V2m2_2E0)))))) # label(thm_2Eoption_2EOPTION__CHOICE__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.63 1378 (all A_27a (s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) & (all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0x_2E0)))))))) # label(thm_2Eoption_2EIS__NONE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1379 (all A_27a all A_27b all A_27c all V0y_2E0 all V1x_2E0 all V2f_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0y_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1x_2E0))),s(A_27c,V0y_2E0))))) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,V0y_2E0))))) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) # label(thm_2Eoption_2EOPTION__MAP2__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1380 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1381 (all A_27a all V0R_2E0 ((all V1x_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0))))) -> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0),s(tyop_2Eoption_2Eoption(A_27a),V2x_2E0))))))) # label(thm_2Eoption_2EOPTREL__refl) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1382 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1383 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27c),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1384 (all A_27a all A_27b all A_27c all A_27d all V0g_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),V0g_2E0) = s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),V0g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2ESOME_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f_2E0))))) # label(thm_2Eoption_2EOPTION__MCOMP__ID) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1385 (all A_27c all X0_2E0 s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E1(s(A_27c,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2ESOME_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1386 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1387 (all A_27a all V0m2_2E0 all V1m1_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1m1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__CHOICE_2E2(s(tyop_2Eoption_2Eoption(A_27a),V1m1_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0m2_2E0))))) # label(thm_2Eoption_2EOPTION__CHOICE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1388 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f623_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,f623_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef623_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1389 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(A_27b,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1390 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))),s(A_27c,X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MCOMP_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27b)),X1_2E0),s(A_27c,X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2EOPTION__MCOMP_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1391 (all A_27a all A_27b all A_27c all V0o2_2E0 all V1o1_2E0 all V2f_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V1o1_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) | s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27b),V0o2_2E0) <-> s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1o1_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0o2_2E0))))) # label(thm_2Eoption_2EOPTION__MAP2__NONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1392 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTION__ALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTION__ALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__ALL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1393 (all A_27a exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),f605_0_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Esum_2Esum(A_27a,tyop_2Eone_2Eone)),V0rep_2E0))))) # label(thm_2Eoption_2Eoption__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1394 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),c_2Eoption_2ESOME_2E0),s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME_2E1(s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1395 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1396 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0x_2E0)))))) # label(thm_2Eoption_2ESOME__SOME__APPLY) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1397 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))) # label(thm_2Eoption_2EIS__SOME__MAP) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1398 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1399 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1400 (all V0b_2E0 ((s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD_2E1(s(tyop_2Emin_2Ebool,V0b_2E0))) <-> -p(s(tyop_2Emin_2Ebool,V0b_2E0))) & (s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2EOPTION__GUARD_2E1(s(tyop_2Emin_2Ebool,V0b_2E0))) <-> p(s(tyop_2Emin_2Ebool,V0b_2E0))))) # label(thm_2Eoption_2EOPTION__GUARD__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1401 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))) # label(thm_2Eoption_2EOPTION__MAP__CASE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1402 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1403 (all A_27a all V0x_2E0 all V1y_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),V0x_2E0))) <-> s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),V0x_2E0) = s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1y_2E0))))))) # label(thm_2Eoption_2EOPTION__JOIN__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1404 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1405 (all A_27a all V0x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V0x_2E0)))))) # label(thm_2Eoption_2EIS__NONE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1406 (all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27d)),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1407 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1408 (all A_27a all X0_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1409 (all A_27a all A_27b all V0option_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),A_27b)),V0option_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0))))))) # label(thm_2Eoption_2Edatatype__option) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1410 (all A_27a all A_27b all A_27c all V0y_2E0 all V1x_2E0 all V2f_2E0 s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__MAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2EOPTION__APPLY_2E2(s(tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,A_27c)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Eoption_2Eoption(A_27a),V1x_2E0))),s(tyop_2Eoption_2Eoption(A_27b),V0y_2E0)))) # label(thm_2Eoption_2EOPTION__APPLY__MAP2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1411 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1412 (all A_27a all A_27b all V0d_2E0 all V1c_2E0 all V2b_2E0 all V3a_2E0 all V4R2_2E0 all V5R1_2E0 (s(A_27a,V3a_2E0) = s(A_27a,V1c_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R2_2E0),s(A_27b,V2b_2E0))),s(A_27b,V0d_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)),V5R1_2E0),s(A_27a,V3a_2E0))),s(A_27a,V1c_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3a_2E0),s(A_27b,V2b_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1c_2E0),s(A_27b,V0d_2E0)))))))) # label(thm_2Epair_2ELEX__DEF__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1413 (all A_27a all A_27b all V0P_2E0 ((exists V1x_2E0 exists V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f718_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))))) # label(thm_2Epair_2EPEXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1414 (all A_27a all A_27b all A_27c all A_27d all V0P_2E0 all V2N_2E0 all V5x_2E0 all V6y_2E0 s(A_27d,f724_1_2E4(s(tyop_2Emin_2Efun(A_27c,A_27d),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0),s(A_27a,V5x_2E0),s(A_27b,V6y_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V0P_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0),s(A_27a,V5x_2E0))),s(A_27b,V6y_2E0)))))) # label(def0_2Ethm_2Epair_2ELET2__RAND) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1415 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,c_2Epair_2ECURRY_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epair_2ECURRY_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1416 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f693_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))))),f693_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef693_1_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1417 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1418 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f717_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f717_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef717_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1419 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f693_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),f693_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef693_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1420 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1421 (all A_27a all A_27b all A_27c all V2N_2E0 all V3x_2E0 all V4y_2E0 s(A_27c,f724_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0),s(A_27a,V3x_2E0),s(A_27b,V4y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0)))) # label(def1_2Ethm_2Epair_2ELET2__RAND) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1422 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f708_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f708_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0)))) # label(arityeq1_2Ef708_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1423 (all A_27a all A_27b all A_27c all A_27d all V0p_2E0 all V1f_2E0 all V2g_2E0 s(A_27d,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0)))))) # label(thm_2Epair_2ESND__PAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1424 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0))),s(A_27d,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1425 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1426 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),f730_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool)),f730_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef730_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1427 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 all V2p_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_2C_2E2(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))))),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0)))))))) # label(thm_2Epair_2EPAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1428 (all A_27a all A_27b all A_27c all V0P_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,f730_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),f730_2_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0)))))) # label(def1_2Ethm_2Epair_2EPAIR__FUN__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1429 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1430 (all A_27a all A_27b all V0P_2E0 ((all V2p__1_2E0 all V3p__2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2p__1_2E0),s(A_27b,V3p__2_2E0))))))) <-> (all V1p_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))))) # label(thm_2Epair_2EFORALL__PROD) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1431 (all A_27a all A_27b all X0_2E0 s(A_27b,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1432 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f717_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,f717_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef717_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1433 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1434 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1435 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1436 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 all X5_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))))),f693_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27b,X3_2E0))),s(A_27a,X4_2E0))),s(A_27b,X5_2E0))) = s(tyop_2Emin_2Ebool,f693_1_2E6(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0),s(A_27b,X3_2E0),s(A_27a,X4_2E0),s(A_27b,X5_2E0)))) # label(arityeq6_2Ef693_1_2E6_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1437 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 all V2y_2E0 s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0)))) # label(thm_2Epair_2EUNCURRY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1438 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0g_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V1f_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0g_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V1f_2E0))))) # label(thm_2Epair_2ECURRY__ONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1439 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)))),c_2Epair_2E_23_23_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Epair_2E_23_23_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1440 (all A_27a all A_27b all A_27c all A_27d all V0x_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),V1f_2E0))),s(A_27d,V0x_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),V1f_2E0))),s(A_27d,V0x_2E0)))) # label(thm_2Epair_2EC__UNCURRY__L) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1441 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27d_2CA_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1442 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f718_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f718_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef718_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1443 (all A_27b all A_27c all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2Eo_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1444 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1445 (all A_27b all A_27c all X0_2E0 s(A_27b,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1446 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(A_27d,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1447 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1448 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2b_2E0 all V3a_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3a_2E0),s(A_27b,V2b_2E0))) <-> s(A_27b,V2b_2E0) = s(A_27b,V0y_2E0) & s(A_27a,V1x_2E0) = s(A_27a,V3a_2E0))) # label(thm_2Epair_2EPAIR__EQ) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1449 (all A_27a all A_27b exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f682_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0rep_2E0))))) # label(thm_2Epair_2Eprod__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1450 (all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27c,A_27d))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(A_27d,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1451 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1452 (all A_27a all A_27b all V0a_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2ESWAP_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V0a_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V0a_2E0))),s(A_27b,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V0a_2E0)))))) # label(thm_2Epair_2ESWAP__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1453 (all A_27a1 all A_27a2 all A_27b all A_27c all V1N_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),f725_0_2E3(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0),s(A_27a1,V3x_2E0),s(A_27a2,V4y_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0),s(A_27a1,V3x_2E0))),s(A_27a2,V4y_2E0)))) # label(def1_2Ethm_2Epair_2ELET2__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1454 (all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1455 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f719_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f719_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef719_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1456 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1457 (all A_27a all A_27b all V0P_2E0 ((exists V2p__1_2E0 exists V3p__2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2p__1_2E0),s(A_27b,V3p__2_2E0))))))) <-> (exists V1p_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))))) # label(thm_2Epair_2EEXISTS__PROD) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1458 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0)))))) # label(thm_2Epair_2EFORALL__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1459 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1460 (all A_27a all A_27b all V0P_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0))) = s(tyop_2Emin_2Ebool,f718_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V3x_2E0),s(A_27b,V4y_2E0)))) # label(def0_2Ethm_2Epair_2EPEXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1461 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1462 (all A_27a all A_27b all V0P_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f720_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Epair_2EELIM__PFORALL__EVAL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1463 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ERPROD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Epair_2ERPROD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2ERPROD_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1464 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1465 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1466 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1467 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))))))) # label(thm_2Epair_2Esymmetric__LEX) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1468 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1469 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27d_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1470 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 all V2a_2E0 all V3b_2E0 (p(s(tyop_2Emin_2Ebool,f684_0_2E4(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0),s(A_27a,V2a_2E0),s(A_27b,V3b_2E0)))) <-> s(A_27a,V2a_2E0) = s(A_27a,V0x_2E0) & s(A_27b,V3b_2E0) = s(A_27b,V1y_2E0))) # label(def0_2Ethm_2Epair_2ECOMMA__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1471 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Epair_2EFST) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1472 (all A_27a all A_27b all A_27c all V0y_2E0 all V1x_2E0 all V2f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1x_2E0))),s(A_27c,V0y_2E0))) = s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V1x_2E0),s(A_27c,V0y_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0)))) # label(thm_2Epair_2Epair__case__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1473 (all A_27a all A_27b all V0R1_2E0 all V2s_2E0 all V1R2_2E0 all V3t_2E0 all V4u_2E0 all V5v_2E0 (p(s(tyop_2Emin_2Ebool,f693_1_2E6(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0),s(A_27a,V4u_2E0),s(A_27b,V5v_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0))),s(A_27b,V5v_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)),V0R1_2E0),s(A_27a,V2s_2E0))),s(A_27a,V4u_2E0)))))) # label(def0_2Ethm_2Epair_2ERPROD__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1474 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2s_2E0 all V3t_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f693_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f693_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2s_2E0),s(A_27b,V3t_2E0)))) # label(def1_2Ethm_2Epair_2ERPROD__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1475 (all A_27a all A_27b all X0_2E0 s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1476 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2Q_2E0 all V3P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27b,V0y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V1x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0)))))))) # label(thm_2Epair_2EPROD__ALL__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1477 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1478 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 all V2a_2E0 all V3b_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2a_2E0),s(A_27b,V3b_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))) <-> s(A_27b,V3b_2E0) = s(A_27b,V1y_2E0) & s(A_27a,V0x_2E0) = s(A_27a,V2a_2E0))) # label(thm_2Epair_2ECLOSED__PAIR__EQ) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1479 (all A_27a all A_27b all V0x_2E0 exists V1q_2E0 exists V2r_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1q_2E0),s(A_27b,V2r_2E0)))) # label(thm_2Epair_2EABS__PAIR__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1480 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f693_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),f693_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef693_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1481 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EPROD__ALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Epair_2EPROD__ALL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1482 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27c_29_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1483 (all A_27a all A_27b all V0P_2E0 ((exists V1p_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))))) <-> (exists V2p1_2E0 exists V3p2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V2p1_2E0))),s(A_27b,V3p2_2E0))))))) # label(thm_2Epair_2EELIM__PEXISTS) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1484 (all A_27a all A_27b all A_27c all V0p_2E0 all V1f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0),s(A_27b,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27c),V0p_2E0))))),s(A_27c,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27c),V0p_2E0))))) = s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),V0p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0)))) # label(thm_2Epair_2Epair__CASE__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.64 1485 (all A_27a all A_27b all A_27c all V0f_27_2E0 all V1M_2E0 all V2M_27_2E0 all V3f_2E0 (s(tyop_2Epair_2Eprod(A_27b,A_27c),V2M_27_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27c),V1M_2E0) & (all V4x_2E0 all V5y_2E0 (s(tyop_2Epair_2Eprod(A_27b,A_27c),V2M_27_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V4x_2E0),s(A_27c,V5y_2E0))) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_27_2E0),s(A_27b,V4x_2E0))),s(A_27c,V5y_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V3f_2E0),s(A_27b,V4x_2E0))),s(A_27c,V5y_2E0))))) -> s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),V2M_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_27_2E0))) = s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),V1M_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V3f_2E0))))) # label(thm_2Epair_2Epair__case__cong) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1486 (all A_27b all A_27c all X0_2E0 s(A_27c,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1487 (all A_27a all A_27b all V0p_2E0 all V1Q_27_2E0 all V2Q_2E0 all V3P_27_2E0 all V4P_2E0 ((all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27b,V6y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_27_2E0),s(A_27b,V6y_2E0)))))) & (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(A_27a,V5x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V5x_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))))))) # label(thm_2Epair_2EPROD__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1488 (all A_27a all A_27b all V0P_2E0 ((all V2p1_2E0 all V3p2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V2p1_2E0))),s(A_27b,V3p2_2E0))))) <-> (all V1p_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))))))) # label(thm_2Epair_2EELIM__PFORALL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1489 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f718_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f718_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef718_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1490 (all A_27a all A_27b all V0P_2E0 ((all V1p__1_2E0 all V2p__2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1p__1_2E0),s(A_27b,V2p__2_2E0))))))) -> (all V3p_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3p_2E0))))))) # label(thm_2Epair_2Epair__induction) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1491 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1492 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Epair_2ELEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2ELEX_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1493 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27d_29_2Ctyop_2Emin_2Efun_28A_27b_2CA_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27d_2CA_27c_29_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1494 (all A_27a all A_27b all A_27c all V0y_2E0 all V1x_2E0 all V2f_2E0 s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V1x_2E0),s(A_27c,V0y_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V1x_2E0))),s(A_27c,V0y_2E0)))) # label(thm_2Epair_2Epair__case__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1495 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1496 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))))))) # label(thm_2Epair_2Etransitive__LEX) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1497 (all A_27a all A_27b all A_27c all V0f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0f_2E0)) # label(thm_2Epair_2EUNCURRY__CURRY__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1498 (all A_27a all A_27b all A_27c all V0f_2E0 exists V1fn_2E0 all V2x_2E0 all V3y_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V1fn_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) # label(thm_2Epair_2Epair__Axiom) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1499 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1500 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1501 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Epair_2ELEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X3_2E0)))) # label(arityeq4_2Ec_2Epair_2ELEX_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1502 (all A_27a all A_27b all V0P_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V2x_2E0))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f719_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))))) # label(thm_2Epair_2EELIM__PEXISTS__EVAL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1503 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Esymmetric_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1504 (all A_27a all A_27b all A_27c all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0)) # label(thm_2Epair_2ECURRY__UNCURRY__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1505 (all A_27a1 all A_27a2 all A_27b all A_27c all V0M_2E0 all V1N_2E0 all V2b_2E0 s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),f725_1_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0),s(A_27b,V2b_2E0))))),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),V0M_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),f725_0_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0))))),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),V0M_2E0))),s(A_27b,V2b_2E0)))) # label(thm_2Epair_2ELET2__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1506 (all A_27a1 all A_27a2 all A_27b all A_27c all V1N_2E0 all V2b_2E0 all V5x_2E0 all V6y_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0),s(A_27a1,V5x_2E0))),s(A_27a2,V6y_2E0))),s(A_27b,V2b_2E0))) = s(A_27c,f725_1_2E4(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),V1N_2E0),s(A_27b,V2b_2E0),s(A_27a1,V5x_2E0),s(A_27a2,V6y_2E0)))) # label(def0_2Ethm_2Epair_2ELET2__RATOR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1507 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EABS__prod_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f684_0_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0)))) # label(thm_2Epair_2ECOMMA__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1508 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Esymmetric_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1509 (all A_27a all A_27b all A_27c all V0P_2E0 all V1f_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V1f_2E0))) = s(tyop_2Emin_2Ebool,f730_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V1f_2E0)))) # label(def2_2Ethm_2Epair_2EPAIR__FUN__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1510 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1511 (all A_27a all A_27b all V0p_2E0 all V1q_2E0 (s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1q_2E0))) & s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1q_2E0))) = s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))) <-> s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V1q_2E0))) # label(thm_2Epair_2EPAIR__FST__SND__EQ) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1512 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f684_0_2E4(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(A_27a,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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f684_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef684_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1513 (all A_27a all A_27b all A_27c all V0v_2E0 all V1p_2E0 all V2f_2E0 ((exists V3x_2E0 exists V4y_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0),s(A_27b,V3x_2E0))),s(A_27c,V4y_2E0))) = s(A_27a,V0v_2E0) & s(tyop_2Epair_2Eprod(A_27b,A_27c),V1p_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V3x_2E0),s(A_27c,V4y_2E0))))) <-> s(A_27a,V0v_2E0) = s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),V1p_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2f_2E0))))) # label(thm_2Epair_2Epair__case__eq) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1514 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0)))))))) # label(thm_2Epair_2EPROD__ALL__def) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1515 (all A_27a all A_27b all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1516 (all A_27a all A_27b ((all V1r_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1r_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epair_2EREP__prod_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EABS__prod_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1r_2E0))))) <-> (exists V2x_2E0 exists V3y_2E0 all V4x_27_2E0 all V5x_27_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1r_2E0),s(A_27a,V4x_27_2E0))),s(A_27b,V5x_27_27_2E0)))) <-> s(A_27b,V5x_27_27_2E0) = s(A_27b,V3y_2E0) & s(A_27a,V4x_27_2E0) = s(A_27a,V2x_2E0))))) & (all V0a_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),V0a_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EABS__prod_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epair_2EREP__prod_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0a_2E0)))))))) # label(thm_2Epair_2EABS__REP__prod) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1517 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f719_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f719_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef719_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1518 (all A_27a all A_27b all V0R1_2E0 all V2s_2E0 all V1R2_2E0 all V3t_2E0 all V4u_2E0 all V5v_2E0 (p(s(tyop_2Emin_2Ebool,f692_1_2E6(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0),s(A_27a,V4u_2E0),s(A_27b,V5v_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0))),s(A_27b,V5v_2E0)))) & s(A_27a,V4u_2E0) = s(A_27a,V2s_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)),V0R1_2E0),s(A_27a,V2s_2E0))),s(A_27a,V4u_2E0)))))) # label(def0_2Ethm_2Epair_2ELEX__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1519 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),f725_0_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c)))),f725_0_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0)))) # label(arityeq1_2Ef725_0_2E1_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1520 (all A_27a1 all A_27a2 all A_27c all X0_2E0 all X1_2E0 s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),X0_2E0),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a1_2CA_27a2_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1521 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f724_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f724_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0)))) # label(arityeq1_2Ef724_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1522 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f692_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),f692_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef692_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1523 (all A_27a all A_27b all V0P_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Emin_2Ebool,f717_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V3x_2E0),s(A_27b,V4y_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0)))) # label(def0_2Ethm_2Epair_2EPFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1524 (all A_27a all A_27b all V0R_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ERPROD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0)))))))) # label(thm_2Epair_2EWF__RPROD) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1525 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1526 (all A_27a all A_27b all V0y_2E0 all V1p_2E0 ((exists V2x_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27a),V1p_2E0) = s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V2x_2E0),s(A_27a,V0y_2E0)))) <-> s(A_27a,V0y_2E0) = s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V1p_2E0))))) # label(thm_2Epair_2ESND__EQ__EQUIV) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1527 (all A_27a all A_27b all X0_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2EABS__prod_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EABS__prod_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EABS__prod_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1528 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f692_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))))) # label(thm_2Epair_2ELEX__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1529 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2Eo_2E1_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27d_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1530 (all A_27a all A_27b all A_27c all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),f730_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),f730_1_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Epair_2EPAIR__FUN__THM) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1531 (all A_27a all A_27b all A_27c all V0f_27_2E0 all V1f_2E0 all V2M_27_2E0 all V3M_2E0 ((all V4x_2E0 all V5y_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27b,V5y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V2M_27_2E0) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_27_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0))))) & s(tyop_2Epair_2Eprod(A_27a,A_27b),V3M_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V2M_27_2E0) -> s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2M_27_2E0))) = s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3M_2E0))))) # label(thm_2Epair_2EUNCURRY__CONG) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1532 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool)),f730_1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),f730_1_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef730_1_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1533 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27d,f724_1_2E4(s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)))),f724_1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef724_1_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1534 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))))) # label(thm_2Epair_2Ereflexive__LEX) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1535 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 all X5_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))))),f692_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27b,X3_2E0))),s(A_27a,X4_2E0))),s(A_27b,X5_2E0))) = s(tyop_2Emin_2Ebool,f692_1_2E6(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0),s(A_27b,X3_2E0),s(A_27a,X4_2E0),s(A_27b,X5_2E0)))) # label(arityeq6_2Ef692_1_2E6_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1536 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1537 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1538 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epair_2EREP__prod_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2EREP__prod_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EREP__prod_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1539 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1540 (all A_27a all A_27b all V0P_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f719_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Epair_2EELIM__PEXISTS__EVAL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1541 (all A_27a all A_27b all A_27c all V0pair_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),A_27c),V0pair_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0))))))) # label(thm_2Epair_2Edatatype__pair) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1542 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1543 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1544 (all A_27a all A_27b all V0p_2E0 all V1p_27_2E0 all V2P_2E0 all V3P_27_2E0 all V4Q_2E0 all V5Q_27_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0) & (all V6x_2E0 all V7y_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27b,V7y_2E0))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V6x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V6x_2E0))))) & (all V8x_2E0 all V9y_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V8x_2E0),s(A_27b,V9y_2E0))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V9y_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Q_27_2E0),s(A_27b,V9y_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5Q_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2EPROD__ALL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))))) # label(thm_2Epair_2EPROD__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1545 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 all V2y_2E0 s(A_27c,c_2Epair_2ECURRY_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0f_2E0),s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0)))))) # label(thm_2Epair_2ECURRY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1546 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27c,f725_1_2E4(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27b,X1_2E0),s(A_27a1,X2_2E0),s(A_27a2,X3_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a2,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)))),f725_1_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a1,X2_2E0))),s(A_27a2,X3_2E0)))) # label(arityeq4_2Ef725_1_2E4_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1547 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1548 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1549 (all A_27a all A_27b all X0_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2ESWAP_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2ESWAP_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESWAP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1550 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1551 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1552 (all A_27c all A_27d all X0_2E0 s(A_27d,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),A_27d),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1553 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a1,A_27a2),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a1_2CA_27a2_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1554 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2s_2E0 all V3t_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f692_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27a,V2s_2E0),s(A_27b,V3t_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f692_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V3t_2E0)))))) # label(def1_2Ethm_2Epair_2ELEX__DEF) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1555 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1556 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,f724_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f724_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef724_0_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1557 (all A_27a all A_27b all A_27c all A_27d all V0p_2E0 all V1f_2E0 all V2g_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0))))) = s(A_27c,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0p_2E0)))))) # label(thm_2Epair_2EFST__PAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1558 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1559 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Emin_2Efun_28A_27b_2CA_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27d_2CA_27c_29_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1560 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1561 (all A_27a all A_27b all V0P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f720_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))) <-> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V2x_2E0))))))))) # label(thm_2Epair_2EELIM__PFORALL__EVAL) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1562 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2EUNCURRY_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1563 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1564 (all A_27a all A_27b all A_27c all A_27d all V0g_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V0g_2E0)))))) # label(thm_2Epair_2ES__UNCURRY__R) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1565 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27d,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27d,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1566 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1567 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1568 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))),f730_2_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),f730_2_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef730_2_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1569 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1570 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f684_0_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f684_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef684_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1571 (all A_27a all A_27b all A_27c all V0f_2E0 all V1v_2E0 s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0)))))) # label(thm_2Epair_2EUNCURRY__VAR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1572 (all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27b,A_27d))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27d,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1573 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f720_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f720_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef720_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1574 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),f724_1_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)))),f724_1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ef724_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1575 (all A_27a all A_27b all A_27c all A_27d all V0g_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(A_27d,A_27c),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V0g_2E0)))))) # label(thm_2Epair_2Eo__UNCURRY__R) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1576 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1577 (all A_27a all A_27b all V0x_2E0 exists V1q_2E0 exists V2r_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1q_2E0),s(A_27b,V2r_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0)) # label(thm_2Epair_2Epair__CASES) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1578 (all A_27a1 all A_27a2 all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),A_27c)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1579 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1580 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.57/107.65 1581 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1582 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,f708_0_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),f708_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef708_0_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1583 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)))),c_2Epair_2E_23_23_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27c),X2_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Epair_2E_23_23_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1584 (all A_27a all A_27b all A_27c all V0P_2E0 all V1x_2E0 s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f708_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0P_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0)))) # label(thm_2Epair_2ELAMBDA__PROD) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1585 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,f682_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f682_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef682_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1586 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27b,V1y_2E0) = s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0)))))) # label(thm_2Epair_2ESND) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1587 (all A_27a all A_27b all A_27c all V0f_2E0 all V1x_2E0 s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0)))))) # label(thm_2Epair_2EELIM__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1588 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1589 (all A_27a all A_27b all A_27c all A_27d all V0P_2E0 all V1M_2E0 all V2N_2E0 s(A_27d,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),f724_1_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0))))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1M_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V0P_2E0),s(A_27c,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),f724_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2N_2E0))))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1M_2E0)))))) # label(thm_2Epair_2ELET2__RAND) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1590 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a1,A_27a2),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1591 (all A_27a all A_27b all V0x_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0)) # label(thm_2Epair_2EPAIR) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1592 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1593 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool)),f730_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Ebool,f730_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ef730_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.57/107.66 1594 (all A_27a all A_27b all A_27c all V2p_2E0 all V3a_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0))),s(A_27a,V3a_2E0))),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0))),s(A_27a,V3a_2E0))))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),f730_2_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),V2p_2E0),s(A_27a,V3a_2E0)))) # label(def0_2Ethm_2Epair_2EPAIR__FUN__THM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1595 (all A_27a all A_27b all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1596 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2R4_2E0 all V3R3_2E0 all V4R2_2E0 all V5R1_2E0 ((all V6x_2E0 all V7y_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)),V5R1_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_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)),V4R2_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))) & (all V8x_2E0 all V9y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R3_2E0),s(A_27b,V8x_2E0))),s(A_27b,V9y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R4_2E0),s(A_27b,V8x_2E0))),s(A_27b,V9y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R3_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R4_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0y_2E0))))))) # label(thm_2Epair_2ELEX__MONO) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1597 (all A_27a all A_27b all X0_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1598 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0)))))))) # label(thm_2Epair_2Etotal__LEX) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1599 (all A_27a all A_27b all V1p_2E0 (p(s(tyop_2Emin_2Ebool,f682_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1p_2E0)))) <-> (exists V2x_2E0 exists V3y_2E0 all V4x_27_2E0 all V5x_27_27_2E0 (s(A_27a,V2x_2E0) = s(A_27a,V4x_27_2E0) & s(A_27b,V5x_27_27_2E0) = s(A_27b,V3y_2E0) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1p_2E0),s(A_27a,V4x_27_2E0))),s(A_27b,V5x_27_27_2E0)))))))) # label(def0_2Ethm_2Epair_2Eprod__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1600 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1601 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))),f730_2_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),f730_2_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0)))) # label(arityeq1_2Ef730_2_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1602 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f730_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Ebool)),f730_1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),X1_2E0)))) # label(arityeq2_2Ef730_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1603 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1604 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_2C_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V1g_2E0),s(A_27c,V3y_2E0))))) = s(tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epair_2E_23_23_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V1g_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27c,V3y_2E0)))))) # label(thm_2Epair_2EPAIR__MAP__THM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1605 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27a,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),A_27a)),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1606 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 all V2v1_2E0 all V3v2_2E0 all V4R1_27_2E0 all V5R2_27_2E0 all V6v1_27_2E0 all V7v2_27_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V2v1_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V6v1_27_2E0) & s(tyop_2Epair_2Eprod(A_27a,A_27b),V7v2_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v2_2E0) & (all V12a_2E0 all V13b_2E0 all V14c_2E0 all V15d_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V7v2_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V14c_2E0),s(A_27b,V15d_2E0))) & s(A_27a,V12a_2E0) = s(A_27a,V14c_2E0) & s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V12a_2E0),s(A_27b,V13b_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V6v1_27_2E0) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5R2_27_2E0),s(A_27b,V13b_2E0))),s(A_27b,V15d_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,V13b_2E0))),s(A_27b,V15d_2E0))))) & (all V8a_2E0 all V9b_2E0 all V10c_2E0 all V11d_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),V6v1_27_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V8a_2E0),s(A_27b,V9b_2E0))) & s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V10c_2E0),s(A_27b,V11d_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V7v2_27_2E0) -> 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)),V4R1_27_2E0),s(A_27a,V8a_2E0))),s(A_27a,V10c_2E0))) = 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)),V0R1_2E0),s(A_27a,V8a_2E0))),s(A_27a,V10c_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2v1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2ELEX_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R1_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5R2_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V6v1_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V7v2_27_2E0))))) # label(thm_2Epair_2ELEX__CONG) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1607 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1608 (all A_27a all A_27b all A_27c all V0P_2E0 all V2p1_2E0 all V3p2_2E0 s(A_27c,f708_0_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0P_2E0),s(A_27a,V2p1_2E0),s(A_27b,V3p2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2p1_2E0),s(A_27b,V3p2_2E0)))))) # label(def0_2Ethm_2Epair_2ELAMBDA__PROD) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1609 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27d,A_27c))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27d,A_27c))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27d_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1610 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0g_2E0))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0g_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1f_2E0))) # label(thm_2Epair_2EUNCURRY__ONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1611 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),f692_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f692_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef692_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1612 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1613 (all A_27a all A_27b all V0R1_2E0 all V1R2_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ERPROD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f693_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0)))))) # label(thm_2Epair_2ERPROD__DEF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1614 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1615 (all A_27a all A_27b all V0x_2E0 all V1p_2E0 ((exists V2y_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V2y_2E0)))) <-> s(A_27a,V0x_2E0) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))))) # label(thm_2Epair_2EFST__EQ__EQUIV) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1616 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1617 (all A_27a all A_27b all A_27c all V0f_2E0 all V1v_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0))))) = s(A_27c,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V1v_2E0)))) # label(thm_2Epair_2EUNCURRY) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1618 (all A_27a all A_27b all V0R_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2ELEX_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0)))))))) # label(thm_2Epair_2EWF__LEX) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1619 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),f725_1_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,A_27c)))),f725_1_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef725_1_2E2_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1620 (all A_27a1 all A_27a2 all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c)))),f725_0_2E0),s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27a1,X1_2E0))),s(A_27a2,X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),f725_0_2E3(s(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27a1,X1_2E0),s(A_27a2,X2_2E0)))) # label(arityeq3_2Ef725_0_2E3_2Emono_2EA_27a1_20mono_2EA_27a2_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1621 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f720_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f720_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef720_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1622 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Esymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Esymmetric_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Esymmetric_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1623 (all A_27a all A_27b all V0P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f717_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))) <-> (all V1x_2E0 all V2y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0))))))) # label(thm_2Epair_2EPFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1624 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f692_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))))),f692_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef692_1_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1625 (all A_27c all A_27d all X0_2E0 s(A_27c,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),A_27c),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1626 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1627 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Eprim__rec_2ELESS__SUC__REFL) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1628 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Eprim__rec_2ELESS__0) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1629 (all A_27a all V0f_2E0 all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,f765_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) <-> s(A_27a,V4y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V3x_2E0))))) # label(def1_2Ethm_2Eprim__rec_2ERTC__IM__TC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1630 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2Emeasure_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1631 (all A_27a all V0f_2E0 all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,f765_1_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5x_2E0),s(A_27a,V6y_2E0)))) <-> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V5x_2E0))) = s(A_27a,V6y_2E0))) # label(def0_2Ethm_2Eprim__rec_2ERTC__IM__TC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1632 (all V4x_2E0 all V5y_2E0 (s(tyop_2Enum_2Enum,V5y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4x_2E0))) <-> p(s(tyop_2Emin_2Ebool,f764_1_2E2(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,V5y_2E0)))))) # label(def0_2Ethm_2Eprim__rec_2ETC__IM__RTC__SUC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1633 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1634 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),c_2Eprim__rec_2ESIMP__REC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2ESIMP__REC_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2ESIMP__REC_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1635 (all A_27a all V0P_2E0 all V1R_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2a_2E0)))) & (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) -> (exists V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4y_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)),V1R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))))) -> (exists V5f_2E0 (s(A_27a,V2a_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & (all V6n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,V6n_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)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,V6n_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V6n_2E0)))))))))))))) # label(thm_2Eprim__rec_2EDC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1636 (all A_27a s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0)))) # label(thm_2Eprim__rec_2Emeasure__def) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1637 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Eprim__rec_2EEQ__LESS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1638 (all A_27a all V0f_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2y_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Emeasure_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) # label(thm_2Eprim__rec_2Emeasure__thm) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1639 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Eprim__rec_2ELESS__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1640 (all A_27a all V0x_2E0 all V1f_27_2E0 all V2n_2E0 exists V3g_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_27_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_27_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Eprim__rec_2ESIMP__REC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1641 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1642 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1643 (all V0n_2E0 -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Eprim__rec_2ELESS__REFL) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1644 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f747_0_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f747_1_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Eprim__rec_2EPRE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1645 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) -> (s(tyop_2Enum_2Enum,V0m_2E0) != s(tyop_2Enum_2Enum,V1n_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Eprim__rec_2ELESS__SUC__IMP) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1646 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,f766_0_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,V1y_2E0))) # label(def0_2Ethm_2Eprim__rec_2ELESS__ALT) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1647 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),c_2Eprim__rec_2EPRIM__REC__FUN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ec_2Eprim__rec_2EPRIM__REC__FUN_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1648 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1649 (all A_27a all V0x_2E0 all V1f_2E0 all V2n_2E0 exists V3fun_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3fun_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Eprim__rec_2ESIMP__REC__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1650 (all A_27a all V0e_2E0 all V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),f785_0_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0))))))) # label(thm_2Eprim__rec_2Enum__Axiom__old) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1651 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1652 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool))),f785_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),f785_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0)))) # label(arityeq2_2Ef785_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1653 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f779_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,f779_0_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef779_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1654 (all V0m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) # label(thm_2Eprim__rec_2ELESS__SUC__SUC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1655 (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,f764_0_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))) <-> s(tyop_2Enum_2Enum,V3y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))) # label(def1_2Ethm_2Eprim__rec_2ETC__IM__RTC__SUC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1656 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f764_0_2E0),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f764_1_2E0),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Eprim__rec_2ETC__IM__RTC__SUC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1657 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1658 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1659 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1660 (all A_27a all V0x_2E0 all V1f_2E0 all V2g1_2E0 all V3g2_2E0 all V4m1_2E0 all V5m2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g1_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4m1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g2_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V5m2_2E0)))) -> (all V6n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,V5m2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,V4m1_2E0)))) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g2_2E0),s(tyop_2Enum_2Enum,V6n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g1_2E0),s(tyop_2Enum_2Enum,V6n_2E0))))))) # label(thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1661 (all A_27a all V0x_2E0 all V1f_2E0 ((all V2n_2E0 s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,V0x_2E0)) & (all V3m_2E0 all V4n_2E0 s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3m_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))),s(tyop_2Enum_2Enum,V4n_2E0)))))) # label(thm_2Eprim__rec_2EPRIM__REC__EQN) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1662 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1663 (all A_27a all V0x_2E0 all V1f_2E0 all V2n_2E0 all V3y_2E0 ((exists V4g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4g_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))) & s(A_27a,V3y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4g_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) <-> p(s(tyop_2Emin_2Ebool,f779_0_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V3y_2E0)))))) # label(def0_2Ethm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE__RESULT) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1664 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Eprim__rec_2EPRIM__REC_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Eprim__rec_2EPRIM__REC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1665 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> (exists V2P_2E0 ((all V3n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Eprim__rec_2ELESS__DEF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1666 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Eprim__rec_2ELESS__MONO) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1667 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,V0m_2E0) != s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Eprim__rec_2ELESS__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1668 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1669 (all A_27a all V0x_2E0 all V1f_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f779_0_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) # label(thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE__RESULT) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1670 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Emeasure_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eprim__rec_2Emeasure_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1671 (all A_27a all V0x_2E0 all V2n_2E0 s(A_27a,f750_0_2E2(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,V0x_2E0)) # label(def1_2Ethm_2Eprim__rec_2EPRIM__REC__FUN) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1672 (all A_27a all V0x_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2ESIMP__REC_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f750_0_2E1(s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),f750_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2EPRIM__REC__FUN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0)))) # label(thm_2Eprim__rec_2EPRIM__REC__FUN) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1673 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1674 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1675 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1676 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Eprim__rec_2ESUC__LESS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1677 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1678 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1679 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1680 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Eprim__rec_2ELESS__SUC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.66 1681 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f765_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f765_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ef765_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1682 (all A_27a all V0x_2E0 all V1f_2E0 (s(A_27a,V0x_2E0) = s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & (all V2m_2E0 s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2m_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))))) # label(thm_2Eprim__rec_2ESIMP__REC__THM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1683 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f764_1_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f764_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef764_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1684 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1685 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1686 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f764_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,f764_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef764_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1687 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,f750_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),f750_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef750_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1688 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f788_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f788_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef788_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1689 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))) = s(tyop_2Enum_2Enum,V0m_2E0)) # label(thm_2Eprim__rec_2EPRE_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1690 (all V0m_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,f747_0_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(def0_2Ethm_2Eprim__rec_2EPRE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1691 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Eprim__rec_2ELESS__LEMMA2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1692 (all A_27a all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1693 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1694 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f747_1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f747_1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef747_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1695 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f765_1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f765_1_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef765_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1696 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f766_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f766_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef766_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1697 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) != s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Eprim__rec_2ESUC__ID) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1698 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1699 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1700 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),f750_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(A_27a,f750_0_2E2(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef750_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1701 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),f750_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),f750_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0)))) # label(arityeq1_2Ef750_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1702 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0) <-> p(s(tyop_2Emin_2Ebool,f747_1_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(def1_2Ethm_2Eprim__rec_2EPRE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1703 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Eprim__rec_2ELESS__MONO__REV) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1704 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1705 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Eprim__rec_2ESIMP__REC__REL_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ec_2Eprim__rec_2ESIMP__REC__REL_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1706 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1707 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Ewellfounded_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Eprim__rec_2Ewellfounded_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2Ewellfounded_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1708 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1709 (all A_27a all V0f_2E0 all V1m_2E0 all V2n_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f765_1_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(A_27a,V1m_2E0),s(A_27a,V2n_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f765_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V1m_2E0))),s(A_27a,V2n_2E0)))) # label(thm_2Eprim__rec_2ERTC__IM__TC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1710 (all X0_2E0 s(tyop_2Emin_2Ebool,f747_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f747_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef747_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1711 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Ewellfounded_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> -(exists V1f_2E0 all V2n_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)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))) # label(thm_2Eprim__rec_2Ewellfounded__def) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1712 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2Einv__image_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv__image_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv__image_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1713 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1714 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1715 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1716 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),c_2Eprim__rec_2EPRIM__REC__FUN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Eprim__rec_2EPRIM__REC__FUN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2EPRIM__REC__FUN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1717 (all A_27a all V0x_2E0 all V1f_2E0 all V2m_2E0 s(A_27a,c_2Eprim__rec_2EPRIM__REC__FUN_2E4(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V2m_2E0))))) = s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))) # label(thm_2Eprim__rec_2EPRIM__REC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1718 (all A_27a all V0fun_2E0 all V1x_2E0 all V2f_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2ESIMP__REC__REL_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) <-> (all V4m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4m_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(tyop_2Enum_2Enum,V4m_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4m_2E0))))))) & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0fun_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V1x_2E0))) # label(thm_2Eprim__rec_2ESIMP__REC__REL) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1719 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f747_1_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f747_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef747_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1720 (all A_27a all 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_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1721 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1722 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,f788_0_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) <-> s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))) # label(def0_2Ethm_2Eprim__rec_2EWF__PRED) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1723 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eprim__rec_2EPRE_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1724 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1725 (all A_27a all V1f_2E0 all V3fun_2E0 all V4n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3fun_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))),s(tyop_2Enum_2Enum,V4n_2E0))) = s(A_27a,f750_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3fun_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))) # label(def0_2Ethm_2Eprim__rec_2EPRIM__REC__FUN) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1726 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Eprim__rec_2EINV__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1727 (all A_27a all V0e_2E0 all V1f_2E0 exists V2fn_2E0 ((all V3n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))) & s(A_27a,V0e_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Eprim__rec_2Enum__Axiom) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1728 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Eprim__rec_2ESIMP__REC_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Eprim__rec_2ESIMP__REC_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Eprim__rec_2ESIMP__REC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1729 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Eprim__rec_2ELESS__THM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1730 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f765_1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f765_1_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ef765_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1731 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Eprim__rec_2ELESS__LEMMA1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1732 (all V0n_2E0 -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Eprim__rec_2ENOT__LESS__0) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1733 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f765_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f765_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef765_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1734 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool))),f785_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,f785_0_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0)))) # label(arityeq3_2Ef785_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1735 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1736 (all A_27a all V0m_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0))))))) # label(thm_2Eprim__rec_2EWF__measure) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1737 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) -> -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Eprim__rec_2ENOT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1738 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f779_0_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f779_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef779_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1739 (all A_27a all V0e_2E0 all V1f_2E0 all V2fn1_2E0 (p(s(tyop_2Emin_2Ebool,f785_0_2E3(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0)))) <-> (all V3n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,V3n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))) & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2fn1_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V0e_2E0))) # label(def0_2Ethm_2Eprim__rec_2Enum__Axiom__old) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1740 (all A_27a all V0x_2E0 all V1f_2E0 (s(A_27a,V0x_2E0) = s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & (all V2m_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0))))),s(tyop_2Enum_2Enum,V2m_2E0))) = s(A_27a,c_2Eprim__rec_2EPRIM__REC_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2m_2E0)))))))) # label(thm_2Eprim__rec_2EPRIM__REC__THM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1741 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1742 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),f750_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f750_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef750_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1743 (all A_27a all V0R_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2Ewellfounded_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) # label(thm_2Eprim__rec_2EWF__IFF__WELLFOUNDED) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1744 (all V3f_2E0 all V4a_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f815_3_2E2(s(tyop_2Enum_2Enum,V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),V3f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),f815_2_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),V3f_2E0),s(tyop_2Enum_2Enum,V4a_2E0)))) # label(def5_2Ethm_2Earithmetic_2Efindq__def) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1745 (all V6n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V6n_2E0) <-> p(s(tyop_2Emin_2Ebool,f815_4_2E1(s(tyop_2Enum_2Enum,V6n_2E0)))))) # label(def2_2Ethm_2Earithmetic_2Efindq__def) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1746 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f816_1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f816_1_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ef816_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1747 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Earithmetic_2EODD__DOUBLE) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1748 (all V0P_2E0 all V1c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1c_2E0)))) -> ((all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1c_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1c_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) & (all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1c_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))))) # label(thm_2Earithmetic_2EBOUNDED__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1749 (all V0m_2E0 all V1n_2E0 -(p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ELESS__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1750 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Earithmetic_2EFACT__LESS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1751 (all V0b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0)))) -> (all V1n_2E0 all V2m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EEXP__BASE__LT__MONO) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1752 (all V0f_2E0 ((all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))))) -> (all V2m_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))))))) # label(thm_2Earithmetic_2ESTRICTLY__INCREASING__TC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1753 (all V0n_2E0 all V1p_2E0 all V2q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2q_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,V2q_2E0))))))) # label(thm_2Earithmetic_2EMOD__COMMON__FACTOR) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1754 (all V0c_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0c_2E0),s(tyop_2Enum_2Enum,V0c_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Earithmetic_2ESUB__EQUAL__0) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1755 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1756 (all V0y_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))))),s(tyop_2Enum_2Enum,V0y_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V0y_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))))))) # label(thm_2Earithmetic_2EMOD__SUC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1757 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1758 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0)) # label(thm_2Earithmetic_2ENUMERAL__DEF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1759 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2EMAX__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1760 (all V0m_2E0 all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))))) # label(thm_2Earithmetic_2ELESS__ADD__SUC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1761 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELE__SUB__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1762 (all V0n_2E0 -(p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EEVEN__AND__ODD) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1763 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EMULT__SUC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1764 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EODD_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1765 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1m_2E0))) # label(thm_2Earithmetic_2EMAX__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1766 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELEFT__ADD__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1767 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EMULT__SYM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1768 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,f1167_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(def0_2Ethm_2Earithmetic_2EDIVMOD__THM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1769 (all V0n_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EODD__EVEN) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1770 (all V1a_2E0 all V0f_2E0 all V2m_2E0 all V3n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f816_3_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f816_4_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f816_2_2E4(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) # label(def2_2Ethm_2Earithmetic_2EDIVMOD__DEF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1771 (all A_27a all V0x_2E0 all V1f_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V0x_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(A_27a,V0x_2E0)))) # label(thm_2Earithmetic_2EFUNPOW__1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1772 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EONE__MOD__IFF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1773 (all V0n_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EADD__MODULUS__RIGHT) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1774 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2ELESS__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1775 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2ELESS__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1776 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ERIGHT__ADD__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1777 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1j_2E0 all V2k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,V2k_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMOD__TIMES2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1778 (all V0x_2E0 all V1y_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,V0x_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,V1y_2E0))) # label(thm_2Earithmetic_2EMULT__EQ__1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1779 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EMIN__COMM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1780 (all V1m_2E0 all V2a_2E0 all V3d_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V3d_2E0))),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V3d_2E0))))))))) = s(tyop_2Enum_2Enum,f1164_1_2E3(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3d_2E0)))) # label(def1_2Ethm_2Earithmetic_2Efindq__thm) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1781 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) # label(thm_2Earithmetic_2ELESS__SUC__NOT) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1782 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1783 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELT__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1784 (all V0n_2E0 all V1m_2E0 ((s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1m_2E0) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1785 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__OR) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1786 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1787 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__0) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1788 (all A_27a all V0y_2E0 all V1x_2E0 all V2n_2E0 all V3R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) <-> (exists V4z_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)),V3R_2E0),s(A_27a,V4z_2E0))),s(A_27a,V0y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V1x_2E0),s(A_27a,V4z_2E0)))))))) # label(thm_2Earithmetic_2ENRC__SUC__RECURSE__LEFT) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1789 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2ENOT__ZERO__LT__ZERO) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1790 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1082_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f1082_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1082_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1791 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1792 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> (exists V2p_2E0 s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__ADD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1793 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) # label(thm_2Earithmetic_2EABS__DIFF__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1794 (all A_27a all V0R_2E0 all V1m_2E0 all V2n_2E0 all V3x_2E0 all V4z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V3x_2E0),s(A_27a,V4z_2E0)))) -> (exists V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,V1m_2E0),s(A_27a,V3x_2E0),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V5y_2E0),s(A_27a,V4z_2E0)))))))) # label(thm_2Earithmetic_2ENRC__ADD__E) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1795 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EADD__SUC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1796 (all X0_2E0 s(tyop_2Emin_2Ebool,f1164_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1164_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1164_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1797 (all V0P_2E0 ((all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) <-> (all V1n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Earithmetic_2ESUC__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1798 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0m_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) & s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))) # label(thm_2Earithmetic_2EMULT__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1799 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EMAX__DEF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1800 (all V0P_2E0 ((exists V1n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) -> (exists V2n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & (all V3m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3m_2E0)))))))))) # label(thm_2Earithmetic_2EWOP) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1801 (all V0n_2E0 all V1k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V1k_2E0))) # label(thm_2Earithmetic_2ELESS__MOD) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1802 (all V0a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V0a_2E0)))) # label(thm_2Earithmetic_2ESUC__SUB) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1803 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Earithmetic_2EMODEQ_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2EMODEQ_2E3) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1804 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) # label(thm_2Earithmetic_2EEXP__1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1805 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f815_4_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f815_4_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef815_4_2E1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1806 (all V0x_2E0 all V1n_2E0 all V2k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2k_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2k_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2EMOD__LIFT__PLUS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1807 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1808 (all V0x_2E0 all V1y_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))))))) # label(thm_2Earithmetic_2EABS__DIFF__TRIANGLE__lem) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1809 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) != s(tyop_2Enum_2Enum,V0m_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ENOT__NUM__EQ) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1810 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2ESUB__MOD) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1811 (all V0f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f816_1_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f816_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0)))) # label(def4_2Ethm_2Earithmetic_2EDIVMOD__DEF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1812 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))))) # label(thm_2Earithmetic_2ESUB__LEFT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1813 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Earithmetic_2ESUB__LESS__0) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1814 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))))) # label(thm_2Earithmetic_2ELESS__MONO__ADD) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1815 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,V2p_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Earithmetic_2ESUB__RIGHT__EQ) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1816 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2ELESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1817 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))))))) # label(thm_2Earithmetic_2EBIT2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1818 (all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Earithmetic_2EADD_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1819 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Earithmetic_2EADD_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1820 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EMULT__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1821 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),f816_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f816_2_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0)))) # label(arityeq2_2Ef816_2_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1822 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) <-> s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0))) # label(thm_2Earithmetic_2ENRC__0) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1823 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Earithmetic_2EABS__DIFF__SUC) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1824 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1825 (all V0n_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EADD__MODULUS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1826 (all V2n_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Earithmetic_2EADD__MODULUS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.67 1827 (all V0P_2E0 ((exists V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V4x_2E0)))) & (all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V5y_2E0),s(tyop_2Enum_2Enum,V4x_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V5y_2E0)))))))) <-> (exists V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))))) & (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))))) # label(thm_2Earithmetic_2EEXISTS__GREATEST) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1828 (all V0f_2E0 ((all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))))) -> (all V2b_2E0 exists V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))))) # label(thm_2Earithmetic_2ESTRICTLY__INCREASING__UNBOUNDED) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1829 (all V0q_2E0 s(tyop_2Enum_2Enum,V0q_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0q_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Earithmetic_2EDIV__1) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1830 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1831 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0) & s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Earithmetic_2EABS__DIFF__ZERO) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1832 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Earithmetic_2EODD__EXP__IFF) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1833 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> (exists V2p_2E0 s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__ADD) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1834 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ESUB__RIGHT__LESS) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1835 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMAX_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMAX_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1836 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1837 (all V0m_2E0 all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Earithmetic_2ELESS__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 107.66/107.68 1838 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ESUB__LESS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1839 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ESUB__LEFT__LESS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1840 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1841 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) -> (all V2c_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V2c_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))))) # label(thm_2Earithmetic_2ELESS__EQ__SUB__LESS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1842 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Ebool_2EONE__ONE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1843 (all V0m_2E0 all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))))))) # label(thm_2Earithmetic_2EZERO__LESS__EXP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1844 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0)) # label(thm_2Earithmetic_2EADD__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1845 (all V4a_2E0 all V3f_2E0 all V5m_2E0 all V6n_2E0 s(tyop_2Enum_2Enum,f815_3_2E4(s(tyop_2Enum_2Enum,V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),V3f_2E0),s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,V6n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f815_4_2E1(s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Enum_2Enum,V4a_2E0),s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f815_5_2E3(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),V3f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V6n_2E0)))))))) # label(def4_2Ethm_2Earithmetic_2Efindq__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1846 (all V0n_2E0 all V1m_2E0 all V2a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1164_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1164_1_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2Efindq__thm) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1847 (all V0n_2E0 all V1m_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1m_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))))) & (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Earithmetic_2ELE__MULT__CANCEL__RBARE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1848 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f815_5_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f815_5_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ef815_5_2E3) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1849 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Earithmetic_2EPRE__SUB1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1850 (all V0n_2E0 ((exists V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EEVEN__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1851 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Earithmetic_2EMOD__2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1852 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) -> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EADD__INV__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1853 (all V0x_2E0 all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2z_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V2z_2E0))))))) # label(thm_2Earithmetic_2EDIV__LE__X) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1854 (all V0p_2E0 all V1q_2E0 all V2n_2E0 all V3m_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,V3m_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1q_2E0))),s(tyop_2Enum_2Enum,V0p_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1q_2E0))),s(tyop_2Enum_2Enum,V0p_2E0))))))) # label(thm_2Earithmetic_2EMULT__EXP__MONO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1855 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f816_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f816_3_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef816_3_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1856 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1857 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ESUB__RIGHT__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1858 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELEFT__SUB__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1859 (all V0p_2E0 all V1n_2E0 all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0p_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V2m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V2m_2E0)))) # label(thm_2Earithmetic_2ESUB__CANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1860 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1861 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2Emeasure_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1862 (all A_27a ((all V2n_2E0 all V3v_2E0 all V4f_2E0 s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V3v_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4f_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4f_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & (all V0v_2E0 all V1f_2E0 s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))) = s(A_27a,V0v_2E0)))) # label(thm_2Earithmetic_2Enum__case__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1863 (all V0n_2E0 all V1a_2E0 all V2b_2E0 all V3p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V3p_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V3p_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EADD__MOD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1864 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EZERO__LESS__MULT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1865 (all V0n_2E0 all V1m_2E0 all V2i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2ELESS__SUB__ADD__LESS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1866 (all V0y_2E0 all V1x_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0y_2E0)))))))) # label(thm_2Earithmetic_2EMODEQ__SUC__CONG) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1867 (all V0x_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0)))) | s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))))))) # label(thm_2Earithmetic_2EX__LT__EXP__X__IFF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1868 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eprim__rec_2EPRE_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1869 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2ESUC__NOT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1870 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1m_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) | s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Earithmetic_2EADD__DIV__RWT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1871 (all V0n_2E0 all V1m_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Earithmetic_2EMAX__LT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1872 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EFACT_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EFACT_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1873 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) -> (s(tyop_2Enum_2Enum,V2p_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EADD__EQ__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1874 (all V0n_2E0 all V1m2_2E0 all V2m1_2E0 (s(tyop_2Enum_2Enum,V1m2_2E0) = s(tyop_2Enum_2Enum,V2m1_2E0) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2m1_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1m2_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2m1_2E0),s(tyop_2Enum_2Enum,V1m2_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__THM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1875 (all V0m_2E0 all V1n_2E0 (s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) != s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EODD__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1876 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (exists V2p_2E0 s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQUAL__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1877 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ESUB__LEFT__GREATER) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1878 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1879 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EZERO__LESS__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1880 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) # label(thm_2Earithmetic_2EADD__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1881 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1x_2E0 all V2r_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EADD__DIV__ADD__DIV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1882 (all V0n_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) -> (exists V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) -> (exists V2m_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2m_2E0))))))))) # label(thm_2Earithmetic_2EEVEN__ODD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1883 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1884 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1885 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EADD__COMM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1886 (all V0x_2E0 all V1z_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1z_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1z_2E0))))))))) # label(thm_2Earithmetic_2EABS__DIFF__SUC__LE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1887 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EPRE__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1888 (all V0z_2E0 all V1y_2E0 all V2x_2E0 ((s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))),s(tyop_2Enum_2Enum,V1y_2E0)))) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))),s(tyop_2Enum_2Enum,V1y_2E0))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2x_2E0)))))))))) # label(thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1889 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) | (exists V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2ELESS__OR__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1890 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V2p_2E0))) # label(thm_2Earithmetic_2EEQ__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1891 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1892 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> (exists V2p_2E0 s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) # label(thm_2Earithmetic_2ELESS__ADD__1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1893 (all V0z_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V0z_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0))),s(tyop_2Enum_2Enum,V0z_2E0)))) # label(thm_2Earithmetic_2EEXP__BASE__MULT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1894 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f816_4_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))),f816_4_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef816_4_2E4) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1895 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EODD__EXP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1896 (all V0m_2E0 all V1i_2E0 all V2n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V1i_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1i_2E0)))) # label(thm_2Earithmetic_2ELESS__MULT__MONO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1897 (all V0z_2E0 all V1y_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V0z_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0z_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))))) # label(thm_2Earithmetic_2ELE__SUB__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1898 (all V0m_2E0 all V1n_2E0 all V2i_2E0 all V3j_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2i_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V3j_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V3j_2E0)))))))) # label(thm_2Earithmetic_2ELESS__MONO__MULT2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1899 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0m_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EMULT__INCREASES) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1900 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1901 (all V0f_2E0 all V1a_2E0 all V2m_2E0 all V3n_2E0 all V4q_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V4q_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V4q_2E0))))),s(tyop_2Enum_2Enum,V3n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f816_4_2E5(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V4q_2E0)))) # label(def1_2Ethm_2Earithmetic_2EDIVMOD__DEF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1902 (all V0n_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EADD__MODULUS__LEFT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1903 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Earithmetic_2EMIN__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1904 (all V0n_2E0 all V1q_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EMOD__TIMES__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1905 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EZERO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1906 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EEVEN__MULT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1907 (all A_27a all V0zc_2E0 all V1v_2E0 all V2sc_2E0 all V3n_2E0 (s(A_27a,V1v_2E0) = s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,V3n_2E0),s(A_27a,V0zc_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2sc_2E0))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V3n_2E0) & s(A_27a,V0zc_2E0) = s(A_27a,V1v_2E0) | (exists V4x_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4x_2E0))) = s(tyop_2Enum_2Enum,V3n_2E0) & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2sc_2E0),s(tyop_2Enum_2Enum,V4x_2E0))) = s(A_27a,V1v_2E0))))) # label(thm_2Earithmetic_2Enum__case__eq) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1908 (all V0m_2E0 all V1n_2E0 -(p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1909 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EMIN__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1910 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ESUB__LEFT__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1911 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EODD__MULT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1912 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EINV__PRE__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1913 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) # label(thm_2Earithmetic_2EONE__MOD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1914 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),f815_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),f815_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef815_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1915 (all V0n_2E0 all V1m_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__IMP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1916 (all V0n_2E0 all V1m_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Earithmetic_2EMAX__LE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1917 (all V0n_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EDIV__LE__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1918 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) != s(tyop_2Enum_2Enum,V1n_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__SUC__EQ__COR) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1919 (all V0b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0)))) -> (all V1n_2E0 all V2m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EEXP__BASE__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1920 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__MONO__ADD__INV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1921 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,V1m_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Earithmetic_2EADD__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1922 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f821_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f821_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef821_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1923 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1164_1_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1164_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1164_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1924 (all V0y_2E0 all V1x_2E0 all V2n_2E0 all V3e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V3e_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V3e_2E0)))))))) # label(thm_2Earithmetic_2EMODEQ__EXP__CONG) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1925 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f815_6_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,f815_6_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef815_6_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1926 (all V0m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2ELESS__0__CASES) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1927 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Earithmetic_2EEVEN__DOUBLE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1928 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2Enat__elim____magic_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Earithmetic_2Enat__elim____magic) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1929 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),f815_2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),f815_2_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef815_2_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1930 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1k_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1k_2E0))))))) # label(thm_2Earithmetic_2EDIV__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1931 (all V0q_2E0 all V1n_2E0 all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0q_2E0))),s(tyop_2Enum_2Enum,V2m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0q_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0q_2E0))))) # label(thm_2Earithmetic_2EDIV__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1932 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ELESS__CASES) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1933 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> (all V2x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EDIV__DIV__DIV__MULT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1934 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EEVEN_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1935 (all V0n_2E0 all V1k_2E0 all V2r_2E0 ((exists V3q_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))) = s(tyop_2Enum_2Enum,V1k_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V2r_2E0))) # label(thm_2Earithmetic_2EMOD__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1936 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1937 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))))) # label(thm_2Earithmetic_2ELE__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1938 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f816_4_2E5(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0),s(tyop_2Enum_2Enum,X4_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))),f816_4_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))),s(tyop_2Enum_2Enum,X4_2E0)))) # label(arityeq5_2Ef816_4_2E5) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1939 (all V0P_2E0 ((all V1n_2E0 ((all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) -> (all V3n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))) # label(thm_2Earithmetic_2ECOMPLETE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1940 (all V0m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> (all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EINV__PRE__LESS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1941 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EODD_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1942 (all V0b1_2E0 all V1b2_2E0 all V2x_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1b2_2E0),s(tyop_2Enum_2Enum,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b1_2E0),s(tyop_2Enum_2Enum,V2x_2E0))) <-> s(tyop_2Enum_2Enum,V1b2_2E0) = s(tyop_2Enum_2Enum,V0b1_2E0) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V2x_2E0))) # label(thm_2Earithmetic_2EEXP__EXP__INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1943 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) != s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2ENOT__ODD__EQ__EVEN) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1944 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Earithmetic_2ENRC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Earithmetic_2ENRC_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1945 (all A_27a all V0f_2E0 all V1n_2E0 all V2x_2E0 s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(A_27a,V2x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Earithmetic_2EFUNPOW__SUC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1946 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) | s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Earithmetic_2EGREATER__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1947 (all V0p_2E0 all V1m_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,V1m_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0p_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0p_2E0))))))) # label(thm_2Earithmetic_2EMULT__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1948 (all V0m_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))))) # label(thm_2Earithmetic_2ELESS__EQ__SUC__REFL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1949 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))) & s(tyop_2Enum_2Enum,V1k_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Earithmetic_2EDIVISION) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1950 (all V0n_2E0 all V1m_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))))) # label(thm_2Earithmetic_2Efindq__divisor) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1951 (all V0m_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) | (exists V1n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2Enum__CASES) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1952 (all A_27a all V0R_2E0 all V1n_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0)))))) # label(thm_2Earithmetic_2ENRC__RTC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1953 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2EABS__DIFF__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1954 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) | s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2EADD__EQ__1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1955 (all V0n_2E0 all V1k_2E0 all V2q_2E0 ((exists V3r_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V3r_2E0))) = s(tyop_2Enum_2Enum,V1k_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V2q_2E0))) # label(thm_2Earithmetic_2EDIV__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1956 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2ESUC__ADD__SYM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1957 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1958 (all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EEVEN__MOD2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1959 (all V0b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0)))) -> (all V1n_2E0 all V2m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V2m_2E0))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V2m_2E0))))) # label(thm_2Earithmetic_2EEXP__BASE__INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1960 (all V0a_2E0 all V1m_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))) # label(thm_2Earithmetic_2Efindq__eq__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1961 (all V0n_2E0 all V1d_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1d_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1d_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EDIV__LESS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1962 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ENOT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1963 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EZERO__MOD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1964 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))))) # label(thm_2Earithmetic_2ELT__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1965 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ERIGHT__SUB__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.68 1966 (all V0z_2E0 all V1y_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0z_2E0),s(tyop_2Enum_2Enum,V2x_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0z_2E0),s(tyop_2Enum_2Enum,V2x_2E0))) = s(tyop_2Enum_2Enum,V1y_2E0) <-> s(tyop_2Enum_2Enum,V0z_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))))) # label(thm_2Earithmetic_2EMULT__EQ__DIV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1967 (all V0P_2E0 all V1m_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) <-> (all V3q_2E0 all V4r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4r_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V4r_2E0))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3q_2E0))))))))) # label(thm_2Earithmetic_2EDIV__P__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1968 (all V0n_2E0 all V1m_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2ESUB__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1969 (all V0k_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (exists V2r_2E0 exists V3q_2E0 (s(tyop_2Enum_2Enum,V0k_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EDA) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1970 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))))) # label(thm_2Earithmetic_2EBIT1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1971 (all V0n_2E0 all V1m_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2ENOT__SUC__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1972 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2EEQ__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1973 (all A_27a all V0f_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))))))) # label(thm_2Earithmetic_2Etransitive__measure) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1974 (all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Earithmetic_2ELE__LT1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1975 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) # label(thm_2Earithmetic_2ESUB__LESS__OR) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1976 (all V0m_2E0 all V1n_2E0 (s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EEVEN__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1977 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f815_3_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f815_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ef815_3_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1978 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,f815_3_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f815_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef815_3_2E4) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1979 (all V0c_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0c_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> (all V2a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0c_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0c_2E0)))))))) # label(thm_2Earithmetic_2ELESS__EQ__ADD__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1980 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1981 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1982 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EEXP__EXP__LT__MONO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1983 (all V0n_2E0 all V1q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,V1q_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EMULT__DIV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1984 (all V0y1_2E0 all V1y0_2E0 all V2x1_2E0 all V3x0_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V3x0_2E0),s(tyop_2Enum_2Enum,V2x1_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V1y0_2E0),s(tyop_2Enum_2Enum,V0y1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3x0_2E0),s(tyop_2Enum_2Enum,V1y0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2x1_2E0),s(tyop_2Enum_2Enum,V0y1_2E0))))))))) # label(thm_2Earithmetic_2EMODEQ__PLUS__CONG) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1985 (all V0x_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EX__LE__X__EXP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1986 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2EABS__DIFF__COMM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1987 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1988 (all V0f_2E0 -(all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2ENOT__STRICTLY__DECREASING) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1989 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Earithmetic_2ELE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1990 (all V1m_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) | s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2ELE_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1991 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2EADD__MONO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1992 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EZERO__DIV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1993 (all V0x_2E0 all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2z_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))))) # label(thm_2Earithmetic_2EX__LE__DIV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1994 (all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0)))) -> (all V1b_2E0 exists V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))) # label(thm_2Earithmetic_2EONE__ONE__UNBOUNDED) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1995 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2ESUB__LEFT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1996 (all A_27a all V0num_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),A_27a)),V0num_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0))))))) # label(thm_2Earithmetic_2Edatatype__num) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1997 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1998 (all V0n_2E0 all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) # label(thm_2Earithmetic_2EMODEQ__REFL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 1999 (all V0a_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f815_6_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),f815_0_2E1(s(tyop_2Enum_2Enum,V0a_2E0)))) # label(def1_2Ethm_2Earithmetic_2Efindq__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2000 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f816_2_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),f816_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef816_2_2E4) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2001 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2ESUB__LEFT__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2002 (all V0m_2E0 all V1n_2E0 all V2p_2E0 all V3q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V3q_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V3q_2E0)))))))) # label(thm_2Earithmetic_2ELESS__EQ__LESS__EQ__MONO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2003 (all V0n_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V2q_2E0 s(tyop_2Enum_2Enum,V2q_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EDIV__MULT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2004 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ESUB__RIGHT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2005 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ENOT__LESS__EQUAL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2006 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2007 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) | s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EEXP__EXP__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2008 (all V0m_2E0 all V1n_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))))) # label(thm_2Earithmetic_2EDIVMOD__CORRECT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2009 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EABS__DIFF_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EABS__DIFF_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2010 (all V0P_2E0 all V1x_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & (all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2EMOD__ELIM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2011 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EEVEN__ODD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2012 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ESUB__LEFT__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2013 (all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0)))) -> (all V1b_2E0 exists V2a_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V2a_2E0)))))))) # label(thm_2Earithmetic_2EONE__ONE__INV__IMAGE__BOUNDED) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2014 (all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,f815_6_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(def0_2Ethm_2Earithmetic_2Efindq__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2015 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) != s(tyop_2Enum_2Enum,V0m_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EMIN__MAX__LT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2016 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),f1167_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1167_1_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1167_1_2E3) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2017 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ETC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2018 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2EEQ__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2019 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2020 (all V0x_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__MOD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2021 (all V0n1_2E0 all V1n2_2E0 all V2m1_2E0 all V3m2_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n1_2E0),s(tyop_2Enum_2Enum,V1n2_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2m1_2E0),s(tyop_2Enum_2Enum,V3m2_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n1_2E0),s(tyop_2Enum_2Enum,V2m1_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V1n2_2E0),s(tyop_2Enum_2Enum,V3m2_2E0))))))))) # label(thm_2Earithmetic_2EABS__DIFF__SUMS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2022 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EINV__PRE__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2023 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2024 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ESUB__RIGHT__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2025 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__LESS__EQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2026 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1k_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMOD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2027 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) # label(thm_2Earithmetic_2EEXP2__LT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2028 (all V0x_2E0 all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2z_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))))))) # label(thm_2Earithmetic_2EX__LT__DIV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2029 (all V0b_2E0 all V1c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1c_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))) -> (all V2a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1c_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V1c_2E0))),s(tyop_2Enum_2Enum,V0b_2E0)))))) # label(thm_2Earithmetic_2ESUB__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2030 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Earithmetic_2EDIVMOD__ID) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2031 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMIN_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2032 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2033 (all V2n_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,f821_0_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(def0_2Ethm_2Earithmetic_2Enum__case__compute) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2034 (all V0z_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0))),s(tyop_2Enum_2Enum,V0z_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V0z_2E0)))))) # label(thm_2Earithmetic_2EEXP__EXP__MULT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2035 (all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2ESUB_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2036 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2ESUB_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2037 (all V0m2_2E0 all V1m1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m1_2E0),s(tyop_2Enum_2Enum,V0m2_2E0)))) <-> s(tyop_2Enum_2Enum,V1m1_2E0) = s(tyop_2Enum_2Enum,V0m2_2E0))) # label(thm_2Earithmetic_2EMODEQ__0__CONG) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2038 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),f815_2_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),f815_2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef815_2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2039 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2040 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EPRE__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2041 (all V0n_2E0 all V1k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) <-> (exists V2d_2E0 s(tyop_2Enum_2Enum,V1k_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Earithmetic_2EMOD__EQ__0__DIVISOR) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2042 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELE__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2043 (all V0x_2E0 all V1n_2E0 all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2e_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2e_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2EEXP__MOD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2044 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2Earithmetic_2EONE__LT__EXP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2045 (all V0x_2E0 all V1n_2E0 all V2k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2k_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2k_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))))))) # label(thm_2Earithmetic_2EMOD__LIFT__PLUS__IFF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2046 (all V0m_2E0 all V1n_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ENOT__LESS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2047 (all V0P_2E0 all V1p_2E0 all V2q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2q_2E0)))) -> (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,V2q_2E0)))))) <-> (exists V3k_2E0 exists V4r_2E0 (s(tyop_2Enum_2Enum,V1p_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2Enum_2Enum,V2q_2E0))),s(tyop_2Enum_2Enum,V4r_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4r_2E0),s(tyop_2Enum_2Enum,V2q_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V4r_2E0))))))))) # label(thm_2Earithmetic_2EMOD__P) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2048 (all V0x_2E0 (s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,f1082_0_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(def0_2Ethm_2Earithmetic_2EZERO__EXP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2049 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERTC_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2050 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__LESS__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2051 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,f1164_1_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1164_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1164_1_2E3) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2052 (all V0m_2E0 all V1n_2E0 -(p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))))) # label(thm_2Earithmetic_2ELESS__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2053 (all A_27a ((all V0f_2E0 all V1x_2E0 s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V1x_2E0))) = s(A_27a,V1x_2E0)) & (all V2f_2E0 all V3n_2E0 all V4x_2E0 s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,V4x_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Earithmetic_2EFUNPOW) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2054 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (exists V2k_2E0 s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2k_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQUAL__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2055 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,V0m_2E0)) # label(thm_2Earithmetic_2EMULT__RIGHT__1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2056 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELT__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2057 (all V0n_2E0 -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Earithmetic_2ENOT__SUC__LESS__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2058 (all A_27a all V0g_2E0 all V1f_2E0 all V2n_2E0 s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0g_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f821_0_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0g_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2Enum__case__compute) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2059 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) & (all V2n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))))) <-> (all V1n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Earithmetic_2EFORALL__NUM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2060 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Earithmetic_2EEQ__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2061 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),f815_1_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),f815_1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef815_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2062 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2063 (all V0P_2E0 all V1m_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2EMIN__MAX__PRED) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2064 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) | s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Earithmetic_2ELESS__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2065 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Earithmetic_2EMAX__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2066 (all V0m_2E0 all V1n_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ENOT__GREATER) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2067 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2EABS__DIFF__SYM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2068 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1082_0_2E1(s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Earithmetic_2EZERO__EXP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2069 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2070 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) | (exists V2m_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2m_2E0))))))) <-> (exists V1n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Earithmetic_2EEXISTS__NUM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2071 (all V0n_2E0 all V1m_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))))))) # label(thm_2Earithmetic_2EMIN__LT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2072 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2073 (all V0x_2E0 all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2z_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2z_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,V0x_2E0))))) # label(thm_2Earithmetic_2EDIV__LT__X) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2074 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ELE__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2075 (all V0x_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))))),s(tyop_2Enum_2Enum,V1n_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2EEXP__SUB__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2076 (all V0q_2E0 all V1n_2E0 all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0q_2E0))),s(tyop_2Enum_2Enum,V2m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0q_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2EMOD__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2077 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2ESUC__ONE__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2078 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2079 (all V0P_2E0 all V1c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1c_2E0)))) -> (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1c_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) | (exists V3n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1c_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) <-> (exists V2n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1c_2E0))))))))) # label(thm_2Earithmetic_2EBOUNDED__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2080 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2ESUB__EQ__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2081 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Earithmetic_2EDIV2__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2082 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2EADD__INV__0__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2083 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2ESUC__MOD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2084 (all V0p_2E0 all V1q_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1q_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1q_2E0)))))) # label(thm_2Earithmetic_2EDOUBLE__LT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2085 (all V0z_2E0 all V1y_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V0z_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0z_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0z_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) # label(thm_2Earithmetic_2ELT__SUB__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2086 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2087 (all V0n_2E0 all V1m_2E0 all V2p_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))))) # label(thm_2Earithmetic_2EMIN__LE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2088 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2089 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2090 (all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Earithmetic_2EEXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2091 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Earithmetic_2EEXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2092 (all V0n_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> (all V2m_2E0 ((s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2m_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V2m_2E0))))) & (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))))) # label(thm_2Earithmetic_2EPRE__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2093 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1j_2E0 all V2k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,V2k_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMOD__PLUS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2094 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) -> (exists V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))))))) # label(thm_2Earithmetic_2ERTC__NRC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2095 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EMULT__COMM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2096 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Earithmetic_2ESUB__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2097 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2098 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,V0m_2E0)) # label(thm_2Earithmetic_2ESUC__SUB1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2099 (all A_27a all V0R_2E0 all V1m_2E0 all V2n_2E0 all V3x_2E0 all V4y_2E0 all V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V4y_2E0),s(A_27a,V5z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,V1m_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V3x_2E0),s(A_27a,V5z_2E0)))))) # label(thm_2Earithmetic_2ENRC__ADD__I) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2100 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) -> (s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))))) # label(thm_2Earithmetic_2EX__MOD__Y__EQ__X) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2101 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EADD__SYM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2102 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Earithmetic_2EABS__DIFF__EQS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2103 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V1n_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2ELESS__ADD__NONZERO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2104 (all V0k_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0k_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Earithmetic_2EMOD__ONE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2105 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EDIV2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2106 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) <-> p(s(tyop_2Emin_2Ebool,f1164_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(def0_2Ethm_2Earithmetic_2Efindq__thm) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2107 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ESUB__RIGHT__GREATER) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2108 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2109 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2110 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2111 (all V2m_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))))))) # label(thm_2Earithmetic_2EDIVMOD__CALC_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2112 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))))))) # label(thm_2Earithmetic_2EDIVMOD__CALC_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2113 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2114 (all V0P_2E0 ((all V1n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) & (all V2n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))))) # label(thm_2Earithmetic_2EFORALL__NUM__THM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.69 2115 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))))) # label(thm_2Earithmetic_2ELESS__MONO__MULT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2116 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELT__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2117 (all V0m_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1p_2E0)))) -> (all V2n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Earithmetic_2ESUB__LESS__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2118 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a))),c_2Earithmetic_2Enum__CASE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0))) = s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2Enum__CASE_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2119 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EMOD__LESS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2120 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EGREATER__DEF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2121 (all V0a_2E0 all V1b_2E0 all V2c_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V2c_2E0)))) # label(thm_2Earithmetic_2ESUB__PLUS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2122 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2123 (all V0p_2E0 all V1m_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0p_2E0))))))) # label(thm_2Earithmetic_2ESUB__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2124 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,f815_5_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f815_5_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef815_5_2E4) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2125 (all A_27a all V0v_27_2E0 all V1f_27_2E0 all V2M_2E0 all V3M_27_2E0 all V4v_2E0 all V5f_2E0 ((s(tyop_2Enum_2Enum,V3M_27_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> s(A_27a,V0v_27_2E0) = s(A_27a,V4v_2E0)) & (all V6n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V6n_2E0))) = s(tyop_2Enum_2Enum,V3M_27_2E0) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,V6n_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_27_2E0),s(tyop_2Enum_2Enum,V6n_2E0))))) & s(tyop_2Enum_2Enum,V3M_27_2E0) = s(tyop_2Enum_2Enum,V2M_2E0) -> s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,V2M_2E0),s(A_27a,V4v_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0))) = s(A_27a,c_2Earithmetic_2Enum__CASE_2E3(s(tyop_2Enum_2Enum,V3M_27_2E0),s(A_27a,V0v_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_27_2E0))))) # label(thm_2Earithmetic_2Enum__case__cong) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2126 (all V0z_2E0 all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0z_2E0))))))) # label(thm_2Earithmetic_2EABS__DIFF__LE__SUM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2127 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1q_2E0 all V2r_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMOD__TIMES) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2128 (all A_27a ((all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) <-> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))) & (all V3R_2E0 all V4n_2E0 all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4n_2E0))),s(A_27a,V5x_2E0),s(A_27a,V6y_2E0)))) <-> (exists V7z_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)),V3R_2E0),s(A_27a,V5x_2E0))),s(A_27a,V7z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Enum_2Enum,V4n_2E0),s(A_27a,V7z_2E0),s(A_27a,V6y_2E0)))))))))) # label(thm_2Earithmetic_2ENRC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2129 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIVMOD_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EDIVMOD_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2130 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__MONO__REV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2131 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EMAX__COMM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2132 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2ELESS__MULT2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2133 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Earithmetic_2Efindq_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2Efindq_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2134 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2135 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V2p_2E0))) # label(thm_2Earithmetic_2EEQ__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2136 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Earithmetic_2EADD1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2137 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> (all V2x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EMOD__MULT__MOD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2138 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2ELE__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2139 (all V0m_2E0 all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Earithmetic_2EMIN__MAX__LE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2140 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Earithmetic_2ENOT__EXP__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2141 (all V0m_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))) # label(thm_2Earithmetic_2ELESS__EQ__REFL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2142 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2143 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2144 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EEVEN__EXP__IFF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2145 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) # label(thm_2Earithmetic_2EEXP__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2146 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2EMIN__MAX__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2147 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> (all V2p_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))))))) # label(thm_2Earithmetic_2ELESS__IMP__LESS__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2148 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))))) # label(thm_2Earithmetic_2ELT__SUB__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2149 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f831_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f831_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef831_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2150 (all V0r_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2ELESS__DIV__EQ__ZERO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2151 (all X0_2E0 s(tyop_2Emin_2Ebool,f1167_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1167_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1167_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2152 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2EOR__LESS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2153 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2154 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2EGREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2155 (all V0p_2E0 all V1q_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1q_2E0),s(tyop_2Enum_2Enum,V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V0p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1q_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1q_2E0))))))) # label(thm_2Earithmetic_2EEXP__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2156 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EFACT_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2157 (all V0n_2E0 all V1m2_2E0 all V2m1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1m2_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2m1_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2m1_2E0),s(tyop_2Enum_2Enum,V1m2_2E0))))))) # label(thm_2Earithmetic_2EMODEQ__NONZERO__MODEQUALITY) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2158 (all A_27a all V0x_2E0 all V1f_2E0 all V2m_2E0 all V3n_2E0 s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,V0x_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2m_2E0),s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Earithmetic_2EFUNPOW__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2159 (all V0m_2E0 all V1n_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0m_2E0) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V2p_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))) # label(thm_2Earithmetic_2EEQ__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2160 (all V0n_2E0 ((exists V1m_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Enum_2Enum,V0n_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EODD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2161 (all V0m_2E0 all V1n_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ENOT__LEQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2162 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ESUB__LEFT__SUC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2163 (all V3n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V3n_2E0) <-> p(s(tyop_2Emin_2Ebool,f816_3_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))) # label(def0_2Ethm_2Earithmetic_2EDIVMOD__DEF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2164 (all A_27a all V0z_2E0 all V1x_2E0 all V2n_2E0 all V3m_2E0 all V4R_2E0 ((exists V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Enum_2Enum,V3m_2E0),s(A_27a,V1x_2E0),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V5y_2E0),s(A_27a,V0z_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(A_27a,V1x_2E0),s(A_27a,V0z_2E0)))))) # label(thm_2Earithmetic_2ENRC__ADD__EQN) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2165 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1167_1_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),f1167_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef1167_1_2E4) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2166 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Earithmetic_2EMULT_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2167 (all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Earithmetic_2EMULT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2168 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__MONO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2169 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2ESUB__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2170 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> (s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2EPRE__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2171 (all V0y_2E0 all V1x_2E0 all V2n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) # label(thm_2Earithmetic_2EMODEQ__SYM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2172 (all V0x_2E0 all V1y_2E0 all V2z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2z_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V2z_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,V1y_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Earithmetic_2EDIV__EQ__X) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2173 (all V0P_2E0 all V1m_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) <-> (all V3q_2E0 all V4r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4r_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V4r_2E0))) = s(tyop_2Enum_2Enum,V1m_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V4r_2E0))))))))) # label(thm_2Earithmetic_2EMOD__P__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2174 (all V0x_2E0 all V1y_2E0 all V2z_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2z_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,V2z_2E0))))))))) # label(thm_2Earithmetic_2EABS__DIFF__TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2175 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2ETC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) <-> (exists V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))))))) # label(thm_2Earithmetic_2ETC__eq__NRC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2176 (all V0b_2E0 all V1a_2E0 all V2P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))))) <-> (all V3d_2E0 ((s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V3d_2E0))) = s(tyop_2Enum_2Enum,V0b_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V3d_2E0))) = s(tyop_2Enum_2Enum,V1a_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Enum_2Enum,V3d_2E0))))))))) # label(thm_2Earithmetic_2ESUB__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2177 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2ETIMES2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2178 (all A_27a all V0R_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) & (all V2n_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)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))))))) -> (all V3m_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,V4n_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)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))))))) # label(thm_2Earithmetic_2Etransitive__monotone) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2179 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2EMAX__IDEM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2180 (all V5m_2E0 all V4a_2E0 all V3f_2E0 all V7d_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,V7d_2E0))),s(tyop_2Enum_2Enum,V4a_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),V3f_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V4a_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,V7d_2E0))))))))) = s(tyop_2Enum_2Enum,f815_5_2E4(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),V3f_2E0),s(tyop_2Enum_2Enum,V7d_2E0)))) # label(def3_2Ethm_2Earithmetic_2Efindq__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2181 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2182 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2Enat__elim____magic_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2Enat__elim____magic_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2Enat__elim____magic_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2183 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) != s(tyop_2Enum_2Enum,V0m_2E0) & -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ELESS__CASES__IMP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2184 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eprim__rec_2Emeasure_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eprim__rec_2Emeasure_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2Emeasure_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2185 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f816_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f816_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ef816_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2186 (all V0m_2E0 s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2EMULT__LEFT__1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2187 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Earithmetic_2EADD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2188 (all V0f_2E0 ((all V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0)))))) # label(thm_2Earithmetic_2ESTRICTLY__INCREASING__ONE__ONE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2189 (all V0m_2E0 all V1i_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V1i_2E0))) <-> s(tyop_2Enum_2Enum,V1i_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2EMULT__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2190 (all V0p_2E0 all V1n_2E0 all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))) -> (s(tyop_2Enum_2Enum,V2m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0p_2E0)))))) # label(thm_2Earithmetic_2ECANCEL__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2191 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EMULT__LESS__EQ__SUC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2192 (all V0n_2E0 all V1m_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) # label(thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2193 (all A_27a all V0x_2E0 all V1f_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V0x_2E0)))) # label(thm_2Earithmetic_2EFUNPOW__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2194 (all V0p_2E0 all V1q_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V0p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1q_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1q_2E0)))))) # label(thm_2Earithmetic_2EEXP__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2195 (all V0x_2E0 all V1z_2E0 all V2y_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V1z_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1z_2E0))))))))) # label(thm_2Earithmetic_2EABS__DIFF__PLUS__LE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2196 (all V0m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0m_2E0))))))) # label(thm_2Earithmetic_2ESUC__PRE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2197 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) -> (exists V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Earithmetic_2ELESS__STRONG__ADD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2198 (all V0y_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V0y_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))))),s(tyop_2Enum_2Enum,V0y_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0)))))) # label(thm_2Earithmetic_2EMOD__SUC__IFF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2199 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2200 (all V0y1_2E0 all V1y0_2E0 all V2x1_2E0 all V3x0_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V3x0_2E0),s(tyop_2Enum_2Enum,V2x1_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V1y0_2E0),s(tyop_2Enum_2Enum,V0y1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3x0_2E0),s(tyop_2Enum_2Enum,V1y0_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2x1_2E0),s(tyop_2Enum_2Enum,V0y1_2E0))))))))) # label(thm_2Earithmetic_2EMODEQ__MULT__CONG) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2201 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2202 (all V0n_2E0 all V1m_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))))) # label(thm_2Earithmetic_2EMODEQ__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2203 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2204 (all V0q_2E0 s(tyop_2Enum_2Enum,V0q_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0q_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Earithmetic_2EDIV__ONE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2205 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2206 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) | s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) # label(thm_2Earithmetic_2EEXP__EQ__1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2207 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2208 (all V0y_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0)))))) # label(thm_2Earithmetic_2EMOD__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2209 (all V0n_2E0 all V1m_2E0 all V2b_2E0 (s(tyop_2Enum_2Enum,V2b_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V2b_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) | s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,V2b_2E0) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2b_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EEXP__BASE__LE__IFF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2210 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2211 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f816_1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f816_1_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef816_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2212 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))) # label(thm_2Earithmetic_2EMULT__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2213 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Earithmetic_2EMIN__DEF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2214 (all V0P_2E0 all V1p_2E0 all V2q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2q_2E0)))) -> ((exists V3k_2E0 exists V4r_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2Enum_2Enum,V2q_2E0))),s(tyop_2Enum_2Enum,V4r_2E0))) = s(tyop_2Enum_2Enum,V1p_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4r_2E0),s(tyop_2Enum_2Enum,V2q_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3k_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,V2q_2E0))))))))) # label(thm_2Earithmetic_2EDIV__P) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2215 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))))))) # label(thm_2Earithmetic_2EONE__LT__MULT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2216 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2217 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) | s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2ELESS__LESS__CASES) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2218 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2219 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2220 (all V0m_2E0 all V1n_2E0 all V2k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2k_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2k_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2k_2E0))))) # label(thm_2Earithmetic_2EDIV__MOD__MOD__DIV) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2221 (all V0n_2E0 all V1m_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Earithmetic_2ELESS__EXP__SUC__MONO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2222 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2ESUB__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2223 (all V0x_2E0 all V1y_2E0 (s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) <-> p(s(tyop_2Emin_2Ebool,f831_0_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))))) # label(def0_2Ethm_2Earithmetic_2ELESS__OR__EQ__ALT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2224 (all V0p_2E0 all V1q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1q_2E0)))))))) # label(thm_2Earithmetic_2EONE__LT__MULT__IMP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2225 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Earithmetic_2EEVEN__EXP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2226 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Earithmetic_2ELESS__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2227 (all V0y_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0y_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))))))) # label(thm_2Earithmetic_2EZERO__LT__EXP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2228 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> (exists V2p_2E0 s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2229 (all V0n_2E0 all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V3z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V3z_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2230 (all V0n_2E0 all V1m_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Earithmetic_2ELT__MULT__CANCEL__LBARE) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2231 (all V0n_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2232 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Earithmetic_2ELESS__NOT__SUC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2233 (all V0a_2E0 all V1c_2E0 s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1c_2E0))),s(tyop_2Enum_2Enum,V1c_2E0)))) # label(thm_2Earithmetic_2EADD__SUB) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2234 (all A_27a all V0f_2E0 all V1g_2E0 ((all V2n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))) <-> (all V4n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))))))) & (all V3n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))))))) # label(thm_2Earithmetic_2ESUC__ELIM__NUMERALS) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2235 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Earithmetic_2EMULT__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2236 (all V0n_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1r_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V2q_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2q_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1r_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V1r_2E0)))) # label(thm_2Earithmetic_2EMOD__MULT) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2237 (all V0b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0)))) -> (all V1n_2E0 exists V2m_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V2m_2E0))))))))) # label(thm_2Earithmetic_2EEXP__ALWAYS__BIG__ENOUGH) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2238 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2239 (all V0m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))) # label(thm_2Earithmetic_2ESUB__0) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2240 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2241 (all A_27a all V0y_2E0 all V1x_2E0 all V2R_2E0 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)),V2R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V0y_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) # label(thm_2Earithmetic_2ENRC__1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2242 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2243 (all V0n_2E0 all V1e1_2E0 all V2e0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2e0_2E0),s(tyop_2Enum_2Enum,V1e1_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1e1_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2e0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__INTRO__CONG) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2244 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 ((exists V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) # label(thm_2Earithmetic_2ERTC__eq__NRC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2245 (all V0x_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))))))) # label(thm_2Earithmetic_2EX__LT__EXP__X) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2246 (all V3f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),f815_2_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),V3f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),f815_1_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),V3f_2E0)))) # label(def6_2Ethm_2Earithmetic_2Efindq__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2247 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Earithmetic_2ELESS__EQUAL__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2248 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2249 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2250 (all V0n_2E0 all V1m_2E0 all V2a_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1167_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1167_1_2E3(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EDIVMOD__THM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2251 (all V0k_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Earithmetic_2EMOD__1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2252 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2253 (all V0m_2E0 all V1n_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))) # label(thm_2Earithmetic_2EMIN__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.70 2254 (all V2a_2E0 all V1m_2E0 all V0n_2E0 all V3q_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3q_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V3q_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1167_1_2E4(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V3q_2E0)))) # label(def1_2Ethm_2Earithmetic_2EDIVMOD__THM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2255 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EEVEN__OR__ODD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2256 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))))) # label(thm_2Earithmetic_2ELESS__EQ__IMP__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2257 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1n_2E0) | s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Earithmetic_2EMULT__EQ__ID) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2258 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2259 (all V0n_2E0 exists V1m_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))) | s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) # label(thm_2Earithmetic_2EODD__OR__EVEN) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2260 (all V0n_2E0 all V1m_2E0 all V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Earithmetic_2EABS__DIFF__ADD__SAME) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2261 (all V0f_2E0 all V1a_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f816_2_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f816_1_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))) # label(def3_2Ethm_2Earithmetic_2EDIVMOD__DEF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2262 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Earithmetic_2EMOD__MOD) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2263 (all V0n_2E0 all V1m1_2E0 all V2m2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EMODEQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m1_2E0),s(tyop_2Enum_2Enum,V2m2_2E0)))) <-> (exists V3a_2E0 exists V4b_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V4b_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2m2_2E0)))))) # label(thm_2Earithmetic_2EMODEQ__DEF) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2264 (all V0n_2E0 all V1m_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__SUC__IMP) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2265 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Earithmetic_2EMIN__IDEM) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2266 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2Earithmetic_2ELESS__EQ__CASES) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2267 (all V0m_2E0 all V1n_2E0 -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,V0m_2E0))))) # label(thm_2Earithmetic_2ENOT__SUC__ADD__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2268 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1199_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0))) = s(tyop_2Emin_2Ebool,f1199_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0)))) # label(arityeq4_2Ef1199_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2269 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1211_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f1211_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1211_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2270 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eposet_2Erelation_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eposet_2Erelation_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Eposet_2Erelation_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2271 (all A_27a all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) <-> (all V1c_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0),s(A_27a,V2x_2E0))))) & (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0),s(A_27a,V3x_2E0))))))))) # label(thm_2Eposet_2Ecomplete__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2272 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3y_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)),V1r_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ebottom_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(A_27a,V2x_2E0)))))) # label(thm_2Eposet_2Ebottom__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2273 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2274 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Eposet_2Ecomplete_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Eposet_2Ecomplete_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2275 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Eposet_2Efunction_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eposet_2Efunction_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Efunction_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2276 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2277 (all A_27a all V0s_2E0 all V1r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0)))))) # label(thm_2Eposet_2Ecarrier__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2278 (all A_27a all V0s_2E0 all V1r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eposet_2Erelation_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0)))))) # label(thm_2Eposet_2Erelation__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2279 (all A_27a all V0p_2E0 all V1f_2E0 all V2x_2E0 all V3x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V3x_27_2E0)))) -> s(A_27a,V3x_27_2E0) = s(A_27a,V2x_2E0))) # label(thm_2Eposet_2Egfp__unique) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2280 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eposet_2Etop_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Etop_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Etop_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2281 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eposet_2Eglb_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Eglb_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2282 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))))),c_2Eposet_2Epointwise__lift_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),c_2Eposet_2Epointwise__lift_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Epointwise__lift_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2283 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2284 (all A_27a all V0s_2E0 all V1r_2E0 all V2p_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1211_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V3x_2E0)))) # label(thm_2Eposet_2Eglb__pred) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2285 (all A_27a all A_27b all V0t_2E0 all V2r_2E0 all V3f_2E0 all V4g_2E0 ((all V5x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(A_27a,V5x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2r_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V5x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4g_2E0),s(A_27a,V5x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,f1199_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2r_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4g_2E0)))))) # label(def0_2Ethm_2Eposet_2Epointwise__lift__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2286 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2287 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Echain_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eposet_2Echain_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Echain_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2288 (all A_27a all V0s_2E0 all V1r_2E0 all V2p_2E0 all V3x_2E0 ((all V5z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V5z_2E0)))) & (all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V6y_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)),V1r_2E0),s(A_27a,V5z_2E0))),s(A_27a,V6y_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)),V1r_2E0),s(A_27a,V5z_2E0))),s(A_27a,V3x_2E0)))))) & (all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4y_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)),V1r_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V3x_2E0)))))) # label(thm_2Eposet_2Eglb__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2289 (all A_27a all V0s_2E0 all V3c_2E0 all V2f_2E0 all V5y_2E0 ((exists V6z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0),s(A_27a,V6z_2E0)))) & s(A_27a,V5y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V6z_2E0))))) <-> p(s(tyop_2Emin_2Ebool,f1202_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V5y_2E0)))))) # label(def0_2Ethm_2Eposet_2Edown__continuous__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2290 (all A_27a all V0p_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Emonotonic_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Eknaster__tarski__gfp) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2291 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2292 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0)))))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Eposet__nonempty) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2293 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2294 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1199_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),f1199_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef1199_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2295 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1201_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,f1201_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef1201_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2296 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2297 (all A_27a all V0s_2E0 all V1r_2E0 all V2f_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0)))) <-> s(A_27a,V3x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0))) & (all V4y_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)),V1r_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4y_2E0))))),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4y_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)),V1r_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_2E0)))))) # label(thm_2Eposet_2Elfp__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2298 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2299 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2300 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Eposet_2Ecomplete_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Eposet_2Ecomplete_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2301 (all A_27a all V0s_2E0 all V1r_2E0 all V2f_2E0 ((all V3c_2E0 all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Echain_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1201_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eup__continuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0)))))) # label(thm_2Eposet_2Eup__continuous__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2302 (all A_27a all V0s_2E0 all V1r_2E0 all V2p_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1210_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0))),s(A_27a,V3x_2E0)))) # label(thm_2Eposet_2Elub__pred) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2303 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eposet_2Eup__continuous_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Eup__continuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Eup__continuous_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2304 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eposet_2Elfp_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Elfp_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2305 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1201_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1201_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0)))) # label(arityeq3_2Ef1201_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2306 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_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)),V1r_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0)))))) # label(thm_2Eposet_2Eposet__refl) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2307 (all A_27a all V0s_2E0 all V2p_2E0 all V4j_2E0 (p(s(tyop_2Emin_2Ebool,f1211_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V4j_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4j_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V4j_2E0)))))) # label(def0_2Ethm_2Eposet_2Eglb__pred) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2308 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2r_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eposet_2Efunction_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),f1199_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2r_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Eposet_2Epointwise__lift_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2r_2E0)))))) # label(thm_2Eposet_2Epointwise__lift__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2309 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eposet_2Egfp_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Egfp_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2310 (all A_27a all V0s_2E0 all V3c_2E0 all V2f_2E0 all V5y_2E0 ((exists V6z_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V6z_2E0))) = s(A_27a,V5y_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V6z_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,f1201_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V5y_2E0)))))) # label(def0_2Ethm_2Eposet_2Eup__continuous__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2311 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Eposet_2Efunction_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Efunction_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2312 (all A_27a all V0p_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Emonotonic_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Eknaster__tarski__lfp) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2313 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2314 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f1210_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1210_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1210_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2315 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2316 (all A_27a all V0s_2E0 all V1r_2E0 all V2f_2E0 ((all V3c_2E0 all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Echain_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1202_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3c_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Edown__continuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0)))))) # label(thm_2Eposet_2Edown__continuous__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2317 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2318 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2319 (all A_27a all V0s_2E0 all V1r_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0))))) & (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_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)),V1r_2E0),s(A_27a,V3x_2E0))),s(A_27a,V3x_2E0)))))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V5y_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)),V1r_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V1r_2E0),s(A_27a,V5y_2E0))),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4x_2E0)))) -> s(A_27a,V5y_2E0) = s(A_27a,V4x_2E0))) & (all V6x_2E0 all V7y_2E0 all V8z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V7y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V8z_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)),V1r_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_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)),V1r_2E0),s(A_27a,V7y_2E0))),s(A_27a,V8z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V6x_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)),V1r_2E0),s(A_27a,V6x_2E0))),s(A_27a,V8z_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0)))))))) # label(thm_2Eposet_2Eposet__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2320 (all A_27a all A_27b all V0p_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),c_2Eposet_2Epointwise__lift_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))))))) # label(thm_2Eposet_2Ecomplete__pointwise) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2321 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1210_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1210_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1210_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2322 (all A_27a all V0p_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Econtinuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eup__continuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Edown__continuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))))) # label(thm_2Eposet_2Econtinuous__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2323 (all A_27a all V0p_2E0 all V1f_2E0 all V2x_2E0 all V3x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V3x_27_2E0)))) -> s(A_27a,V2x_2E0) = s(A_27a,V3x_27_2E0))) # label(thm_2Eposet_2Elfp__unique) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2324 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2325 (all A_27a all V0s_2E0 all V1r_2E0 all V2c_2E0 ((all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2c_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2c_2E0),s(A_27a,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_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)),V1r_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_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)),V1r_2E0),s(A_27a,V4y_2E0))),s(A_27a,V3x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Echain_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2c_2E0)))))) # label(thm_2Eposet_2Echain__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2326 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Eposet_2Efunction_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Efunction_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2327 (all A_27a all V0s_2E0 all V1r_2E0 all V2p_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_2E0)))) & (all V5z_2E0 ((all V6y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V6y_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)),V1r_2E0),s(A_27a,V6y_2E0))),s(A_27a,V5z_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V5z_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)),V1r_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0)))))) & (all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V4y_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)),V1r_2E0),s(A_27a,V4y_2E0))),s(A_27a,V3x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V3x_2E0)))))) # label(thm_2Eposet_2Elub__def) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2328 (all A_27a all V0p_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Emonotonic_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2x_2E0))))) & (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V3x_2E0))))))) # label(thm_2Eposet_2Eknaster__tarski) # label(axiom) # label(non_clause). [assumption]. 107.68/107.71 2329 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2330 (all A_27a all V0s_2E0 all V2p_2E0 all V4j_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V4j_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4j_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f1210_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(A_27a,V4j_2E0)))))) # label(def0_2Ethm_2Eposet_2Elub__pred) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2331 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Emonotonic_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eposet_2Emonotonic_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Emonotonic_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2332 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eposet_2Elub_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eposet_2Elub_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2333 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 all V3y_2E0 all V4z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_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)),V1r_2E0),s(A_27a,V3y_2E0))),s(A_27a,V4z_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)),V1r_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4z_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3y_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)),V1r_2E0),s(A_27a,V2x_2E0))),s(A_27a,V4z_2E0)))))) # label(thm_2Eposet_2Eposet__trans) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2334 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),c_2Eposet_2Eposet_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Eposet_2Eposet_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2335 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_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)),V1r_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_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)),V1r_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0)))))) -> s(A_27a,V3y_2E0) = s(A_27a,V2x_2E0))) # label(thm_2Eposet_2Eposet__antisym) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2336 (all A_27a all V0p_2E0 all V1c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eglb_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Ecomplete__down) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2337 (all A_27a all V0s_2E0 all V1r_2E0 all V2f_2E0 ((all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4y_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)),V1r_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_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)),V1r_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4y_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eposet_2Emonotonic_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0)))))) # label(thm_2Eposet_2Emonotonic__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2338 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2339 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f1202_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1202_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef1202_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2340 (all A_27a all V0s_2E0 all V1r_2E0 all V2f_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Egfp_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0)))) <-> (all V4y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V4y_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)),V1r_2E0),s(A_27a,V4y_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4y_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)),V1r_2E0),s(A_27a,V4y_2E0))),s(A_27a,V3x_2E0)))))) & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0))) = s(A_27a,V3x_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3x_2E0)))))) # label(thm_2Eposet_2Egfp__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2341 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1202_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1202_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0)))) # label(arityeq3_2Ef1202_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2342 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2343 (all A_27a all A_27b all V0a_2E0 all V1b_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Efunction_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0)))))))))) # label(thm_2Eposet_2Efunction__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2344 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Ebottom_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eposet_2Ebottom_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Ebottom_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2345 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Etop_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))),s(A_27a,V2x_2E0)))) <-> (all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3y_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)),V1r_2E0),s(A_27a,V3y_2E0))),s(A_27a,V2x_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Eposet_2Etop__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2346 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Edown__continuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eposet_2Edown__continuous_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Edown__continuous_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2347 (all A_27a all V0p_2E0 all V1c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Elub_2E3(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1c_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Eposet_2Ecomplete__up) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2348 (all A_27a all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Etop_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(A_27a,V1x_2E0))))))) # label(thm_2Eposet_2Ecomplete__top) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2349 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2350 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2351 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1211_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1211_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1211_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2352 (all A_27a all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eposet_2Eposet_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ecomplete_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0)))) -> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Eposet_2Ebottom_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0p_2E0),s(A_27a,V1x_2E0))))))) # label(thm_2Eposet_2Ecomplete__bottom) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2353 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2354 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2355 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Eposet_2Epointwise__lift_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))))),c_2Eposet_2Epointwise__lift_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Epointwise__lift_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2356 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eposet_2Econtinuous_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eposet_2Econtinuous_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eposet_2Econtinuous_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2357 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eposet_2Ecarrier_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eposet_2Ecarrier_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Eposet_2Ecarrier_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2358 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2359 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2360 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2361 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2362 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2363 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2364 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMAX_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMAX_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2365 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2366 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)))),c_2Enumeral_2EiBIT__cases_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X3_2E0))) = s(A_27a,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X3_2E0)))) # label(arityeq4_2Ec_2Enumeral_2EiBIT__cases_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2367 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2368 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1262_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1262_1_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1262_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2369 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2370 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1230_0_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Enumeral_2Eexactlog__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2371 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)) # label(thm_2Enumeral_2Eexactlog__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2372 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2373 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,f1262_1_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1262_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1262_1_2E3) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2374 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2375 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2Eexactlog_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2Eexactlog_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2376 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2377 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EODD_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2378 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiZ_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2EiZ_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2379 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIVMOD_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EDIVMOD_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2380 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,f1226_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1226_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2381 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,f1226_2_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1226_2_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2382 (all V0y_2E0 all V1x_2E0 all V5m_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1262_3_2E3(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))))) = s(tyop_2Enum_2Enum,f1262_2_2E3(s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V5m_2E0)))) # label(def3_2Ethm_2Enumeral_2Eenumeral__mult) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2383 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2384 (all V9b_2E0 all V10n_2E0 all V11x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V9b_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,V11x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_1_2E1(s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_3_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,V11x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_3_2E1(s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_5_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,V9b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Enum_2Enum,V11x_2E0)))) # label(thm_2Enumeral_2EiSUB__DEF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2385 (all V2b_2E0 all V3n_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2b_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_0_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_2_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_2_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_4_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,V2b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V4x_2E0)))) # label(thm_2Enumeral_2EiSUB__DEF_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2386 (all V0b_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) # label(thm_2Enumeral_2EiSUB__DEF_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2387 (all V3n_2E0 all V8m_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V8m_2E0))))) = s(tyop_2Enum_2Enum,f1226_4_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V8m_2E0)))) # label(def2_2Ethm_2Enumeral_2EiSUB__DEF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2388 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Enumeral_2Enumeral__add) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2389 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2Eonecount_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumeral_2Eonecount_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2390 (all V0n_2E0 all V1m_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) & (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))))) & s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) # label(thm_2Enumeral_2Enumeral__lte) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2391 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1262_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1262_2_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1262_2_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2392 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2393 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))) & (all V1n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) & (all V2n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))) -> (all V3n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))) # label(thm_2Enumeral_2Ebit__induction) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2394 (all A_27a all V0zf_2E0 all V1b1f_2E0 all V2b2f_2E0 exists V3f_2E0 ((all V4n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V1b1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))) & (all V5n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V5n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V2b2f_2E0),s(tyop_2Enum_2Enum,V5n_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,V5n_2E0)))))) & s(A_27a,V0zf_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) # label(thm_2Enumeral_2Ebit__initiality) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2395 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2396 (all V1a_2E0 all V0m_2E0 all V2n_2E0 all V3q_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1252_0_2E4(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3q_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V3q_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3q_2E0))))),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(def0_2Ethm_2Enumeral_2Edivmod__POS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2397 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2398 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2399 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2400 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1226_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2401 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2402 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2403 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2404 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2405 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_3_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_3_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1226_3_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2406 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,f1226_5_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_5_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1226_5_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2407 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))) & s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))))))) # label(thm_2Enumeral_2Einternal__mult__characterisation) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2408 (all V0x_2E0 s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral_2EiZ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2409 (all V1x_2E0 all V0y_2E0 all V3n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))))),s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))))) = s(tyop_2Enum_2Enum,f1262_0_2E3(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) # label(def1_2Ethm_2Enumeral_2Eenumeral__mult) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2410 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1226_2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2411 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X3_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum)))),c_2Enumeral_2EiBIT__cases_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X3_2E0)))) # label(arityeq4_2Ec_2Enumeral_2EiBIT__cases_2E4_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2412 (all V1n_2E0 all V2acc_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2acc_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2acc_2E0)))) # label(thm_2Enumeral_2Etexp__help__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2413 (all V0acc_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0acc_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0acc_2E0)))) # label(thm_2Enumeral_2Etexp__help__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2414 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMIN_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2415 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2416 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1262_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1262_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1262_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2417 (all V3n_2E0 all V6m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V6m_2E0))))) = s(tyop_2Enum_2Enum,f1226_2_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V6m_2E0)))) # label(def5_2Ethm_2Enumeral_2EiSUB__DEF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2418 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiiSUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2EiiSUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2419 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2420 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))) # label(thm_2Enumeral_2Enumeral__exp_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2421 (all V3n_2E0 all V4m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V4m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4m_2E0)))))) # label(thm_2Enumeral_2Enumeral__exp_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2422 (all V1n_2E0 all V2m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))))) # label(thm_2Enumeral_2Enumeral__exp_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2423 (all V0n_2E0 all V1a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))) # label(thm_2Enumeral_2Etexp__help__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2424 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral_2EiSQR) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2425 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2426 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,f1226_4_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_4_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1226_4_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2427 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enumeral_2EiiSUC) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2428 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__fact_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2429 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))))) # label(thm_2Enumeral_2Enumeral__fact_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2430 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiSQR_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2EiSQR_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2431 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2432 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2EiDUB_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2433 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,f1226_3_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1226_3_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2434 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2435 (all V0n_2E0 all V1a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))))) -> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) # label(thm_2Enumeral_2Eonecount__characterisation) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2436 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2437 (all V0y_2E0 all V1x_2E0 (s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) & s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) # label(thm_2Enumeral_2Enumeral__MAX) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2438 (all V0n_2E0 all V1m_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Enumeral_2Enumeral__sub) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2439 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Enumeral_2EiDUB__removal) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2440 (all V0n_2E0 all V1m_2E0 ((s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))) <-> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,V1m_2E0)) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) <-> s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,V0n_2E0)) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumeral_2Enumeral__eq) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2441 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumeral_2EiSUB_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumeral_2EiSUB_2E3) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2442 (all X0_2E0 s(tyop_2Enum_2Enum,f1230_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1230_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1230_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2443 (all A_27a ((all V3n_2E0 all V4zf_2E0 all V5bf1_2E0 all V6bf2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5bf1_2E0),s(tyop_2Enum_2Enum,V3n_2E0))) = s(A_27a,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(A_27a,V4zf_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5bf1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V6bf2_2E0)))) & (all V7n_2E0 all V8zf_2E0 all V9bf1_2E0 all V10bf2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V10bf2_2E0),s(tyop_2Enum_2Enum,V7n_2E0))) = s(A_27a,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V7n_2E0))),s(A_27a,V8zf_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V9bf1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V10bf2_2E0)))) & (all V0zf_2E0 all V1bf1_2E0 all V2bf2_2E0 s(A_27a,V0zf_2E0) = s(A_27a,c_2Enumeral_2EiBIT__cases_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(A_27a,V0zf_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1bf1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2bf2_2E0)))))) # label(thm_2Enumeral_2EiBIT__cases) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2444 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2445 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.72/107.72 2446 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__evenodd) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2447 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2448 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))))))) # label(thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2449 (all V4m_2E0 all V5n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V4m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5n_2E0))))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V4m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5n_2E0)))))))))))) # label(thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2450 (all V6m_2E0 all V7n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V6m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V7n_2E0))))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V6m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V7n_2E0)))))))))))) # label(thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2451 (all V2m_2E0 all V3n_2E0 s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))) # label(thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2452 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral_2EiDUB) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2453 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Enumeral_2Eexactlog__characterisation) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2454 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2455 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2456 (all V3n_2E0 all V5m_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V5m_2E0))))) = s(tyop_2Enum_2Enum,f1226_0_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V5m_2E0)))) # label(def1_2Ethm_2Enumeral_2EiSUB__DEF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2457 (all V0m_2E0 all V1a_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1252_0_2E3(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))) # label(thm_2Enumeral_2Edivmod__POS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2458 (all V2x_2E0 s(tyop_2Enum_2Enum,f1230_0_2E1(s(tyop_2Enum_2Enum,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1230_1_2E1(s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0)))))) # label(def1_2Ethm_2Enumeral_2Eexactlog__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2459 (all V0y_2E0 all V1x_2E0 all V4m_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V4m_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V4m_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))))),s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))))) = s(tyop_2Enum_2Enum,f1262_1_2E3(s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V4m_2E0)))) # label(def0_2Ethm_2Enumeral_2Eenumeral__mult) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2460 (all V0x_2E0 all V1b_2E0 all V2n_2E0 all V3m_2E0 (s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,V2n_2E0) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V2n_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,V1b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0x_2E0))))) # label(thm_2Enumeral_2EiSUB__THM) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2461 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))) = s(tyop_2Enum_2Enum,V0x_2E0)) # label(thm_2Enumeral_2EDIV2__BIT1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2462 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Enumeral_2Etexp__help0) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2463 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,f1262_0_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1262_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1262_0_2E3) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2464 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1230_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f1230_1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1230_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2465 (all A_27a all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2466 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2467 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum),c_2Earithmetic_2Efindq_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2Efindq_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2468 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1226_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2469 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),f1252_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1252_0_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1252_0_2E3) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2470 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1262_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,f1262_2_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1262_2_2E3) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2471 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_4_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_4_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1226_4_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2472 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2473 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1262_3_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f1262_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1262_3_2E3) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2474 (all A_27a all V0x_2E0 all V1n_2E0 all V2f_2E0 (s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V0x_2E0))))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(A_27a,V0x_2E0))) & s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(A_27a,V0x_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V0x_2E0))))) & s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0))) # label(thm_2Enumeral_2Enumeral__funpow) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2475 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enumeral_2Enumeral__div2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2476 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__div2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2477 (all V5m_2E0 all V0y_2E0 all V1x_2E0 all V6n_2E0 s(tyop_2Enum_2Enum,f1262_3_2E4(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V6n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V5m_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V5m_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))))),s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0)))))))))) # label(def2_2Ethm_2Enumeral_2Eenumeral__mult) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2478 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,f1226_1_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1226_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2479 (all V0y_2E0 all V1x_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1262_2_2E2(s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))))) & s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1262_1_2E2(s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1262_0_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) # label(thm_2Enumeral_2Eenumeral__mult) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2480 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2481 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) # label(thm_2Enumeral_2Enumeral__iisuc) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2482 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2Einternal__mult_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Einternal__mult_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumeral_2Einternal__mult_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2483 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2484 (all V0y_2E0 all V1x_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Enumeral_2Enumeral__MIN) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2485 (all V2x_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,V2x_2E0) <-> p(s(tyop_2Emin_2Ebool,f1230_1_2E1(s(tyop_2Enum_2Enum,V2x_2E0)))))) # label(def0_2Ethm_2Enumeral_2Eexactlog__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2486 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2487 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2488 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Enumeral_2Enumeral__mult) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2489 (all V10n_2E0 all V13m_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V13m_2E0))))) = s(tyop_2Enum_2Enum,f1226_3_2E2(s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V13m_2E0)))) # label(def0_2Ethm_2Enumeral_2EiSUB__DEF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2490 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,f1262_3_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f1262_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef1262_3_2E4) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2491 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) # label(thm_2Enumeral_2ETWO__EXP__THM) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2492 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1252_0_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),f1252_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef1252_0_2E4) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2493 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EDIV2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2494 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EFACT_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EFACT_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2495 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0)) # label(thm_2Enumeral_2Eonecount__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2496 (all V3n_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V4x_2E0)))) # label(thm_2Enumeral_2Eonecount__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2497 (all V1n_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Eonecount_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2x_2E0)))) # label(thm_2Enumeral_2Eonecount__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2498 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2499 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral_2Etexp__help_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumeral_2Etexp__help_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2500 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__pre_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2501 (all V2n_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Enumeral_2Enumeral__pre_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2502 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Enumeral_2Enumeral__pre_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2503 (all V10n_2E0 all V15m_2E0 s(tyop_2Enum_2Enum,f1226_5_2E2(s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V15m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V15m_2E0)))))) # label(def4_2Ethm_2Enumeral_2EiSUB__DEF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2504 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1226_5_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1226_5_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1226_5_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2505 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2506 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2507 (all V0n_2E0 all V1acc_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1acc_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V1acc_2E0))) & s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1acc_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1acc_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1acc_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral_2Etexp__help_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1acc_2E0))))) # label(thm_2Enumeral_2Enumeral__texp__help) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2508 (all V10n_2E0 all V12m_2E0 s(tyop_2Enum_2Enum,f1226_1_2E2(s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V12m_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiSUB_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V12m_2E0)))))) # label(def3_2Ethm_2Enumeral_2EiSUB__DEF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2509 (all V0n_2E0 all V1m_2E0 (s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) & s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) & s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) & s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(thm_2Enumeral_2Enumeral__lt) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2510 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eprim__rec_2EPRE_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2511 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumeral_2Enumeral__suc_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2512 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Enumeral_2Enumeral__suc_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2513 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2514 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2515 (all V1n_2E0 s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2516 (all V5n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V5n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2517 (all V10n_2E0 all V11m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V10n_2E0),s(tyop_2Enum_2Enum,V11m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V10n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V11m_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2518 (all V17n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V17n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V17n_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2519 (all V18n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V18n_2E0))))) = s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V18n_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2520 (all V19n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V19n_2E0))) <-> s(tyop_2Enum_2Enum,V19n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2521 (all V25n_2E0 all V26m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V25n_2E0),s(tyop_2Enum_2Enum,V26m_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V25n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V26m_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2522 (all V29n_2E0 all V30m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V30m_2E0),s(tyop_2Enum_2Enum,V29n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V29n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V30m_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2523 (all V33n_2E0 all V34m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V33n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V34m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V33n_2E0),s(tyop_2Enum_2Enum,V34m_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2524 (all V36n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V36n_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V36n_2E0))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2525 (all V40n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V40n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V40n_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2526 (all V39n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V39n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V39n_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2527 (all V37n_2E0 all V38m_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V37n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V38m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V38m_2E0),s(tyop_2Enum_2Enum,V37n_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2528 (all V35n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V35n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2529 (all V32n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V32n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V32n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2530 (all V31n_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V31n_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2531 (all V28n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V28n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V28n_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2532 (all V27n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V27n_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2533 (all V24n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0),s(tyop_2Enum_2Enum,V24n_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V24n_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2534 (all V23n_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V23n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2535 (all V21n_2E0 all V22m_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V21n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V22m_2E0))) <-> s(tyop_2Enum_2Enum,V22m_2E0) = s(tyop_2Enum_2Enum,V21n_2E0))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2536 (all V20n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V20n_2E0))) <-> s(tyop_2Enum_2Enum,V20n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2537 (all V15n_2E0 all V16m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V15n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V16m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V15n_2E0),s(tyop_2Enum_2Enum,V16m_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2538 (all V14n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V14n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2539 (all V13n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V13n_2E0)))))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2540 (all V12n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V12n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2541 (all V9n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V9n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,V9n_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2542 (all V8n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V8n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2543 (all V6n_2E0 all V7m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V7m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Enum_2Enum,V7m_2E0)))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2544 (all V4n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2545 (all V2n_2E0 all V3m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V3m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0)))))))) # label(thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2546 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2547 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2548 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2549 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2550 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1281_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1281_1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1281_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2551 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2552 (all V0x_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,f1278_1_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) <-> s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,V2n_2E0))) # label(def0_2Ethm_2Ewhile_2ELEAST__EQ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2553 (all V0x_2E0 (s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1281_0_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))) & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1281_2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0) & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1281_3_2E0))) & s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1281_1_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))))) # label(thm_2Ewhile_2EOLEAST__EQNS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2554 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2555 (all V0Q_2E0 all V1P_2E0 (((all V2n_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))))) & (all V3n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) & (all V4m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4m_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V4m_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Ewhile_2EOLEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2556 (all A_27a all V0G_2E0 all V1f_2E0 all V2s_2E0 all V4n_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0),s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0),s(A_27a,V2s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,f1268_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2s_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))) # label(def1_2Ethm_2Ewhile_2EOWHILE__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2557 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Ewhile_2EHOARE__SPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ewhile_2EHOARE__SPEC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Ewhile_2EHOARE__SPEC_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2558 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ewhile_2EOLEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ewhile_2EOLEAST_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2559 (all V0p_2E0 ((exists V1n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0)))))) & (all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Ewhile_2ELEAST__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2560 (all V0P_2E0 ((all V1n_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) <-> s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))) # label(thm_2Ewhile_2EOLEAST__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2561 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2562 (all V3n_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,f1281_2_2E1(s(tyop_2Enum_2Enum,V3n_2E0)))) # label(def1_2Ethm_2Ewhile_2EOLEAST__EQNS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2563 (all A_27a all V0P_2E0 all V1g_2E0 all V2x_2E0 s(A_27a,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))),s(A_27a,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(A_27a,V2x_2E0))))),s(A_27a,V2x_2E0)))) # label(thm_2Ewhile_2EWHILE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2564 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2565 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2566 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ewhile_2EWHILE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ewhile_2EWHILE_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2567 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2568 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1271_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1271_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1271_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2569 (all V0x_2E0 s(tyop_2Emin_2Ebool,f1279_0_2E1(s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(def0_2Ethm_2Ewhile_2ELEAST__T) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2570 (all V0P_2E0 s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1267_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1267_1_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))))))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Ewhile_2EOLEAST__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2571 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1281_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1281_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1281_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2572 (all A_27a all V0s_27_2E0 all V1s_2E0 all V2f_2E0 all V3G_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0s_27_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V1s_2E0))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3G_2E0),s(A_27a,V0s_27_2E0)))))) # label(thm_2Ewhile_2EOWHILE__ENDCOND) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2573 (all V0x_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,f1281_1_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(def2_2Ethm_2Ewhile_2EOLEAST__EQNS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2574 (all A_27a all V0P_2E0 all V2B_2E0 all V6s_2E0 (p(s(tyop_2Emin_2Ebool,f1271_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0),s(A_27a,V6s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V6s_2E0)))) & -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0),s(A_27a,V6s_2E0)))))) # label(def0_2Ethm_2Ewhile_2EWHILE__RULE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2575 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1281_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f1281_3_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1281_3_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2576 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1267_1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1267_1_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef1267_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2577 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2578 (all V0x_2E0 (s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1278_1_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))) = s(tyop_2Enum_2Enum,V0x_2E0) & s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1278_0_2E1(s(tyop_2Enum_2Enum,V0x_2E0))))) = s(tyop_2Enum_2Enum,V0x_2E0))) # label(thm_2Ewhile_2ELEAST__EQ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2579 (all A_27a all A_27b all V0P_2E0 all V1C_2E0 all V2Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ewhile_2EHOARE__SPEC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1C_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0)))) <-> (all V3s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1C_2E0),s(A_27a,V3s_2E0)))))))))) # label(thm_2Ewhile_2EHOARE__SPEC__DEF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2580 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1271_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f1271_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1271_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2581 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2582 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),f1268_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1268_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1268_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2583 (all V0n_2E0 all V1P_2E0 ((all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0))))) # label(thm_2Ewhile_2EOLEAST__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2584 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2585 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,f1267_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) <-> (exists V1n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(def0_2Ethm_2Ewhile_2EOLEAST__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2586 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2587 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2588 (all V0p_2E0 ((exists V1n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) -> (all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0p_2E0)))))))) # label(thm_2Ewhile_2ELEAST__EXISTS__IMP) # label(axiom) # label(non_clause). [assumption]. 107.72/107.73 2589 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f1268_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1268_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1268_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2590 (all A_27a all V0P_2E0 all V1G_2E0 all V2f_2E0 ((all V4s1_2E0 all V5s2_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)),V0P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4s1_2E0))))),s(A_27a,V5s2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1G_2E0),s(A_27a,V4s1_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)),V0P_2E0),s(A_27a,V4s1_2E0))),s(A_27a,V5s2_2E0)))))) & (all V3s_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1G_2E0),s(A_27a,V3s_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)),V0P_2E0),s(A_27a,V3s_2E0))),s(A_27a,V3s_2E0)))))) -> (all V6s1_2E0 all V7s2_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7s2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V6s1_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)),V0P_2E0),s(A_27a,V6s1_2E0))),s(A_27a,V7s2_2E0)))))))) # label(thm_2Ewhile_2EOWHILE__IND) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2591 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))) = s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2592 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2593 (all V0P_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Ewhile_2ELESS__LEAST) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2594 (all A_27a all V0B_2E0 all V1C_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0)))) & (all V3s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0),s(A_27a,V3s_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)),V2R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1C_2E0),s(A_27a,V3s_2E0))))),s(A_27a,V3s_2E0)))))) -> (all V4P_2E0 ((all V5s_2E0 ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0),s(A_27a,V5s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1C_2E0),s(A_27a,V5s_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(A_27a,V5s_2E0)))))) -> (all V6v_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P_2E0),s(A_27a,V6v_2E0))))))))) # label(thm_2Ewhile_2EWHILE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2595 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1278_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1278_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1278_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2596 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1271_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1271_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1271_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2597 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),f1268_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Emin_2Ebool,f1268_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(A_27a,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef1268_1_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2598 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f1271_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1271_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1271_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2599 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2600 (all V0P_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Ewhile_2ELEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2601 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),c_2Ewhile_2EOWHILE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ewhile_2EOWHILE_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2602 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1281_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f1281_2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1281_2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2603 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ewhile_2EWHILE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ewhile_2EWHILE_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2604 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2605 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1278_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1278_1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1278_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2606 (all A_27a all V0P_2E0 all V2B_2E0 all V5s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0),s(A_27a,V5s_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f1271_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0),s(A_27a,V5s_2E0)))))) # label(def1_2Ethm_2Ewhile_2EWHILE__RULE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2607 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2608 (all A_27a all V0s_2E0 all V1f_2E0 all V2G_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2G_2E0),s(A_27a,V0s_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V0s_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0s_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V0s_2E0)))) # label(thm_2Ewhile_2EOWHILE__THM) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2609 (all V0Q_2E0 all V1P_2E0 ((all V3n_2E0 ((all V4m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4m_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V4m_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) & (exists V2n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0Q_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Ewhile_2ELEAST__ELIM) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2610 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2611 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2612 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2613 (all V0x_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,f1281_0_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(def3_2Ethm_2Ewhile_2EOLEAST__EQNS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2614 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1267_1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,f1267_1_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1267_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2615 (all V0P_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Enum_2Enum,V1x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Ewhile_2EFULL__LEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2616 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2617 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2618 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1281_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,f1281_1_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1281_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2619 (all A_27a all V0s_27_2E0 all V1s_2E0 all V2f_2E0 all V3G_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0s_27_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V1s_2E0))) -> s(A_27a,V0s_27_2E0) = s(A_27a,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V1s_2E0))))) # label(thm_2Ewhile_2EOWHILE__WHILE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2620 (all V4n_2E0 s(tyop_2Emin_2Ebool,f1281_3_2E1(s(tyop_2Enum_2Enum,V4n_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(def0_2Ethm_2Ewhile_2EOLEAST__EQNS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2621 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Ewhile_2EHOARE__SPEC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Ewhile_2EHOARE__SPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Ewhile_2EHOARE__SPEC_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2622 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2623 (all A_27a all V0G_2E0 all V1f_2E0 all V2s_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1268_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2s_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1268_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2s_2E0))))),s(A_27a,V2s_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) # label(thm_2Ewhile_2EOWHILE__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2624 (all A_27a all V0P_2E0 all V1g_2E0 exists V2f_2E0 all V3x_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))),s(A_27a,V3x_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(A_27a,V3x_2E0))))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3x_2E0)))) # label(thm_2Ewhile_2EITERATION) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2625 (all A_27a all V0G_2E0 all V1f_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,f1268_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V2s_2E0)))) <-> (exists V3n_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0G_2E0),s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(A_27a,V2s_2E0))))))))) # label(def0_2Ethm_2Ewhile_2EOWHILE__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2626 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f1267_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,f1267_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef1267_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2627 (all A_27a all V0s_2E0 all V1f_2E0 all V2G_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,V0s_2E0))) <-> (all V3n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2G_2E0),s(A_27a,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(A_27a,V0s_2E0))))))))) # label(thm_2Ewhile_2EOWHILE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2628 (all V0P_2E0 all V2n_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Emin_2Ebool,f1267_1_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(def1_2Ethm_2Ewhile_2EOLEAST__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2629 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2630 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2631 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2632 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2ESOME_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2633 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1278_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,f1278_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1278_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2634 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2635 (all A_27a all V0P_2E0 all V1G_2E0 all V2f_2E0 all V3s_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1G_2E0),s(A_27a,V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V4x_2E0)))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3s_2E0)))) -> (all V5s_27_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Ewhile_2EOWHILE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1G_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V3s_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5s_27_2E0))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5s_27_2E0)))))))) # label(thm_2Ewhile_2EOWHILE__INV__IND) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2636 (all V0x_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,f1278_0_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0x_2E0))) # label(def1_2Ethm_2Ewhile_2ELEAST__EQ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2637 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2638 (all A_27a all V0P_2E0 all V1R_2E0 all V2B_2E0 all V3C_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0)))) & (all V4s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0),s(A_27a,V4s_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)),V1R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V3C_2E0),s(A_27a,V4s_2E0))))),s(A_27a,V4s_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Ewhile_2EHOARE__SPEC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1271_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V3C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ewhile_2EHOARE__SPEC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ewhile_2EWHILE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V3C_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1271_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2B_2E0))))))))) # label(thm_2Ewhile_2EWHILE__RULE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2639 (all X0_2E0 s(tyop_2Emin_2Ebool,f1279_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1279_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1279_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2640 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ewhile_2EWHILE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ewhile_2EWHILE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ewhile_2EWHILE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2641 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1278_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,f1278_1_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1278_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2642 (all V0P_2E0 s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Enum_2Enum,c_2Ewhile_2EWHILE_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Ewhile_2ELEAST__DEF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2643 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f1281_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1281_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1281_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2644 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Ewhile_2ELEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ewhile_2ELEAST_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2645 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2646 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2647 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Enum_2Enum),c_2EbasicSize_2Eone__size_2E0),s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Enum_2Enum,c_2EbasicSize_2Eone__size_2E1(s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ec_2EbasicSize_2Eone__size_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2648 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2649 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2650 (all A_27a all A_27b ((all V3f_2E0 all V4g_2E0 all V5y_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Esum__size_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V4g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,V5y_2E0))))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V4g_2E0),s(A_27b,V5y_2E0)))) & (all V0f_2E0 all V1g_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Esum__size_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2x_2E0))))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2EbasicSize_2Esum__size__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2651 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2652 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),f1291_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)))),f1291_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ef1291_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2653 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2654 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),c_2EbasicSize_2Epair__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum))),c_2EbasicSize_2Epair__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2EbasicSize_2Epair__size_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2655 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),f1291_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),c_2EbasicSize_2Epair__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0)))) # label(thm_2EbasicSize_2Epair__size__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2656 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2657 (all V0b_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,V0b_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2EbasicSize_2Ebool__size__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2658 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Eone__size_2E1(s(tyop_2Eone_2Eone,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2EbasicSize_2Eone__size__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2659 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2660 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Eoption__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Enum_2Enum)),c_2EbasicSize_2Eoption__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2EbasicSize_2Eoption__size_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2661 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2662 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2663 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2664 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2665 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2666 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2667 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Enum_2Enum))),c_2EbasicSize_2Esum__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0))) = s(tyop_2Enum_2Enum,c_2EbasicSize_2Esum__size_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2EbasicSize_2Esum__size_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2668 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Enum_2Enum,f1291_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1g_2E0),s(A_27b,V3y_2E0)))))) # label(def0_2Ethm_2EbasicSize_2Epair__size__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2669 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2670 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Enum_2Enum),c_2EbasicSize_2Ebool__size_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Enum_2Enum,c_2EbasicSize_2Ebool__size_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2EbasicSize_2Ebool__size_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2671 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2672 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2673 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2674 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)))),f1291_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Enum_2Enum,f1291_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef1291_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2675 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2676 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2677 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2678 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2679 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2680 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2681 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2682 (all A_27a ((all V0f_2E0 s(tyop_2Enum_2Enum,c_2EbasicSize_2Eoption__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) & (all V1f_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V2x_2E0))))) = s(tyop_2Enum_2Enum,c_2EbasicSize_2Eoption__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0)))))))) # label(thm_2EbasicSize_2Eoption__size__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2683 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2684 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Edivides_2ELEQ__DIVIDES__FACT) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2685 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) | s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Edivides_2EDIVIDES__MULT__LEFT) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2686 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2687 (all V0x_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Edivides_2EDIVIDES__ONE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2688 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2689 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Edivides_2EDIVIDES__ADD__2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2690 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Edivides_2EPRIMES_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Edivides_2EPRIMES_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2691 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Edivides_2Eprime__divides__only__self) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2692 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Edivides_2EprimePRIMES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2693 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2694 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2695 (all V0n_2E0 exists V1i_2E0 ((all V2j_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2j_2E0),s(tyop_2Enum_2Enum,V1i_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V2j_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1i_2E0)))))))) # label(thm_2Edivides_2ENEXT__LARGER__PRIME) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2696 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Edivides_2ELT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2697 (all X0_2E0 s(tyop_2Emin_2Ebool,f1336_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1336_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1336_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2698 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0))))) # label(thm_2Edivides_2EONE__DIVIDES__ALL) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2699 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Ewhile_2ELEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ewhile_2ELEAST_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2700 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2701 (all V0a_2E0 all V1b_2E0 s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1336_0_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Emin_2Ebool,f1336_0_2E1(s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1336_1_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1336_0_2E1(s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,f1336_0_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))))))))))) # label(thm_2Edivides_2Ecompute__divides) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2702 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))))) # label(thm_2Edivides_2EDIVIDES__ADD__1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2703 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2704 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2705 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Edivides_2EALL__DIVIDES__0) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2706 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2707 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2708 (all V0m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Edivides_2EZERO__DIVIDES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2709 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f1297_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1297_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1297_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2710 (all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0p_2E0)))))) # label(thm_2Edivides_2EPRIME__POS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2711 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Edivides_2EDIVIDES__LE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2712 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2713 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> s(tyop_2Enum_2Enum,V1b_2E0) = s(tyop_2Enum_2Enum,V0a_2E0))) # label(thm_2Edivides_2EDIVIDES__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2714 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))))) # label(thm_2Edivides_2EDIVIDES__SUB) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2715 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2716 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Edivides_2EZERO__LT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2717 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2718 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2719 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) # label(thm_2Edivides_2EINFINITE__PRIMES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.74 2720 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2721 (all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) <-> (exists V1i_2E0 s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1i_2E0))) = s(tyop_2Enum_2Enum,V0p_2E0)))) # label(thm_2Edivides_2EPRIME__INDEX) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2722 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Edivides_2Eprime_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Edivides_2Eprime_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2723 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2724 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2725 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EFACT_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EFACT_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2726 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Edivides_2EDIVIDES__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2727 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Edivides_2Edivides_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Edivides_2Edivides_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2728 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Edivides_2EINDEX__LESS__PRIMES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2729 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Edivides_2EONE__LT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2730 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Edivides_2ENOT__LT__DIVIDES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2731 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Edivides_2EDIVIDES__LEQ__OR__ZERO) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2732 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2733 (all V0n_2E0 exists V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))))) # label(thm_2Edivides_2EEUCLID) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2734 (all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) -> (exists V1i_2E0 s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1i_2E0))) = s(tyop_2Enum_2Enum,V0p_2E0)))) # label(thm_2Edivides_2EPRIMES__ONTO) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2735 (all V0a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0a_2E0)))) <-> (all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) -> s(tyop_2Enum_2Enum,V1b_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) | s(tyop_2Enum_2Enum,V1b_2E0) = s(tyop_2Enum_2Enum,V0a_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) != s(tyop_2Enum_2Enum,V0a_2E0))) # label(thm_2Edivides_2Eprime__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2736 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) -> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Edivides_2EPRIMES__11) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2737 (all X0_2E0 s(tyop_2Emin_2Ebool,f1336_1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1336_1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1336_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2738 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1297_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1297_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1297_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2739 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))))) # label(thm_2Edivides_2EDIVIDES__MULT) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2740 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2741 (all V0a_2E0 (p(s(tyop_2Emin_2Ebool,f1336_0_2E1(s(tyop_2Enum_2Enum,V0a_2E0)))) <-> s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(def1_2Ethm_2Edivides_2Ecompute__divides) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2742 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2743 (all V0p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0p_2E0)))))) # label(thm_2Edivides_2EONE__LT__PRIME) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2744 (all V0b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E1(s(tyop_2Enum_2Enum,V0b_2E0)))))))) # label(thm_2Edivides_2EDIVIDES__FACT) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2745 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2746 (all V0n_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,f1297_0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1p_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))))) # label(def0_2Ethm_2Edivides_2EPRIMES__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2747 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2748 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) <-> (exists V2q_2E0 s(tyop_2Enum_2Enum,V1b_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2q_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))))) # label(thm_2Edivides_2Edivides__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2749 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2750 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2751 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2752 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2753 (all V0n_2E0 exists V1i_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V1i_2E0))))))) # label(thm_2Edivides_2EEUCLID__PRIMES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2754 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2755 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1297_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Edivides_2EPRIMES__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2756 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2757 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))) # label(thm_2Edivides_2EDIVIDES__REFL) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2758 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2759 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2760 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) != s(tyop_2Enum_2Enum,V0n_2E0) -> (exists V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Edivides_2EPRIME__FACTOR) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2761 (all A_27a all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2762 (all V0a_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,V0a_2E0) <-> p(s(tyop_2Emin_2Ebool,f1336_1_2E1(s(tyop_2Enum_2Enum,V0a_2E0)))))) # label(def0_2Ethm_2Edivides_2Ecompute__divides) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2763 (all V0n_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Enum_2Enum,c_2Edivides_2EPRIMES_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2Edivides_2EPRIMES__NO__GAP) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2764 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2765 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,f1373_0_2E3(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),f1373_0_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1373_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2766 (all A_27a s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0)) # label(thm_2Eind__type_2EBOTTOM) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2767 (all A_27a all A_27b all V0Fn_2E0 exists V1f_2E0 all V2c_2E0 all V3i_2E0 all V4r_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),V1f_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V2c_2E0),s(A_27a,V3i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V4r_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),A_27b)))),V0Fn_2E0),s(tyop_2Enum_2Enum,V2c_2E0))),s(A_27a,V3i_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V4r_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),f1373_0_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V4r_2E0)))))) # label(thm_2Eind__type_2ECONSTR__REC) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2768 (all A_27a all A_27b all V0g_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0)))) -> (all V2P_2E0 ((all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V4x_2E0))))))) <-> (all V3x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0))))))) & (all V8a_2E0 all V9b_2E0 (s(A_27a,V8a_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V9b_2E0))) <-> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V8a_2E0))) = s(A_27b,V9b_2E0))) & (all V5P_2E0 ((exists V7x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V0g_2E0),s(A_27b,V7x_2E0))))))) <-> (exists V6x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5P_2E0),s(A_27a,V6x_2E0))))))))) # label(thm_2Eind__type_2EISO__USAGE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2769 (all A_27a all A_27b all A_27c all A_27d all V0g_27_2E0 all V3f_2E0 all V6h_2E0 all V7a_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V0g_27_2E0),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6h_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(A_27a,V7a_2E0))))))) = s(A_27b,f1376_1_2E4(s(tyop_2Emin_2Efun(A_27d,A_27b),V0g_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V6h_2E0),s(A_27a,V7a_2E0)))) # label(def0_2Ethm_2Eind__type_2EISO__FUN) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2770 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2771 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2772 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),f1376_1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))),s(A_27a,X3_2E0))) = s(A_27b,f1376_1_2E4(s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef1376_1_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2773 (all A_27a all V0a1_2E0 all V1a2_2E0 (s(A_27a,V0a1_2E0) = s(A_27a,V1a2_2E0) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJA_2E1(s(A_27a,V0a1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJA_2E1(s(A_27a,V1a2_2E0))))) # label(thm_2Eind__type_2EINJA__INJ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2774 (all A_27A all A_27B all A_27C all V0P_2E0 ((all V1x1_2E0 all V2y1_2E0 all V3x2_2E0 all V4y2_2E0 (s(A_27A,V3x2_2E0) = s(A_27A,V1x1_2E0) & s(A_27B,V4y2_2E0) = s(A_27B,V2y1_2E0) <-> s(A_27C,app_2E2(s(tyop_2Emin_2Efun(A_27B,A_27C),app_2E2(s(tyop_2Emin_2Efun(A_27A,tyop_2Emin_2Efun(A_27B,A_27C)),V0P_2E0),s(A_27A,V1x1_2E0))),s(A_27B,V2y1_2E0))) = s(A_27C,app_2E2(s(tyop_2Emin_2Efun(A_27B,A_27C),app_2E2(s(tyop_2Emin_2Efun(A_27A,tyop_2Emin_2Efun(A_27B,A_27C)),V0P_2E0),s(A_27A,V3x2_2E0))),s(A_27B,V4y2_2E0))))) -> (exists V5X_2E0 exists V6Y_2E0 all V7x_2E0 all V8y_2E0 (s(A_27A,app_2E2(s(tyop_2Emin_2Efun(A_27C,A_27A),V5X_2E0),s(A_27C,app_2E2(s(tyop_2Emin_2Efun(A_27B,A_27C),app_2E2(s(tyop_2Emin_2Efun(A_27A,tyop_2Emin_2Efun(A_27B,A_27C)),V0P_2E0),s(A_27A,V7x_2E0))),s(A_27B,V8y_2E0))))) = s(A_27A,V7x_2E0) & s(A_27B,V8y_2E0) = s(A_27B,app_2E2(s(tyop_2Emin_2Efun(A_27C,A_27B),V6Y_2E0),s(A_27C,app_2E2(s(tyop_2Emin_2Efun(A_27B,A_27C),app_2E2(s(tyop_2Emin_2Efun(A_27A,tyop_2Emin_2Efun(A_27B,A_27C)),V0P_2E0),s(A_27A,V7x_2E0))),s(A_27B,V8y_2E0))))))))) # label(thm_2Eind__type_2EINJ__INVERSE2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2775 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2776 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,f1374_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(def0_2Ethm_2Eind__type_2EFCONS__DEST) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2777 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2778 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2779 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Eind__type_2EFCONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,c_2Eind__type_2EFCONS_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2EFCONS_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2780 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1351_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1351_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X0_2E0)))) # label(arityeq1_2Ef1351_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2781 (all A_27a all V0P_2E0 ((all V1c_2E0 all V2i_2E0 all V3r_2E0 ((all V4n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V3r_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V1c_2E0),s(A_27a,V2i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V3r_2E0)))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0)))) -> (all V5x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V5x_2E0))))))) # label(thm_2Eind__type_2ECONSTR__IND) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2782 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eind__type_2ENUMPAIR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2ENUMPAIR_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2783 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2784 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2785 (all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool)),c_2Eind__type_2EISO_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2786 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2787 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJA_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJA_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2EINJA_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2788 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2Edest__rec_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2Edest__rec_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2789 (all A_27a all V0m_2E0 all V1x_2E0 all V2x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJN_2E3(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(A_27a,V2x_27_2E0)))) <-> s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(thm_2Eind__type_2EINJN) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2790 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2791 (all A_27a all A_27b all V1f_2E0 all V4r_2E0 all V5n_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),V1f_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V4r_2E0),s(tyop_2Enum_2Enum,V5n_2E0))))) = s(A_27b,f1373_0_2E3(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V4r_2E0),s(tyop_2Enum_2Enum,V5n_2E0)))) # label(def0_2Ethm_2Eind__type_2ECONSTR__REC) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2792 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2793 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJN_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2EINJN_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2794 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2795 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool)),c_2Eind__type_2EISO_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2796 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2797 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2798 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2799 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2800 (all A_27a all V0f_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eind__type_2EINJF_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0f_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0f_2E0),s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))),s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND_2E1(s(tyop_2Enum_2Enum,V1x_2E0)))))) # label(thm_2Eind__type_2EINJF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2801 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMRIGHT_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2ENUMRIGHT_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2802 (all A_27a s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f1346_0_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0)) # label(thm_2Eind__type_2EZBOT) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2803 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Eind__type_2EINJP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJP_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Eind__type_2EINJP_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2804 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2805 (all X0_2E0 s(tyop_2Emin_2Ebool,f1374_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1374_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1374_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2806 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2807 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2808 (all A_27a ((all V0a_2E0 all V1f_2E0 s(A_27a,c_2Eind__type_2EFCONS_2E3(s(A_27a,V0a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V0a_2E0)) & (all V2a_2E0 all V3f_2E0 all V4n_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))) = s(A_27a,c_2Eind__type_2EFCONS_2E3(s(A_27a,V2a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))))))) # label(thm_2Eind__type_2EFCONS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2809 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2810 (all A_27a all V0x_2E0 all V1y_2E0 (s(tyop_2Eind__type_2Erecspace(A_27a),V0x_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),V1y_2E0) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),V0x_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),V1y_2E0))))) # label(thm_2Eind__type_2EDEST__REC__INJ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2811 (all A_27a all A_27b all A_27c all A_27d all V1g_2E0 all V2f_27_2E0 all V4h_2E0 all V5a_27_2E0 s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4h_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_27_2E0),s(A_27c,V5a_27_2E0))))))) = s(A_27d,f1376_0_2E4(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4h_2E0),s(A_27c,V5a_27_2E0)))) # label(def1_2Ethm_2Eind__type_2EISO__FUN) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2812 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2813 (all A_27a all V0f1_2E0 all V1f1_27_2E0 all V2f2_2E0 all V3f2_27_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f1_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3f2_27_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f2_2E0))) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f1_27_2E0) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f2_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3f2_27_2E0))) # label(thm_2Eind__type_2EINJP__INJ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2814 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)))),f1376_0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),f1376_0_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0)))) # label(arityeq2_2Ef1376_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2815 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2816 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2817 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2818 (all V0x_2E0 all V1y_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) # label(thm_2Eind__type_2ENUMPAIR) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2819 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eind__type_2ENUMLEFT_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eind__type_2ENUMLEFT_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2ENUMLEFT_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2820 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1351_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f1351_0_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1351_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2821 (all A_27a all V0a0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0a0_2E0)))) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0a0_2E0) | (exists V1c_2E0 exists V2i_2E0 exists V3r_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V1c_2E0),s(A_27a,V2i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0a0_2E0) & (all V4n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))))))) # label(thm_2Eind__type_2EZRECSPACE__cases) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2822 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJF_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2EINJF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2823 (all A_27a all V0c_2E0 all V1i_2E0 all V2r_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1351_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r_2E0))))))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r_2E0)))) # label(thm_2Eind__type_2ECONSTR) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2824 (all A_27a all X0_2E0 s(A_27a,f1375_0_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),f1375_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef1375_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2825 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMFST_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2ENUMFST_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2826 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,V2x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0),s(A_27b,V2x_2E0)))))) & (all V3y_2E0 s(A_27a,V3y_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0)))))) # label(thm_2Eind__type_2EISO) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2827 (all A_27a all X0_2E0 s(A_27a,c_2Eind__type_2EFNIL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Eind__type_2EFNIL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2EFNIL_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2828 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),f1373_0_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),f1373_0_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) # label(arityeq2_2Ef1373_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2829 (all A_27a exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Eind__type_2EZRECSPACE_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0rep_2E0))))) # label(thm_2Eind__type_2Erecspace__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2830 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2831 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2832 (all V0b1_2E0 all V1x1_2E0 all V2b2_2E0 all V3x2_2E0 (s(tyop_2Enum_2Enum,V3x2_2E0) = s(tyop_2Enum_2Enum,V1x1_2E0) & s(tyop_2Emin_2Ebool,V0b1_2E0) = s(tyop_2Emin_2Ebool,V2b2_2E0) <-> s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,V2b2_2E0),s(tyop_2Enum_2Enum,V3x2_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,V0b1_2E0),s(tyop_2Enum_2Enum,V1x1_2E0))))) # label(thm_2Eind__type_2ENUMSUM__INJ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2833 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f1346_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,f1346_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef1346_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2834 (all V0x_2E0 all V1y_2E0 (s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMFST_2E1(s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))) = s(tyop_2Enum_2Enum,V0x_2E0) & s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND_2E1(s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))) = s(tyop_2Enum_2Enum,V1y_2E0))) # label(thm_2Eind__type_2ENUMPAIR__DEST) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2835 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27d,f1376_0_2E4(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(A_27c,X3_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)))),f1376_0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(A_27c,X3_2E0)))) # label(arityeq4_2Ef1376_0_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2836 (all A_27a all V0c1_2E0 all V1i1_2E0 all V2r1_2E0 all V3c2_2E0 all V4i2_2E0 all V5r2_2E0 (s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V3c2_2E0),s(A_27a,V4i2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V5r2_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V0c1_2E0),s(A_27a,V1i1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r1_2E0))) <-> s(A_27a,V4i2_2E0) = s(A_27a,V1i1_2E0) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r1_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V5r2_2E0) & s(tyop_2Enum_2Enum,V0c1_2E0) = s(tyop_2Enum_2Enum,V3c2_2E0))) # label(thm_2Eind__type_2ECONSTR__INJ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2837 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSND_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eind__type_2ENUMSND_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2ENUMSND_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2838 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Eind__type_2EZRECSPACE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2EZRECSPACE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2839 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V1_2E0) = s(A_27a,V0_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2840 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2841 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2842 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eind__type_2Erecspace_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2843 (all A_27a all A_27b all A_27c all A_27d all V0g_27_2E0 all V1g_2E0 all V2f_27_2E0 all V3f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_27_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V0g_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),f1376_0_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),f1376_1_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V0g_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0)))))))) # label(thm_2Eind__type_2EISO__FUN) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2844 (all A_27a all V0x_2E0 all V1y_2E0 (s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1y_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0))) -> (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0)))) -> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1y_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0)))) # label(thm_2Eind__type_2EMK__REC__INJ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.75 2845 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJN_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2EINJN_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2846 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Eind__type_2EINJP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EINJP_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2847 (all V0x1_2E0 all V1y1_2E0 all V2x2_2E0 all V3y2_2E0 (s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V2x2_2E0),s(tyop_2Enum_2Enum,V3y2_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V0x1_2E0),s(tyop_2Enum_2Enum,V1y1_2E0))) -> s(tyop_2Enum_2Enum,V0x1_2E0) = s(tyop_2Enum_2Enum,V2x2_2E0))) # label(thm_2Eind__type_2ENUMPAIR__INJ__LEMMA) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2848 (all A_27a all V0z_2E0 s(tyop_2Emin_2Ebool,f1346_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0z_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(def0_2Ethm_2Eind__type_2EZBOT) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2849 (all A_27a all V0n1_2E0 all V1n2_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E1(s(tyop_2Enum_2Enum,V1n2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E1(s(tyop_2Enum_2Enum,V0n1_2E0))) <-> s(tyop_2Enum_2Enum,V1n2_2E0) = s(tyop_2Enum_2Enum,V0n1_2E0))) # label(thm_2Eind__type_2EINJN__INJ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2850 (all A_27a ((all V0a_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),V0a_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),V0a_2E0)))))) & (all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0)))) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1r_2E0))))) # label(thm_2Eind__type_2Erecspace__repfns) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2851 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),f1375_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),f1375_0_2E0))))) # label(thm_2Eind__type_2EISO__REFL) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2852 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),f1376_1_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),f1376_1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0)))) # label(arityeq2_2Ef1376_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2853 (all V0b_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1x_2E0))))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) # label(thm_2Eind__type_2ENUMSUM) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2854 (all A_27a all V0n_2E0 all V1f_2E0 all V2a_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1374_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(A_27a,V2a_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))) = s(A_27a,c_2Eind__type_2EFCONS_2E3(s(A_27a,V2a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Eind__type_2EFCONS__DEST) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2855 (all A_27a all V0c_2E0 all V1i_2E0 all V2r_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2r_2E0)))) # label(thm_2Eind__type_2EZCONSTR__ZBOT) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2856 (all A_27a ((all V0c_2E0 all V1i_2E0 all V2r_2E0 ((all V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2r_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))) -> p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2r_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0)))))) # label(thm_2Eind__type_2EZRECSPACE__rules) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2857 (all A_27a all V0a_2E0 all V1x_2E0 all V2x_27_2E0 (s(A_27a,V2x_27_2E0) = s(A_27a,V0a_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJA_2E3(s(A_27a,V0a_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(A_27a,V2x_27_2E0)))))) # label(thm_2Eind__type_2EINJA) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2858 (all A_27a all V0f1_2E0 all V1f2_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0f1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1f2_2E0))) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0f1_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1f2_2E0))) # label(thm_2Eind__type_2EINJF__INJ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2859 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Eind__type_2EISO_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2860 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2861 (all A_27a all V0ZRECSPACE_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0)))) & (all V1c_2E0 all V2i_2E0 all V3r_2E0 ((all V4n_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V1c_2E0),s(A_27a,V2i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0)))))))) -> (all V5a0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5a0_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5a0_2E0)))))))) # label(thm_2Eind__type_2EZRECSPACE__strongind) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2862 (all A_27a all V0c_2E0 all V1i_2E0 all V2r_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) != s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r_2E0)))) # label(thm_2Eind__type_2ECONSTR__BOT) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2863 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Eind__type_2EISO_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2864 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Eind__type_2ENUMSUM_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2ENUMSUM_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2865 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eind__type_2EINJF_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJF_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EINJF_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2866 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2867 (all A_27a all V0c_2E0 all V1i_2E0 all V2r_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJN_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0c_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJP_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJA_2E1(s(A_27a,V1i_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EINJF_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2r_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V0c_2E0),s(A_27a,V1i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2r_2E0)))) # label(thm_2Eind__type_2EZCONSTR) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2868 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))),c_2Eind__type_2EZCONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2EZCONSTR_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2869 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2870 (all A_27a all V0ZRECSPACE_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0)))) & (all V1c_2E0 all V2i_2E0 all V3r_2E0 ((all V4n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V1c_2E0),s(A_27a,V2i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3r_2E0)))))))) -> (all V5a0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5a0_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V0ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5a0_2E0)))))))) # label(thm_2Eind__type_2EZRECSPACE__ind) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2871 (all A_27a all V0f1_2E0 all V1f2_2E0 all V2x_2E0 all V3x_27_2E0 s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJP_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0),s(tyop_2Enum_2Enum,V2x_2E0),s(A_27a,V3x_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eind__type_2ENUMLEFT_2E1(s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))),s(A_27a,V3x_27_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0),s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))),s(A_27a,V3x_27_2E0)))))) # label(thm_2Eind__type_2EINJP) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2872 (all A_27a all V0n_2E0 s(A_27a,c_2Ebool_2EARB_2E0) = s(A_27a,c_2Eind__type_2EFNIL_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Eind__type_2EFNIL) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2873 (all A_27a all X0_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2Emk__rec_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2Emk__rec_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Eind__type_2Emk__rec_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2874 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,f1375_0_2E1(s(A_27a,V0x_2E0)))) # label(def0_2Ethm_2Eind__type_2EISO__REFL) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2875 (all V0x1_2E0 all V1y1_2E0 all V2x2_2E0 all V3y2_2E0 (s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V0x1_2E0),s(tyop_2Enum_2Enum,V1y1_2E0))) = s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMPAIR_2E2(s(tyop_2Enum_2Enum,V2x2_2E0),s(tyop_2Enum_2Enum,V3y2_2E0))) <-> s(tyop_2Enum_2Enum,V0x1_2E0) = s(tyop_2Enum_2Enum,V2x2_2E0) & s(tyop_2Enum_2Enum,V1y1_2E0) = s(tyop_2Enum_2Enum,V3y2_2E0))) # label(thm_2Eind__type_2ENUMPAIR__INJ) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2876 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2877 (all A_27a all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eind__type_2EZRECSPACE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0)))) <-> (all V1ZRECSPACE_27_2E0 ((all V2a0_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZBOT_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2a0_2E0) | (exists V3c_2E0 exists V4i_2E0 exists V5r_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2a0_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2EZCONSTR_2E3(s(tyop_2Enum_2Enum,V3c_2E0),s(A_27a,V4i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V5r_2E0))) & (all V6n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V1ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V5r_2E0),s(tyop_2Enum_2Enum,V6n_2E0))))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V1ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2a0_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),V1ZRECSPACE_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0)))))))) # label(thm_2Eind__type_2EZRECSPACE__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2878 (all V0x_2E0 all V1y_2E0 (s(tyop_2Emin_2Ebool,c_2Eind__type_2ENUMLEFT_2E1(s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))) = s(tyop_2Emin_2Ebool,V0x_2E0) & s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMRIGHT_2E1(s(tyop_2Enum_2Enum,c_2Eind__type_2ENUMSUM_2E2(s(tyop_2Emin_2Ebool,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))) = s(tyop_2Enum_2Enum,V1y_2E0))) # label(thm_2Eind__type_2ENUMSUM__DEST) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2879 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eind__type_2EINJA_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EINJA_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2EINJA_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2880 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eind__type_2EISO_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eind__type_2EISO_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EISO_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2881 (all A_27a all V2r_2E0 all V3n_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f1351_0_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r_2E0),s(tyop_2Enum_2Enum,V3n_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eind__type_2Edest__rec_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),V2r_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) # label(def0_2Ethm_2Eind__type_2ECONSTR) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2882 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2883 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2884 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2885 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))) # label(thm_2Egcd_2EIS__GCD__0L) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2886 (all V0a_2E0 all V1b_2E0 all V2c_2E0 s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0))) = s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) # label(thm_2Egcd_2EIS__GCD__SYM) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2887 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) # label(thm_2Egcd_2EGCD__SYM) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2888 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2889 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V0n_2E0) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V1m_2E0) -> (exists V2p_2E0 exists V3q_2E0 (s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V3q_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Egcd_2EFACTOR__OUT__GCD) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2890 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2891 (all V0m_2E0 all V1n_2E0 all V2k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Egcd_2EGCD__COMMON__FACTOR) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2892 (all V0x_2E0 (s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) & s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0))) # label(thm_2Egcd_2ELCM__1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2893 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V2c_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Egcd_2EIS__GCD__MINUS__R) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2894 (all V0a_2E0 s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) # label(thm_2Egcd_2EGCD__REF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2895 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2896 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EODD_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2897 (all V0p_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Egcd_2EPRIME__IS__GCD) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2898 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1409_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f1409_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1409_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2899 (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Egcd_2Egcd__def__compute_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2900 (all V2x_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2x_2E0)))))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2901 (all V3y_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3y_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3y_2E0)))))))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2902 (all V5y_2E0 all V6x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6x_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5y_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6x_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5y_2E0)))))))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2903 (all V7y_2E0 all V8x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7y_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V7y_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V7y_2E0)))))))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2904 (all V9y_2E0 all V10x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V9y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V9y_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V9y_2E0))))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V9y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V9y_2E0)))))))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2905 (all V0y_2E0 s(tyop_2Enum_2Enum,V0y_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) # label(thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2906 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2907 (all V0p_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) # label(thm_2Egcd_2EP__EUCLIDES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2908 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f1379_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1379_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1379_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2909 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2910 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Egcd_2ELCM__LE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2911 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2912 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2913 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2914 (all V0a_2E0 s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) # label(thm_2Egcd_2EGCD__0L) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2915 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,f1379_0_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0m_2E0))) # label(def0_2Ethm_2Egcd_2Elcm__def) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2916 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))) # label(thm_2Egcd_2EIS__GCD__REF) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2917 (all V0x_2E0 (s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) # label(thm_2Egcd_2EGCD__1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2918 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2919 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Egcd_2Eis__gcd_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Egcd_2Eis__gcd_2E3) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2920 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Egcd_2Egcd_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Egcd_2Egcd_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2921 (all V0m_2E0 all V1n_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Egcd_2EBINARY__GCD) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2922 (all V0a_2E0 all V1b_2E0 p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))))) # label(thm_2Egcd_2EGCD__IS__GCD) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2923 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2924 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2925 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2926 (all V0m_2E0 all V1n_2E0 all V2k_2E0 (s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2k_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) -> s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Egcd_2EGCD__CANCEL__MULT) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2927 (all V0b_2E0 all V1a_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))) # label(thm_2Egcd_2ELCM__COMM) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2928 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2929 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Egcd_2Elcm_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Egcd_2Elcm_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2930 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2931 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2932 (all V0a_2E0 all V1b_2E0 all V2c_2E0 all V3d_2E0 (p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V3d_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) -> s(tyop_2Enum_2Enum,V2c_2E0) = s(tyop_2Enum_2Enum,V3d_2E0))) # label(thm_2Egcd_2EIS__GCD__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2933 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2934 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2935 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2936 (all V2a_2E0 all V3b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3b_2E0),s(tyop_2Enum_2Enum,V2a_2E0)))))) # label(thm_2Egcd_2EGCD__ADD__R__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2937 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Egcd_2EGCD__ADD__R__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2938 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2939 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2940 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Egcd_2EIS__GCD__MINUS__L) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2941 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2942 (all V0P_2E0 ((all V1y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))))) & (all V3x_2E0 all V4y_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V4y_2E0),s(tyop_2Enum_2Enum,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V4y_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4y_2E0))))))) & (-p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V4y_2E0),s(tyop_2Enum_2Enum,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V4y_2E0),s(tyop_2Enum_2Enum,V3x_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4y_2E0)))))))) & (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) -> (all V5v_2E0 all V6v1_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V5v_2E0))),s(tyop_2Enum_2Enum,V6v1_2E0))))))) # label(thm_2Egcd_2Egcd__ind) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2943 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Egcd_2EL__EUCLIDES) # label(axiom) # label(non_clause). [assumption]. 107.72/107.76 2944 (all V0P_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V3y_2E0))),s(tyop_2Enum_2Enum,V2x_2E0)))))) & (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V4x_2E0))),s(tyop_2Enum_2Enum,V4x_2E0))))) & (all V5x_2E0 all V6y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V5x_2E0))),s(tyop_2Enum_2Enum,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V5x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V5x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V5x_2E0),s(tyop_2Enum_2Enum,V6y_2E0)))))))) & (all V1y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Enum_2Enum,V1y_2E0))))) -> (all V7m_2E0 all V8n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V7m_2E0))),s(tyop_2Enum_2Enum,V8n_2E0))))))) # label(thm_2Egcd_2EGCD__SUCfree__ind) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2945 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2946 (all V2y_2E0 all V3x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V2y_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2y_2E0))))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V3x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2y_2E0)))))) # label(thm_2Egcd_2Egcd__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2947 (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0)))) # label(thm_2Egcd_2Egcd__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2948 (all V0y_2E0 s(tyop_2Enum_2Enum,V0y_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))) # label(thm_2Egcd_2Egcd__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2949 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & s(tyop_2Enum_2Enum,V1m_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Egcd_2EGCD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2950 (all V0a_2E0 p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))) # label(thm_2Egcd_2EIS__GCD__0R) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2951 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Edivides_2Eprime_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Edivides_2Eprime_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2952 (all A_27a all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2953 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Edivides_2Edivides_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Edivides_2Edivides_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2954 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1409_0_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V0a_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) # label(thm_2Egcd_2EGCD__EFFICIENTLY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2955 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2956 (all V0x_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Egcd_2ELCM__0) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2957 (all V0a_2E0 (s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,f1409_0_2E1(s(tyop_2Enum_2Enum,V0a_2E0)))))) # label(def0_2Ethm_2Egcd_2EGCD__EFFICIENTLY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2958 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2959 (all V0p_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Eprime_2E1(s(tyop_2Enum_2Enum,V0p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) | s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0p_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) # label(thm_2Egcd_2EPRIME__GCD) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2960 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2961 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) # label(thm_2Egcd_2EGCD__ADD__R) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2962 (all V2a_2E0 all V3b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3b_2E0),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,V2a_2E0)))) # label(thm_2Egcd_2EGCD__ADD__L__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2963 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) # label(thm_2Egcd_2EGCD__ADD__L__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2964 (all V0a_2E0 s(tyop_2Enum_2Enum,V0a_2E0) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Egcd_2EGCD__0R) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2965 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2966 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V1b_2E0)))) & (all V2d_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0a_2E0)))))) # label(thm_2Egcd_2EGCD__IS__GREATEST__COMMON__DIVISOR) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2967 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2c_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2c_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & (all V3d_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V3d_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V3d_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V3d_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Egcd_2Eis__gcd_2E3(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) # label(thm_2Egcd_2Eis__gcd__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2968 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.76 2969 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1379_0_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Egcd_2Elcm__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2970 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2971 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V0n_2E0) -> (exists V2p_2E0 exists V3q_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V3q_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Egcd_2ELINEAR__GCD) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2972 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) | -p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))))))) # label(thm_2Egcd_2ELCM__LEAST) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2973 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2974 (all V0a_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0a_2E0)))) # label(thm_2Egcd_2EGCD__ADD__L) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2975 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) & (all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2p_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2p_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Egcd_2Elcm_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Egcd_2ELCM__IS__LEAST__COMMON__MULTIPLE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2976 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2977 (all V0r_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0r_2E0)))) -> (exists V2rt_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2rt_2E0),s(tyop_2Enum_2Enum,V0r_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2rt_2E0))),s(tyop_2Enum_2Enum,V0r_2E0)))))))))) # label(thm_2Elogroot_2EROOT__exists) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2978 (all V2d_2E0 all V3c_2E0 all V4e_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1424_4_2E1(s(tyop_2Enum_2Enum,V4e_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V3c_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V4e_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1424_3_2E3(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V3c_2E0),s(tyop_2Enum_2Enum,V4e_2E0)))) # label(def1_2Ethm_2Elogroot_2EiSQRT2__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2979 (all V0n_2E0 (s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) # label(thm_2Elogroot_2Enumeral__sqrt) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2980 (all V0e_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0e_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) # label(thm_2Elogroot_2ELT__EXP__ISO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2981 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2982 (all V0a_2E0 all V1x_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V2r_2E0))) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))))) # label(thm_2Elogroot_2ELOG__ROOT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2983 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1423_1_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1423_1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1423_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2984 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1424_4_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f1424_4_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1424_4_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2985 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Elogroot_2Enumeral__root2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2986 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1424_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1424_2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1424_2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2987 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2988 (all V0r_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,V0r_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V0r_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,V2p_2E0))) # label(thm_2Elogroot_2EROOT__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2989 (all V0a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Elogroot_2ELOG__1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2990 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1422_0_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1422_0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1422_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2991 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1425_1_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1425_1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1425_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2992 (all V0b_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))) -> s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V2y_2E0))))) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V2y_2E0))),s(tyop_2Enum_2Enum,V1x_2E0))))))) # label(thm_2Elogroot_2ELOG__add__digit) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2993 (all V2d_2E0 all V3c_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1424_3_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V3c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3c_2E0),s(tyop_2Enum_2Enum,V2d_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1424_2_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V3c_2E0)))) # label(def2_2Ethm_2Elogroot_2EiSQRT2__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2994 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2995 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1425_1_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1425_1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1425_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2996 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2997 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1422_1_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1422_1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1422_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2998 (all V1p_2E0 all V2d_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1423_2_2E1(s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1423_1_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0),s(tyop_2Enum_2Enum,V2d_2E0)))) # label(def1_2Ethm_2Elogroot_2EiSQRT1__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 2999 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1424_1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1424_1_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1424_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3000 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1423_1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1423_1_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1423_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3001 (all V0a_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0a_2E0))))))))) # label(thm_2Elogroot_2ELOG__DIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3002 (all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0r_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V2y_2E0))))))))) # label(thm_2Elogroot_2EROOT__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3003 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3004 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3005 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1424_3_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f1424_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1424_3_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3006 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3007 (all V0a_2E0 all V1b_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2r_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2r_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))) # label(thm_2Elogroot_2EEXP__LT__ISO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3008 (all V2d_2E0 all V3c_2E0 all V4e_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1425_3_2E3(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V3c_2E0),s(tyop_2Enum_2Enum,V4e_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1425_4_2E1(s(tyop_2Enum_2Enum,V4e_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V3c_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V4e_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))) # label(def1_2Ethm_2Elogroot_2EiSQRT3__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3009 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3010 (all V0a_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2y_2E0))))))))) # label(thm_2Elogroot_2ELOG__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3011 (all X0_2E0 s(tyop_2Emin_2Ebool,f1423_2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1423_2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1423_2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3012 (all V1p_2E0 all V2d_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1425_1_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0),s(tyop_2Enum_2Enum,V2d_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1425_2_2E1(s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))))))))) # label(def3_2Ethm_2Elogroot_2EiSQRT3__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3013 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3014 (all V0a_2E0 all V1b_2E0 all V2c_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2c_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V2c_2E0)))) # label(thm_2Elogroot_2EEXP__MUL) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3015 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3016 (all V0r_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0r_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1450_0_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0r_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0r_2E0))))))))))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Elogroot_2EROOT__COMPUTE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3017 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2ESQRTd_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2ESQRTd_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3018 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3019 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3020 (all V0a_2E0 all V1n_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2p_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2p_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,V2p_2E0) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Elogroot_2ELOG__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3021 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3022 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2EiSQRT3_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2EiSQRT3_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3023 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3024 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3025 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3026 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3027 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1425_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1425_2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1425_2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3028 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1425_0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1425_0_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1425_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3029 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1424_2_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1424_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1424_2_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3030 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1425_3_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f1425_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1425_3_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3031 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))))))))) # label(thm_2Elogroot_2ELOG__ADD1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3032 (all V0a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) # label(thm_2Elogroot_2ELOG__BASE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3033 (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1423_0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Elogroot_2EiSQRT1__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3034 (all V2d_2E0 all V3c_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1425_2_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V3c_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1425_3_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V3c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3c_2E0))),s(tyop_2Enum_2Enum,V2d_2E0)))))) # label(def2_2Ethm_2Elogroot_2EiSQRT3__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3035 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3036 (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1424_0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Elogroot_2EiSQRT2__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3037 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3038 (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1425_0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT3_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Elogroot_2EiSQRT3__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3039 (all V2d_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V2d_2E0) <-> p(s(tyop_2Emin_2Ebool,f1422_2_2E1(s(tyop_2Enum_2Enum,V2d_2E0)))))) # label(def0_2Ethm_2Elogroot_2EiSQRT0__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3040 (all X0_2E0 s(tyop_2Emin_2Ebool,f1425_4_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1425_4_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1425_4_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3041 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3042 (all V0b_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1x_2E0))))))) # label(thm_2Elogroot_2ELOG__MULT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3043 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3044 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2EiSQRT0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2EiSQRT0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3045 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3046 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2EiSQRT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2EiSQRT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3047 (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))))))))) # label(thm_2Elogroot_2ESQRTd__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3048 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3049 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2ELOG_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elogroot_2ELOG_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3050 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3051 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1a_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))))) # label(thm_2Elogroot_2ELOG__EXP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3052 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f1425_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1425_3_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1425_3_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3053 (all V0a_2E0 all V1b_2E0 all V2c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2c_2E0))))))) = s(tyop_2Enum_2Enum,V2c_2E0))) # label(thm_2Elogroot_2ELOG__ADD) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3054 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3055 (all V1p_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1424_0_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1424_1_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))))))) # label(def4_2Ethm_2Elogroot_2EiSQRT2__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3056 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3057 (all V0a_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))))))) # label(thm_2Elogroot_2ELOG) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3058 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,f1450_0_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1450_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1450_0_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3059 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2EROOT_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elogroot_2EROOT_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3060 (all V4e_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V4e_2E0) <-> p(s(tyop_2Emin_2Ebool,f1425_4_2E1(s(tyop_2Enum_2Enum,V4e_2E0)))))) # label(def0_2Ethm_2Elogroot_2EiSQRT3__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3061 (all V1p_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1425_0_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1425_1_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))))))) # label(def4_2Ethm_2Elogroot_2EiSQRT3__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3062 (all V0e_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0e_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))))) # label(thm_2Elogroot_2ELE__EXP__ISO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3063 (all V1p_2E0 all V2d_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1422_1_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0),s(tyop_2Enum_2Enum,V2d_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1422_2_2E1(s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) # label(def1_2Ethm_2Elogroot_2EiSQRT0__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3064 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3065 (all V0r_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0r_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,V0r_2E0)))))))) # label(thm_2Elogroot_2EROOT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3066 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3067 (all V0m_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0m_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))))))))) # label(thm_2Elogroot_2ELOG__RWT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3068 (exists V0f_2E0 all V1a_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1a_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Elogroot_2ELOG__exists) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3069 (all V1n_2E0 all V0r_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,f1450_0_2E3(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,V0r_2E0))))),s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2x_2E0)))))) # label(def0_2Ethm_2Elogroot_2EROOT__COMPUTE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3070 (all V2d_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V2d_2E0) <-> p(s(tyop_2Emin_2Ebool,f1423_2_2E1(s(tyop_2Enum_2Enum,V2d_2E0)))))) # label(def0_2Ethm_2Elogroot_2EiSQRT1__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3071 (all V1p_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1422_1_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1422_0_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))) # label(def2_2Ethm_2Elogroot_2EiSQRT0__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3072 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3073 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1423_0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1423_0_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1423_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3074 (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1422_0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ESQRTd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT0_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Elogroot_2EiSQRT0__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3075 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1425_2_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1425_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1425_2_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3076 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2EiSQRT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2EiSQRT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2EiSQRT2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3077 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3078 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1424_3_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f1424_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1424_3_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3079 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1450_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1450_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1450_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3080 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3081 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3082 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3083 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3084 (all V1p_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1423_0_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1423_1_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0)))))))) # label(def2_2Ethm_2Elogroot_2EiSQRT1__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3085 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3086 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1422_2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f1422_2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1422_2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3087 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3088 (all V1p_2E0 all V2d_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1424_2_2E1(s(tyop_2Enum_2Enum,V2d_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1424_1_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1p_2E0),s(tyop_2Enum_2Enum,V2d_2E0)))) # label(def3_2Ethm_2Elogroot_2EiSQRT2__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3089 (all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0r_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,V0r_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Elogroot_2EROOT_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V2y_2E0))))) # label(thm_2Elogroot_2EROOT__DIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3090 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Elogroot_2ELOG__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3091 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))))))) # label(thm_2Elogroot_2ELOG__MOD) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3092 (all V4e_2E0 (p(s(tyop_2Emin_2Ebool,f1424_4_2E1(s(tyop_2Enum_2Enum,V4e_2E0)))) <-> s(tyop_2Enum_2Enum,V4e_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(def0_2Ethm_2Elogroot_2EiSQRT2__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3093 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3094 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3095 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3096 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3097 (all V0a_2E0 all V1b_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2r_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2r_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V2r_2E0))))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))) # label(thm_2Elogroot_2EEXP__LE__ISO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3098 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1424_0_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1424_0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1424_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3099 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1424_1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1424_1_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1424_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3100 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1422_1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1422_1_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1422_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3101 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3102 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3103 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3104 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Enumpair_2Enpair__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3105 (all V0n_2E0 exists V1x_2E0 exists V2y_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))) # label(thm_2Enumpair_2Enpair__cases) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3106 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3107 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Enumpair_2Einvtri__lower) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3108 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enapp_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Enapp_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Enapp_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3109 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3110 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3111 (all V0y_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumpair_2Encons__not__nnil) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3112 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.77 3113 (all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) & (all V1h_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2t_2E0)))))))) -> (all V3n_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))) # label(thm_2Enumpair_2Enlist__ind) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3114 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) # label(thm_2Enumpair_2Etri__LT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3115 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enlen_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enlen_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Enlen_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3116 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumpair_2Einvtri__linverse) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3117 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3118 (all A_27a all V3a_2E0 s(A_27a,f1461_0_2E1(s(A_27a,V3a_2E0))) = s(A_27a,V3a_2E0)) # label(def1_2Ethm_2Enumpair_2Enfoldl__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3119 (all V0y_2E0 all V1x_2E0 all V2t_2E0 all V3h_2E0 (s(tyop_2Enum_2Enum,V3h_2E0) = s(tyop_2Enum_2Enum,V1x_2E0) & s(tyop_2Enum_2Enum,V2t_2E0) = s(tyop_2Enum_2Enum,V0y_2E0) <-> s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V3h_2E0),s(tyop_2Enum_2Enum,V2t_2E0))))) # label(thm_2Enumpair_2Encons__11) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3120 (all V0y_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) -> s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1x_2E0))),s(tyop_2Enum_2Enum,V0y_2E0))))))) # label(thm_2Enumpair_2Einvtri__linverse__r) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3121 (all V0y2_2E0 all V1y1_2E0 all V2x2_2E0 all V3x1_2E0 (s(tyop_2Enum_2Enum,V3x1_2E0) = s(tyop_2Enum_2Enum,V2x2_2E0) & s(tyop_2Enum_2Enum,V0y2_2E0) = s(tyop_2Enum_2Enum,V1y1_2E0) <-> s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V3x1_2E0),s(tyop_2Enum_2Enum,V1y1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V2x2_2E0),s(tyop_2Enum_2Enum,V0y2_2E0))))) # label(thm_2Enumpair_2Enpair__11) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3122 (all V0f_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enlistrec_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1460_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0)))) # label(thm_2Enumpair_2Enmap__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3123 (all A_27a all V0t_2E0 all V1n_2E0 all V2h_2E0 all V3f_2E0 (s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V1n_2E0) & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Enum_2Enum,V2h_2E0))),s(tyop_2Enum_2Enum,V0t_2E0))),s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))) = s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V2h_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))))) # label(thm_2Enumpair_2Enlistrec__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3124 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3125 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3126 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Enumpair_2Enlistrec_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumpair_2Enlistrec_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3127 (all V0l1_2E0 all V1l2_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enlistrec_2E3(s(tyop_2Enum_2Enum,V1l2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1462_0_2E0),s(tyop_2Enum_2Enum,V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enapp_2E2(s(tyop_2Enum_2Enum,V0l1_2E0),s(tyop_2Enum_2Enum,V1l2_2E0)))) # label(thm_2Enumpair_2Enapp__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3128 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumpair_2Etwotri__formula) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3129 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3130 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Enmap_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enmap_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Enmap_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3131 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumpair_2Enpair) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3132 (all V0n_2E0 all V1t_2E0 all V2r_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2r_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,f1459_0_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1t_2E0),s(tyop_2Enum_2Enum,V2r_2E0)))) # label(def0_2Ethm_2Enumpair_2Enlen__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3133 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3134 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1459_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,f1459_0_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1459_0_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3135 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,f1462_0_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1462_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1462_0_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3136 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))) # label(thm_2Enumpair_2Einvtri__upper) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3137 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3138 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))))),f1461_1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X3_2E0))),s(A_27a,X4_2E0))) = s(A_27a,f1461_1_2E5(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X3_2E0),s(A_27a,X4_2E0)))) # label(arityeq5_2Ef1461_1_2E5_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3139 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f1460_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1460_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1460_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3140 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3141 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3142 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enmap_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Enmap_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Enmap_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3143 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Enpair_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Enpair_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3144 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumpair_2Einvtri0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Einvtri0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3145 (all V0y_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))))) # label(thm_2Enumpair_2Enfst__npair) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3146 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Enumpair_2Etri__le) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3147 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3148 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Enumpair_2Etri__def__compute_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3149 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))))) # label(thm_2Enumpair_2Etri__def__compute_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3150 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3151 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3152 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Enumpair_2Etri__LE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3153 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Enumpair_2Enfst__le) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3154 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),f1461_1_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))))),f1461_1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0)))) # label(arityeq1_2Ef1461_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3155 (all V0h_2E0 all V1t_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1t_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1t_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Enumpair_2Encons__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3156 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3157 (all A_27a all V0f_2E0 all V1a_2E0 all V2l_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Enumpair_2Enlistrec_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),f1461_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),f1461_1_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0))),s(tyop_2Enum_2Enum,V2l_2E0))),s(A_27a,V1a_2E0))) = s(A_27a,c_2Enumpair_2Enfoldl_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V1a_2E0),s(tyop_2Enum_2Enum,V2l_2E0)))) # label(thm_2Enumpair_2Enfoldl__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3158 (all V0n_2E0 all V1a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))))),s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1a_2E0)))))) # label(thm_2Enumpair_2Einvtri0__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3159 (all V0m_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0m_2E0))) <-> s(tyop_2Enum_2Enum,V0m_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(thm_2Enumpair_2Etri__11) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3160 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Enumpair_2Etri__formula) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3161 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumpair_2Enlistrec_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enlistrec_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumpair_2Enlistrec_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3162 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumpair_2Etri__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3163 (all A_27a all V0n_2E0 all V1l_2E0 all V2f_2E0 s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0),s(tyop_2Enum_2Enum,V1l_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1492_0_2E1(s(tyop_2Enum_2Enum,V1l_2E0))),s(A_27a,V0n_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))),s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))),s(A_27a,c_2Enumpair_2Enlistrec_2E3(s(A_27a,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))))))) # label(thm_2Enumpair_2Enlistrec__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3164 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Enumpair_2Enfoldl_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,c_2Enumpair_2Enfoldl_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumpair_2Enfoldl_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3165 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3166 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3167 (all V0t_2E0 all V1h_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Enlen_2E1(s(tyop_2Enum_2Enum,V0t_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enlen_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumpair_2Enlen_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Enumpair_2Enlen__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3168 (all A_27a all V0f_2E0 all V4n_2E0 all V5t_2E0 all V6r_2E0 all V7a_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V6r_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(A_27a,V7a_2E0))))) = s(A_27a,f1461_1_2E5(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V5t_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V6r_2E0),s(A_27a,V7a_2E0)))) # label(def0_2Ethm_2Enumpair_2Enfoldl__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3169 (all A_27a all X0_2E0 s(A_27a,f1461_0_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),f1461_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef1461_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3170 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enumpair_2Enfst__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3171 (all V0n_2E0 all V1a_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))))))))) # label(thm_2Enumpair_2ESND__invtri0) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3172 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3173 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3174 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3175 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3176 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3177 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Enumpair_2Einvtri__le) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3178 (all V0y_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Enum_2Enum,V0y_2E0)) # label(thm_2Enumpair_2Ensnd__npair) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3179 (all V0n_2E0 all V1a_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))) # label(thm_2Enumpair_2Einvtri0__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3180 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Ensnd_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Ensnd_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3181 (all V1l_2E0 (p(s(tyop_2Emin_2Ebool,f1492_0_2E1(s(tyop_2Enum_2Enum,V1l_2E0)))) <-> s(tyop_2Enum_2Enum,V1l_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(def0_2Ethm_2Enumpair_2Enlistrec__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3182 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))))) # label(thm_2Enumpair_2Etri__LT__I) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3183 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Enumpair_2Einvtri__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3184 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Enumpair_2Ensnd__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3185 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enlistrec_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumpair_2Enlistrec_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Enlistrec_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3186 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,f1460_0_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f1460_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef1460_0_2E4) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3187 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3188 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3189 (all V0f_2E0 all V1n_2E0 all V2t_2E0 all V3r_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V3r_2E0))) = s(tyop_2Enum_2Enum,f1460_0_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2t_2E0),s(tyop_2Enum_2Enum,V3r_2E0)))) # label(def0_2Ethm_2Enumpair_2Enmap__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3190 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3191 (all A_27a all V0P_2E0 ((all V1n_2E0 all V2f_2E0 all V3l_2E0 ((s(tyop_2Enum_2Enum,V3l_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(A_27a,V1n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(A_27a,V1n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0))),s(tyop_2Enum_2Enum,V3l_2E0)))))) -> (all V4v_2E0 all V5v1_2E0 all V6v2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(A_27a,V4v_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),V5v1_2E0))),s(tyop_2Enum_2Enum,V6v2_2E0))))))) # label(thm_2Enumpair_2Enlistrec__ind) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3192 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Etri_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Etri_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3193 (all V2n_2E0 all V3t_2E0 all V4r_2E0 s(tyop_2Enum_2Enum,f1462_0_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3t_2E0),s(tyop_2Enum_2Enum,V4r_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V4r_2E0)))) # label(def0_2Ethm_2Enumpair_2Enapp__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3194 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Encons_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Encons_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3195 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3196 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3197 (all A_27a all V0t_2E0 all V1h_2E0 all V2f_2E0 all V3a_2E0 (s(A_27a,c_2Enumpair_2Enfoldl_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(tyop_2Enum_2Enum,V1h_2E0))),s(A_27a,V3a_2E0))),s(tyop_2Enum_2Enum,V0t_2E0))) = s(A_27a,c_2Enumpair_2Enfoldl_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(A_27a,V3a_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))) & s(A_27a,V3a_2E0) = s(A_27a,c_2Enumpair_2Enfoldl_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(A_27a,V3a_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Enumpair_2Enfoldl__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3198 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enfst_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Enfst_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3199 (all V0n_2E0 ((exists V1h_2E0 exists V2t_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2t_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)) | s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Enumpair_2Enlist__cases) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3200 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3201 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3202 (all V0y_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0y_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0y_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,V0y_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Enumpair_2Einvtri__unique) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3203 (all V0t_2E0 all V1nlist_2E0 all V2h_2E0 (s(tyop_2Enum_2Enum,c_2Enumpair_2Enapp_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V2h_2E0),s(tyop_2Enum_2Enum,V0t_2E0))),s(tyop_2Enum_2Enum,V1nlist_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V2h_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Enapp_2E2(s(tyop_2Enum_2Enum,V0t_2E0),s(tyop_2Enum_2Enum,V1nlist_2E0))))) & s(tyop_2Enum_2Enum,V1nlist_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enapp_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1nlist_2E0))))) # label(thm_2Enumpair_2Enapp__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3204 (all V0P_2E0 ((all V1n_2E0 all V2a_2E0 ((-p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2a_2E0)))))) -> (all V3v_2E0 all V4v1_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Enum_2Enum,V3v_2E0))),s(tyop_2Enum_2Enum,V4v1_2E0))))))) # label(thm_2Enumpair_2Einvtri0__ind) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3205 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Enumpair_2Enlistrec_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Enumpair_2Enlistrec_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumpair_2Enlistrec_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3206 (all V0t_2E0 all V1h_2E0 all V2f_2E0 (s(tyop_2Enum_2Enum,c_2Enumpair_2Enmap_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Encons_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,V1h_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Enmap_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,V0t_2E0))))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enmap_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Enumpair_2Enmap__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3207 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Einvtri_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Einvtri_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Einvtri_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3208 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Enumpair_2Ensnd__le) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3209 (all V0n_2E0 ((s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0)) & (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) <-> s(tyop_2Enum_2Enum,c_2Enumpair_2Etri_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumpair_2Etri__eq__0) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3210 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3211 (all X0_2E0 s(tyop_2Emin_2Ebool,f1492_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1492_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1492_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3212 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3213 (all V0h1_2E0 all V1l1_2E0 all V2h2_2E0 all V3l2_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2h2_2E0),s(tyop_2Enum_2Enum,V1l1_2E0))),s(tyop_2Enum_2Enum,V0h1_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2h2_2E0),s(tyop_2Enum_2Enum,V1l1_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3l2_2E0),s(tyop_2Enum_2Enum,V1l1_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V2h2_2E0),s(tyop_2Enum_2Enum,V3l2_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h1_2E0),s(tyop_2Enum_2Enum,V1l1_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))) # label(thm_2Ebit_2EBITS__COMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3214 (all V0l_2E0 all V2n_2E0 all V1h_2E0 all V3m_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1h_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0l_2E0))))),s(tyop_2Enum_2Enum,V3m_2E0))),s(tyop_2Enum_2Enum,V3m_2E0))) = s(tyop_2Enum_2Enum,f1514_0_2E4(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V3m_2E0)))) # label(def0_2Ethm_2Ebit_2ESIGN__EXTEND__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3215 (all V0b_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Ebit_2EBIT__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3216 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ELOG2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ebit_2ELOG2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3217 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3218 (all V0n_2E0 all V1m_2E0 ((all V2i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) # label(thm_2Ebit_2EBITS__ZERO5) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3219 (all V0n_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Ebit_2EADD__BITS__SUC) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3220 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Ebit_2EBIT__REVERSE__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3221 (all V1n_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Ebit_2EBIT__REVERSE__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3222 (all V0r_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0r_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0r_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))))) # label(thm_2Ebit_2EDIV__MULT__1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3223 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3224 (all V0h_2E0 all V1l_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))))))))) # label(thm_2Ebit_2EBITSLT__THM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3225 (all V0n_2E0 all V1b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) # label(thm_2Ebit_2EBITV__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3226 (all V0n_2E0 all V1k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,V1k_2E0)) # label(thm_2Ebit_2ETWOEXP__DIVISION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3227 (all V0h_2E0 all V1l_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0)))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Ebit_2ESLICE__ZERO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3228 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3229 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EMOD__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EMOD__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3230 (all V0m_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V0m_2E0) -> (exists V1p_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1p_2E0))) = s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Ebit_2ENOT__ZERO__ADD1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3231 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3232 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESIGN__EXTEND_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2ESIGN__EXTEND_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2ESIGN__EXTEND_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3233 (all V0x_2E0 all V1n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EDIVMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0)))))))) # label(thm_2Ebit_2EDIVMOD__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3234 (all V0i_2E0 all V1n_2E0 all V2op_2E0 all V3a_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0i_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0i_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2op_2E0),s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V4b_2E0)))))))) # label(thm_2Ebit_2ENOT__BIT__GT__BITWISE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3235 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ELOWEST__SET__BIT_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ebit_2ELOWEST__SET__BIT_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3236 (all V0h_2E0 all V1l_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))))))))) # label(thm_2Ebit_2EBITSLT__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3237 (all V0h_2E0 all V1l_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Ebit_2EBITS__ZERO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3238 (all V0n_2E0 all V1a_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V1a_2E0) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1a_2E0)))))) # label(thm_2Ebit_2EMOD__ZERO__GT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3239 (all V0n_2E0 all V1a_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) != s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))) # label(thm_2Ebit_2ENOT__BITS2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3240 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Ebit_2EBITS__LOG2__ZERO__ID) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3241 (all V0a_2E0 all V1b_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0a_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) # label(thm_2Ebit_2EDIV__SUB1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3242 (all V0b_2E0 all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0)))))) # label(thm_2Ebit_2ESBIT__MULT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3243 (all V0n_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))))),s(tyop_2Emin_2Ebool,f1592_0_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Emin_2Ebool,f1592_1_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) # label(thm_2Ebit_2EADD__BIT__SUC) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3244 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3245 (all V0h_2E0 all V1l_2E0 all V2a_2E0 all V3b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))))))),s(tyop_2Enum_2Enum,V3b_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V3b_2E0)))) # label(thm_2Ebit_2EBITS__SUM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3246 (all V0x_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Ebit_2EBIT__SLICE__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3247 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3248 (all V0h_2E0 all V1l_2E0 all V2a_2E0 all V3b_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V3b_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2a_2E0))) <-> (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,V0h_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,V2a_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V4x_2E0),s(tyop_2Enum_2Enum,V3b_2E0))))))) # label(thm_2Ebit_2EBIT__BITS__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3249 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Ebit_2EBITS__SLICE__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3250 (all V0h_2E0 all V1l_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0)))))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1l_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Ebit_2EBITS__LT__HIGH) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3251 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3252 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) # label(thm_2Ebit_2EODD__MOD2__LEM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3253 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,f1514_0_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f1514_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef1514_0_2E4) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3254 (all V0h_2E0 all V1h2_2E0 all V2l_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1h2_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1h2_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))))) # label(thm_2Ebit_2EBITS__SLICE__THM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3255 (all V0h_2E0 all V1m_27_2E0 all V2m_2E0 all V3l_2E0 all V4n_2E0 (s(tyop_2Enum_2Enum,V1m_27_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3l_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V3l_2E0),s(tyop_2Enum_2Enum,V4n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1m_27_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V3l_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))))) # label(thm_2Ebit_2ESLICE__COMP__RWT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3256 (all V0n_2E0 all V1i_2E0 s(tyop_2Emin_2Ebool,f1510_0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1i_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(def0_2Ethm_2Ebit_2ELOWEST__SET__BIT__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3257 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f1600_0_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = 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)),f1600_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ef1600_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3258 (all V0h_2E0 all V1l_2E0 all V2x_2E0 all V3n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V3n_2E0)))))) # label(thm_2Ebit_2EBITS__DIV__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.78 3259 (all V0wl_2E0 all V1op_2E0 all V2a_2E0 all V3b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0wl_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1op_2E0),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0wl_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1op_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0wl_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0wl_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V3b_2E0)))))) # label(thm_2Ebit_2EBITWISE__BITS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3260 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ETIMES__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ETIMES__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2ETIMES__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3261 (all V0n_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,V1m_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0)))))))) # label(thm_2Ebit_2EBIT__TWO__POW) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3262 (all V0x_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Ebit_2EDIV__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3263 (all V0a_2E0 all V1b_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0)))))) & s(tyop_2Enum_2Enum,V2n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> (exists V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V3i_2E0)))))))) # label(thm_2Ebit_2EEXISTS__BIT__IN__RANGE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3264 (all V0h_2E0 all V1m_2E0 all V2l_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2l_2E0))))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))) # label(thm_2Ebit_2EBIT__COMP__THM3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3265 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3266 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1510_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Ebit_2ELOWEST__SET__BIT__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3267 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3268 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3269 (all V0n_2E0 all V1a_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))) # label(thm_2Ebit_2ENOT__BITS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3270 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3271 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f1628_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,f1628_0_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1628_0_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3272 (all V0n_2E0 all V1a_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))) # label(thm_2Ebit_2ENOT__BIT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3273 (all V0b_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2EBIT__SLICE__THM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3274 (all V0n_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & (all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Enum_2Enum,V2m_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1P_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0))) # label(thm_2Ebit_2ELEAST__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3275 (all V0a_2E0 all V1b_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))))))) # label(thm_2Ebit_2ELESS__MULT__MONO2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3276 (all V3i_2E0 all V1h_2E0 all V0l_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,f1628_1_2E4(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V1h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(def1_2Ethm_2Ebit_2EBIT__SIGN__EXTEND) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3277 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3278 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3279 (all V0n_2E0 all V1k_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Ebit_2EMOD__2EXP__LT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3280 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f1592_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,f1592_1_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1592_1_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3281 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ebit_2EBIT_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EBIT_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3282 (all V0b_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Ebit_2ESBIT__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3283 (all V0n_2E0 all V1i_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1i_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Ebit_2EBIT__DIV2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3284 (all V0h_2E0 all V1l_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))))))))) # label(thm_2Ebit_2ESLICELT__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3285 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3286 (all V0h_2E0 all V1l_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1l_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Ebit_2EBITS__LT__LOW) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3287 (all V0x_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0)))))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0x_2E0) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2ELT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3288 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Ebit_2ELOG2__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3289 (all V0n_2E0 all V1p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1p_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,V1p_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Ebit_2ELOG2__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3290 (all V0l_2E0 all V1h_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Ebit_2ESLICE__ZERO2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3291 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f1514_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1514_0_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1514_0_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3292 (all V0h1_2E0 all V1l1_2E0 all V2h2_2E0 all V3l2_2E0 all V4n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V0h1_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2h2_2E0),s(tyop_2Enum_2Enum,V1l1_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3l2_2E0),s(tyop_2Enum_2Enum,V1l1_2E0))),s(tyop_2Enum_2Enum,V4n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V2h2_2E0),s(tyop_2Enum_2Enum,V3l2_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h1_2E0),s(tyop_2Enum_2Enum,V1l1_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))))) # label(thm_2Ebit_2EBITS__COMP__THM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3293 (all V0n_2E0 all V1i_2E0 all V2a_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2a_2E0)))) # label(thm_2Ebit_2EBIT__SHIFT__THM4) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3294 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Ebit_2EMOD__2EXP__EQ_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2EMOD__2EXP__EQ_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3295 (all V0y_2E0 all V1x_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0y_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0y_2E0)))))) # label(thm_2Ebit_2EBIT__SLICE__LEM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3296 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f1592_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,f1592_0_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1592_0_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3297 (all V0x_2E0 all V1n_2E0 all V2op_2E0 all V3a_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_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)),V2op_2E0),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V4b_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2op_2E0),s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V4b_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Ebit_2EBITWISE__COR) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3298 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> (exists V2p_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2p_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0)))))) # label(thm_2Ebit_2ELESS__EQ__EXP__MULT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3299 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3300 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3301 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBITV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EBITV_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3302 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ebit_2EMOD__2EXP__MAX_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EMOD__2EXP__MAX_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3303 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3304 (all V0n_2E0 all V1h_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V1h_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2l_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1h_2E0)))))))))))) # label(thm_2Ebit_2EMOD__2EXP__MONO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3305 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))),s(tyop_2Enum_2Enum,V0a_2E0)))))) # label(thm_2Ebit_2EMOD__LEQ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3306 (all V0n_2E0 all V1a_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2s_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2s_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2s_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))))) # label(thm_2Ebit_2EBIT__SHIFT__THM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3307 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V1_2E0) = s(A_27a,V0_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3308 (all V0h_2E0 all V1l_2E0 all V2a_2E0 all V3b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1l_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1l_2E0))))),s(tyop_2Enum_2Enum,V3b_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1l_2E0))))))))) # label(thm_2Ebit_2EBITS__SUM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3309 (all V0x_2E0 all V1n_2E0 all V2f_2E0 all V3a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2f_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2f_2E0),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))))) # label(thm_2Ebit_2EBIT__MODIFY__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3310 (all V0f_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) # label(thm_2Ebit_2EBIT__MODIFY__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3311 (all V2n_2E0 all V3f_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3f_2E0),s(tyop_2Enum_2Enum,V4x_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V4x_2E0))))),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3f_2E0),s(tyop_2Enum_2Enum,V4x_2E0)))) # label(thm_2Ebit_2EBIT__MODIFY__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3312 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0)))))))) # label(thm_2Ebit_2ETWOEXP__MONO2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3313 (all V2y_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V3x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2y_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,V2y_2E0))))))) # label(thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3314 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V1y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V1y_2E0)))))))) # label(thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3315 (all V0h_2E0 all V1l_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Ebit_2EBITS__ZERO2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3316 (all V0b_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,V1n_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0)))))) -> (exists V2i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))))))) # label(thm_2Ebit_2EEXISTS__BIT__LT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3317 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ebit_2EBIT_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebit_2EBIT_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ebit_2EBIT_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3318 (all V0i_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V0i_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0i_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2ENOT__BIT__GT__LOG2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3319 (all V0l_2E0 all V1h_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESIGN__EXTEND_2E3(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f1514_0_2E3(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1h_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0l_2E0)))))))) # label(thm_2Ebit_2ESIGN__EXTEND__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3320 (all V0n_2E0 all V1h_2E0 all V2l_2E0 all V3a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1h_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V3a_2E0))))) # label(thm_2Ebit_2EBIT__OF__BITS__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3321 (all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V1y_2E0))))))))) # label(thm_2Ebit_2ELOG2__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3322 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3323 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EDIVMOD__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2EDIVMOD__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EDIVMOD__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3324 (all V0x_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ETIMES__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2Ebit_2ETIMES__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3325 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2ELOG_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elogroot_2ELOG_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3326 (all V0h_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Ebit_2EBITS__ZERO3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3327 (all V0b_2E0 all V1m_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2n_2E0))))))) # label(thm_2Ebit_2ESBIT__DIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3328 (all V0n_2E0 all V1m_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0)))))))) # label(thm_2Ebit_2EDIV__LT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3329 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Ebit_2EBIT__LOG2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3330 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2ESLICE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2ESLICE_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3331 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3332 (all V0h_2E0 all V1a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0)))))))) -> s(tyop_2Enum_2Enum,V1a_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))) # label(thm_2Ebit_2EBITS__ZEROL) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3333 (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,f1600_0_2E2(s(tyop_2Emin_2Ebool,V3x_2E0),s(tyop_2Emin_2Ebool,V4y_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V3x_2E0)))) # label(def0_2Ethm_2Ebit_2EBITWISE__ONE__COMP__LEM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3334 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3335 (all V0n_2E0 all V1h_2E0 all V2l_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2l_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Ebit_2ESLICE__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3336 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3337 (all V0b_2E0 all V1h_2E0 all V2l_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V0b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) # label(thm_2Ebit_2EBIT__SLICE__THM4) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3338 (all V0n_2E0 all V1i_2E0 all V2a_2E0 (s(tyop_2Enum_2Enum,V1i_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))) | s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) & -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0)))))))))))) # label(thm_2Ebit_2EBIT__COMPLEMENT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3339 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3340 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebit_2EBITWISE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ec_2Ebit_2EBITWISE_2E4) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3341 (all V3a_2E0 all V0n_2E0 (p(s(tyop_2Emin_2Ebool,f1614_0_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(def0_2Ethm_2Ebit_2EBIT__SHIFT__THM5) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3342 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3343 (all V3n_2E0 all V4op_2E0 all V5x_2E0 all V6y_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4op_2E0),s(tyop_2Enum_2Enum,V5x_2E0),s(tyop_2Enum_2Enum,V6y_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4op_2E0),s(tyop_2Enum_2Enum,V5x_2E0),s(tyop_2Enum_2Enum,V6y_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(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)),V4op_2E0),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V5x_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,V6y_2E0))))),s(tyop_2Enum_2Enum,V3n_2E0)))))) # label(thm_2Ebit_2EBITWISE__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3344 (all V0op_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0op_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Ebit_2EBITWISE__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3345 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) != s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(thm_2Ebit_2ENOT__MOD2__LEM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3346 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESBIT_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2ESBIT_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3347 (all V0h_2E0 all V1m_2E0 all V2l_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V0h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V2l_2E0),s(tyop_2Enum_2Enum,V3n_2E0))))) # label(thm_2Ebit_2ESLICE__COMP__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3348 (all V0a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))) # label(thm_2Ebit_2ESUC__SUB) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3349 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1x_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V0n_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Ebit_2EMOD__ADD__1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3350 (all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3351 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1l_2E0)))))) # label(thm_2Ebit_2EBITS__THM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3352 (all V0x_2E0 all V1n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2EDIVMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Ebit_2EDIVMOD__2EXP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3353 (all V0b_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Ebit_2EBIT__ZERO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3354 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1510_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1510_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1510_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3355 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2b_2E0))) <-> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))) # label(thm_2Ebit_2EBIT__SLICE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3356 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Ebit_2ESLICE__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3357 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3358 (all V0n_2E0 all V1op_2E0 all V2a_2E0 all V3b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1op_2E0),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1op_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V3b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))))),s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(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)),V1op_2E0),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V2a_2E0))))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V3b_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Ebit_2EBITWISE__EVAL) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3359 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2b_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) # label(thm_2Ebit_2EMOD__2EXP__EQ__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3360 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) != s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) # label(thm_2Ebit_2ENOT__MOD2__LEM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3361 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Ewhile_2ELEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Ewhile_2ELEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ewhile_2ELEAST_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3362 (all V0n_2E0 all V1a_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2s_2E0)))))))))) # label(thm_2Ebit_2EBIT__SHIFT__THM3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3363 (all V0a_2E0 all V1b_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0))))))) # label(thm_2Ebit_2EEXP__SUB__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3364 (all V0b_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0b_2E0))))))) # label(thm_2Ebit_2EBIT__B) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3365 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,f1592_0_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) <-> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))))) # label(def0_2Ethm_2Ebit_2EADD__BIT__SUC) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3366 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Ebit_2EBITS__SUC__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3367 (all V0h_2E0 all V1l_2E0 all V2x_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))))) # label(thm_2Ebit_2EBIT__OF__BITS__THM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3368 (all V0x_2E0 all V1n_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,V2a_2E0))))) # label(thm_2Ebit_2EBIT__REVERSE__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3369 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3370 (all V0x_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2Ebit_2EMOD__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3371 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1j_2E0 all V2k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1j_2E0),s(tyop_2Enum_2Enum,V2k_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Ebit_2EMOD__PLUS__RIGHT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3372 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Ebit_2ETWOEXP__NOT__ZERO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3373 (all V0l_2E0 all V1h_2E0 all V2n_2E0 all V3i_2E0 (s(tyop_2Enum_2Enum,V0l_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1628_0_2E3(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V3i_2E0))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0l_2E0))))))),s(tyop_2Emin_2Ebool,f1628_1_2E4(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ESIGN__EXTEND_2E3(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) # label(thm_2Ebit_2EBIT__SIGN__EXTEND) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3374 (all V0x_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2Ebit_2EDIV__MULT__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3375 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMIN_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3376 (all V0m_2E0 all V1n_2E0 (s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) != s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Ebit_2EADD__BIT0) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3377 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1x_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Ebit_2EMOD__PLUS__1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3378 (all V0x_2E0 all V1n_2E0 all V2op_2E0 all V3a_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_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)),V2op_2E0),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V4b_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2op_2E0),s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V4b_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Ebit_2EBITWISE__NOT__COR) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3379 (all V0n_2E0 all V1a_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,f1592_1_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,f1592_0_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) # label(def1_2Ethm_2Ebit_2EADD__BIT__SUC) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3380 (all V0i_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0i_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0i_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2EBIT__IMP__GE__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3381 (all V0n_2E0 all V1a_2E0 all V2s_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V2s_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))) # label(thm_2Ebit_2EBIT__SHIFT__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3382 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3383 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3384 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__REVERSE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EBIT__REVERSE_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3385 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3386 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3387 (all V0h_2E0 all V1l_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Ebit_2EBITS__SUC) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3388 (all V0n_2E0 all V1a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1a_2E0))))) # label(thm_2Ebit_2EMOD__2EXP__MAX__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3389 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1l_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Ebit_2EBITS__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3390 (all V0n_2E0 all V1m_2E0 all V2i_2E0 all V3a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1m_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))))))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1614_0_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1m_2E0))))))))))) # label(thm_2Ebit_2EBIT__SHIFT__THM5) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3391 (all V0n_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),f1600_0_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0)))))) # label(thm_2Ebit_2EBITWISE__ONE__COMP__LEM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3392 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EODD_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3393 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1b_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))))))) # label(thm_2Ebit_2EDIV__GT0) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3394 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1614_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,f1614_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1614_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3395 (all V0b_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITV_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0b_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Ebit_2EBITV__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3396 (all V0a_2E0 all V1b_2E0 (s(tyop_2Enum_2Enum,V1b_2E0) != s(tyop_2Enum_2Enum,V0a_2E0) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0)))))))) # label(thm_2Ebit_2EBIT__B__NEQ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3397 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Ebit_2EONE__LE__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3398 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EDIV__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EDIV__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3399 (all V0i_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0i_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0i_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2ENOT__BIT__GT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3400 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3401 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3402 (all V0h_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) # label(thm_2Ebit_2EBITS__SUM3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3403 (all V0n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> (all V1j_2E0 all V2k_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V1j_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V1j_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Ebit_2EMOD__PLUS__LEFT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3404 (all V0b_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Ebit_2EBIT__EXP__SUB1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.79 3405 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Ebit_2EDIV__MULT__THM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3406 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3407 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f1510_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1510_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1510_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3408 (all V0n_2E0 all V1op_2E0 all V2a_2E0 all V3b_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1op_2E0),s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,V3b_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Ebit_2EBITWISE__LT__2EXP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3409 (all V0h_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1a_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) # label(thm_2Ebit_2EBITS__MUL) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3410 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3411 (all V0h_2E0 all V1l_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V0h_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1l_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))) # label(thm_2Ebit_2EBITS__ZERO4) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3412 (all V0a_2E0 all V1b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V1b_2E0)))))))) # label(thm_2Ebit_2ETWOEXP__MONO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3413 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),f1628_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Emin_2Ebool,f1628_1_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef1628_1_2E4) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3414 (all V0h_2E0 all V1l_2E0 all V2x_2E0 all V3y_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Enum_2Enum,V1l_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))) -> s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V4n_2E0))))) # label(thm_2Ebit_2ESLICE__COMP__THM2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3415 (all V0n_2E0 all V1h_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Ebit_2ESLICE__ZERO__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3416 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2EBITS_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2EBITS_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3417 (all V0b_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Ebit_2ESLICE_2E3(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0b_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Ebit_2EBIT__SLICE__THM3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3418 (all V0x_2E0 all V1n_2E0 all V2op_2E0 all V3a_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> 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)),V2op_2E0),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V4b_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebit_2EBIT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2op_2E0),s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V4b_2E0))))))) # label(thm_2Ebit_2EBITWISE__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3419 (all V0l_2E0 all V1h_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,f1628_0_2E3(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V3i_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0l_2E0),s(tyop_2Enum_2Enum,V1h_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V0l_2E0))))))) # label(def0_2Ethm_2Ebit_2EBIT__SIGN__EXTEND) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3420 (all V0h_2E0 all V1l_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0h_2E0))),s(tyop_2Enum_2Enum,V1l_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Ebit_2EBITS__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3421 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3422 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Ebit_2EZERO__LT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3423 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2EBIT__MODIFY_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2EBIT__MODIFY_2E3) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3424 (all V0h_2E0 all V1l_2E0 all V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Ebit_2EBITS_2E3(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,V1l_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Ebit_2EBITS__LEQ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3425 (all A_27a all V0s1_2E0 all V1s2_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))))) # label(thm_2Epred__set_2ESET__EQ__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3426 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3427 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),f1647_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),f1647_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1647_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3428 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EREST_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EREST_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3429 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3430 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2ESND_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) # label(thm_2Epred__set_2EGSPEC__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3431 (all A_27a all V0P_2E0 all V1Q_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2117_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2117_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2117_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Epred__set_2EGSPEC__OR) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3432 (all A_27a all V0s_2E0 -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EPSUBSET__IRREFL) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3433 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1638_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,f1638_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(def1_2Ethm_2Epred__set_2EUNION__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3434 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f2057_0_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),f2057_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2057_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3435 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) = s(A_27a,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3436 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f1662_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1662_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef1662_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3437 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3438 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),f1695_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1695_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1695_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3439 (all A_27a all V0P_2E0 all V1s_2E0 ((all V3t_2E0 all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Epred__set_2EFORALL__IN__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3440 (all A_27a all V0f_2E0 all V2e_2E0 all V3acc_2E0 s(tyop_2Enum_2Enum,f1665_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,V3acc_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,V3acc_2E0)))) # label(def0_2Ethm_2Epred__set_2ESUM__IMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3441 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1663_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),f1663_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1663_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3442 (all A_27a all V0p_2E0 all V1q_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1q_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1q_2E0)))))) # label(thm_2Epred__set_2ECOMPL__SPLITS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3443 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Epred__set_2EFINITE__COUNT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3444 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2EEMPTY__REL_2E0)) # label(thm_2Epred__set_2EREL__RESTRICT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3445 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1660_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f1660_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef1660_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3446 (all A_27a all V0x_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))) # label(thm_2Epred__set_2ECARD__SING) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3447 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3448 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) # label(thm_2Epred__set_2ESUBSET__EQ__CARD) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3449 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))))) # label(thm_2Epred__set_2ECARD__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3450 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epred__set_2EFUNSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EFUNSET_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3451 (all A_27a all V0s_2E0 all V1R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V2t1_2E0 all V3t2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t2_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t2_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t1_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t2_2E0)))))))) # label(thm_2Epred__set_2Epartition__elements__disjoint) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3452 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 all V2Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0)))))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0)))))))) # label(thm_2Epred__set_2EIN__FUNSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3453 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3454 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 ((exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))) -> (exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EBIJ__SYM__IMP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3455 (all A_27a all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (exists V3N_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3N_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EBIJ__FINITE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3456 (all A_27a s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2EUNIV__FUN__TO__BOOL) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3457 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 ((exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) & (exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))) -> (exists V4h_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V4h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2ESCHROEDER__BERNSTEIN) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3458 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),f2133_0_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),f2133_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef2133_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3459 (all A_27a all V0s_2E0 -(exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2Epow__no__surj) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3460 (all A_27a all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3461 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3462 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3463 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3464 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3465 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3466 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2127_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2127_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2127_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3467 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2ECOMPL__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3468 (all A_27a all V0f_2E0 ((all V1m_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) != s(tyop_2Enum_2Enum,V1m_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) -> (all V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))))))))) # label(thm_2Epred__set_2EDISJOINT__COUNT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3469 (all A_27a ((all V3s_2E0 all V4t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3s_2E0)))))) <-> (all V5s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5s_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V3s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5s_27_2E0)))))))) & (all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> (all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))))) # label(thm_2Epred__set_2EDISJOINT__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3470 (all A_27a all V0f_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ESCHROEDER__CLOSED) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3471 (all A_27a all V0f_2E0 all V1s_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1667_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Epred__set_2EPROD__IMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3472 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EINSERT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3473 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3474 (all A_27a all V0x_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2ECOMPL__INTER) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3475 (all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2ECOUNTABLE__NUM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3476 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3477 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))))) # label(thm_2Epred__set_2EDISJOINT__UNION__BOTH) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3478 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3479 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2113_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2113_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2113_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3480 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 ((exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) <-> (exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2EBIJ__SYM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3481 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ECHOICE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3482 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f2169_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EINFINITE__EXPLICIT__ENUMERATE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3483 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1639_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1639_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1639_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3484 (all A_27a all A_27b all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2EPREIMAGE__K) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3485 (all A_27a all V0I_2E0 all V1J_2E0 all V2n_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0)))) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__MIN__SET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3486 (all A_27a all V0y_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2113_0_2E1(s(A_27a,V0y_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2EGSPEC__EQ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3487 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3488 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 all V2Q_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V3x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDFUNSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))))) # label(thm_2Epred__set_2EDFUNSET__applied) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3489 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2Eunion__countable) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3490 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EStrongOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EStrongOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3491 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2114_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2114_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2114_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3492 (all A_27a all A_27b all X0_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3493 (all A_27a all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) <-> (all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EEXTENSION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3494 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3495 (all V0e_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) & s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Enum_2Enum,V0e_2E0))) # label(thm_2Epred__set_2EMAX__SET__REWRITES) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3496 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EREST__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3497 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EDFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EDFUNSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDFUNSET_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3498 (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))))))) # label(thm_2Epred__set_2Ein__max__set) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3499 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2116_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2116_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2116_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3500 (all A_27a all V0s1_2E0 all V1s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__EQN) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3501 (all A_27a all A_27b all V0f_2E0 all V1y_2E0 all V2x_2E0 all V3P_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1y_2E0))) = s(A_27b,V2x_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V1y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),f1693_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0)))))))))) # label(thm_2Epred__set_2EIN__GSPEC) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3502 (all A_27a all V0P_2E0 all V1Q_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2117_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,f2117_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(def1_2Ethm_2Epred__set_2EGSPEC__OR) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3503 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EIN__INTER) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3504 (all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2Enum__to__pair_2E1(s(tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2y_2E0)))))))) # label(thm_2Epred__set_2Epair__to__num__inv_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3505 (all V0x_2E0 s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2Enum__to__pair_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2Epred__set_2Epair__to__num__inv_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3506 (all V0n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2Enum__to__pair_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Epred__set_2Enum__to__pair__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3507 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2ECARD__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3508 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3509 (all A_27a all A_27b all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3510 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2P_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f1692_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0))))))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V0y_2E0)))) # label(thm_2Epred__set_2EPAIR__IN__GSPEC__IFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3511 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2ENOT__EMPTY__SING) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3512 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EUNION_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EUNION__applied) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3513 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3514 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3515 (all A_27a all A_27b all V1s_2E0 all V0f_2E0 all V2y_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,f1654_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27b,V2y_2E0),s(A_27a,V3x_2E0)))) <-> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))) = s(A_27b,V2y_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(def0_2Ethm_2Epred__set_2ELINV__OPT__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3516 (all A_27a all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Epred__set_2EFINITE__DIFF__down) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3517 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2134_1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2134_1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef2134_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.80 3518 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMIN_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3519 (all A_27a all V0x_2E0 all V1y_2E0 all V2s_2E0 (s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINSERT_2E3(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Epred__set_2EINSERT__applied) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3520 (all A_27a all V0R_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__partition) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3521 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ECOMPL__COMPL) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3522 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2s_2E0 all V3f_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27b,V0y_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & s(A_27b,V0y_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V1x_2E0))))) # label(thm_2Epred__set_2ELINV__OPT__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3523 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) -> (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))))))))) # label(thm_2Epred__set_2ECARD__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3524 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3525 (all A_27a all V0P_2E0 all V2x_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2116_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(def0_2Ethm_2Epred__set_2EGSPEC__AND) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3526 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__COMP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3527 (all A_27a all V1x_2E0 s(A_27a,f1865_0_2E1(s(A_27a,V1x_2E0))) = s(A_27a,V1x_2E0)) # label(def0_2Ethm_2Epred__set_2EINJ__ID) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3528 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2ESUBSET__SUBSET__EQ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3529 (all V0n_2E0 all V1m_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1m_2E0)))))))) # label(thm_2Epred__set_2Ecount__add) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3530 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1665_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,f1665_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1665_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3531 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2EPREIMAGE__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3532 (all A_27a all V0P_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Epred__set_2ESPECIFICATION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3533 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2Eis__measure__maximal_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2Eis__measure__maximal_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3534 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3535 (all A_27a all V1s_2E0 all V0R_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Ebool,f1673_3_2E4(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1673_2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) # label(def1_2Ethm_2Epred__set_2Epartition__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3536 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Epred__set_2EFINITE__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3537 (all A_27a all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2e_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2e_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2e_2E0)))))))) # label(thm_2Epred__set_2ESUM__IMAGE__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3538 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3539 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3540 (all A_27a all V0sp_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2026_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EDIFF__BIGINTER1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3541 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) -> (all V1v_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EIN__EQ__UNIV__IMP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3542 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2Einj__countable) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3543 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) -> (all V3e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3e_2E0)))))))))))) # label(thm_2Epred__set_2EBIJ__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3544 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1663_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f1663_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ef1663_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3545 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3546 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EUNION_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EUNION_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3547 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2Einfinite__rest) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3548 (all A_27a all V0P_2E0 all V1s_2E0 all V2t_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) <-> (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5x_2E0)))))) & (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Epred__set_2EFORALL__IN__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3549 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> -(exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EIN__DISJOINT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3550 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3551 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EPREIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3552 (all V0A_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0)))) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0))))))) # label(thm_2Epred__set_2EMIN__SET__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3553 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EEMPTY__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3554 (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) & (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) & (all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))))))))) # label(thm_2Epred__set_2EMAX__SET__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3555 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))),s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0)))) # label(thm_2Epred__set_2EDELETE__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3556 (all A_27a ((all V2s_2E0 all V3t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) & (all V0s_2E0 all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EINTER__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3557 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EEMPTY_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EEMPTY_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3558 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EINFINITE__INJ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3559 (all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ESUM__SET__IN__LE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3560 (all A_27a all V0A_2E0 all V1B_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Epred__set_2EUNION__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3561 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3562 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3563 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EINSERT__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3564 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EIN__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3565 (all A_27a all A_27b all V0f_2E0 ((all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))) & (all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EINJ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3566 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f1662_1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f1662_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef1662_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3567 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__SUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3568 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))),c_2Epred__set_2ELINV__OPT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ELINV__OPT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3569 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1695_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f1695_0_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef1695_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3570 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINSERT_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINSERT_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3571 (all A_27a all A_27b all V0f_2E0 all V1v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))) <-> (exists V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1v_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27b,V2x_2E0)))))) # label(thm_2Epred__set_2EGSPECIFICATION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3572 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3573 (all A_27a all A_27b all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1f_2E0 all V2x_2E0 all V3b_2E0 s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))),s(A_27b,V3b_2E0))))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27b,V3b_2E0)))))) # label(thm_2Epred__set_2EITSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3574 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(A_27b,V3x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Epred__set_2ELINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V3x_2E0))))))))) # label(thm_2Epred__set_2EBIJ__LINV__INV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3575 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1641_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EDIFF__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3576 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EUNIV_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3577 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2ECHOICE__SING) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3578 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),f2073_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),f2073_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ef2073_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3579 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V0n_2E0) <-> p(s(tyop_2Emin_2Ebool,f2134_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(def1_2Ethm_2Epred__set_2Ecount__EQN) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3580 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))))))) # label(thm_2Epred__set_2EIMAGE__INTER) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3581 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> (exists V3g_2E0 ((all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(A_27b,V4y_2E0))))) = s(A_27b,V4y_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ESURJ__INJ__INV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3582 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3583 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) & (all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1908_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))))))))) # label(thm_2Epred__set_2EBIJ__ALT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3584 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) # label(thm_2Epred__set_2EDIFF__DIFF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3585 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3586 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3587 (all A_27a all V0s_2E0 all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EDIFF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3588 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2ESUBSET__REFL) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3589 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,f2057_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(def0_2Ethm_2Epred__set_2EITSET__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3590 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__IMAGE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ESUM__IMAGE_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3591 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))) -> s(A_27a,V4x_2E0) = s(A_27a,V5y_2E0)))))) # label(thm_2Epred__set_2EINJ__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3592 (all A_27a all V0x_2E0 all V1y_2E0 (-p(s(tyop_2Emin_2Ebool,V0x_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0)))))) # label(thm_2Epred__set_2EK__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3593 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Epred__set_2ECARD__COUNT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3594 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Epred__set_2ECOMPL__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3595 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2128_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2128_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2128_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3596 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3597 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2128_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2128_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2128_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3598 (all A_27a all V0sp_2E0 all V2u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2026_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) # label(def0_2Ethm_2Epred__set_2EDIFF__BIGINTER1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3599 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1908_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1908_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ef1908_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3600 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1993_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1993_0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1993_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3601 (all A_27a all V0s1_2E0 all V1s2_2E0 all V2s3_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s3_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s3_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))))) # label(thm_2Epred__set_2ESUBSET__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3602 (all V1p_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V1p_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1p_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2134_1_2E1(s(tyop_2Enum_2Enum,V1p_2E0)))) # label(def0_2Ethm_2Epred__set_2Ecount__EQN) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3603 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EPSUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPSUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3604 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2ESUBSET__FINITE__I) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3605 (all A_27a all V0y_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2114_0_2E1(s(A_27a,V0y_2E0)))))) # label(thm_2Epred__set_2EGSPEC__EQ2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3606 (all A_27a s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2ECARD__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3607 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3608 (all A_27a all A_27b (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2Ecountable__Uprod) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3609 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1673_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),f1673_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1673_2_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3610 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EDIFF__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3611 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3612 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f1692_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1692_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef1692_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3613 (all A_27a ((all V1s_2E0 all V2n_2E0 s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))) & (all V0s_2E0 s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Epred__set_2Echooser__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3614 (all V0s_2E0 ((exists V1n_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))) <-> (exists V2n_2E0 ((all V3m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V3m_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2ENUM__SET__WOP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3615 (all A_27a all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) # label(thm_2Epred__set_2EEMPTY__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3616 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V2f_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2ESUM__IMAGE__PERMUTES) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3617 (all V0n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Epred__set_2ECOUNTABLE__COUNT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3618 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3619 (all A_27a all A_27b all V0s_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EEMPTY__FUNSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3620 (all A_27a all V0x_2E0 all V1y_2E0 all V2z_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2z_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2z_2E0)))) # label(thm_2Epred__set_2EDIFF__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3621 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))))) # label(thm_2Epred__set_2EBIGUNION__PAIR) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3622 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3623 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2s_2E0 all V3t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1e_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))))) # label(thm_2Epred__set_2EBIJ__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3624 (all A_27a all V0g_2E0 all V1f_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),f2073_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))) # label(thm_2Epred__set_2EABS__DIFF__SUM__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3625 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2114_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2114_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2114_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3626 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3627 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Epred__set_2EUNIV__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3628 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) # label(thm_2Epred__set_2ECARD__REST) # label(axiom) # label(non_clause). [assumption]. 107.77/107.81 3629 (all A_27a all V0P_2E0 all V1B_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0)))))) # label(thm_2Epred__set_2EBIGINTER__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3630 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | (exists V3f_27_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3f_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2Einj__surj) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3631 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3632 (all A_27a all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,f1817_0_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0)))) <-> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) # label(def0_2Ethm_2Epred__set_2EDELETE__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3633 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EDISJOINT__SING__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3634 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2117_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2117_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef2117_2_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3635 (all A_27a all V0x_2E0 all V1y_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V0x_2E0))),s(A_27a,V1y_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1y_2E0))),s(A_27a,V0x_2E0)))) # label(thm_2Epred__set_2EDELETE__COMM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3636 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3637 (all A_27a all V0sp_2E0 all V3u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3u_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2027_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3u_2E0)))) # label(def0_2Ethm_2Epred__set_2EDIFF__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3638 (all A_27a all V1x_2E0 all V0y_2E0 (s(A_27a,V0y_2E0) = s(A_27a,V1x_2E0) <-> p(s(tyop_2Emin_2Ebool,f2113_1_2E2(s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))))) # label(def0_2Ethm_2Epred__set_2EGSPEC__EQ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3639 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3640 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) # label(thm_2Epred__set_2ESUBSET__UNION__ABSORPTION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3641 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__POW) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3642 (all A_27a all V0P_2E0 all V1x_2E0 ((all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,f1662_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))))) # label(def0_2Ethm_2Epred__set_2EBIGINTER) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3643 (all A_27a all V0P_2E0 all V1Q_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2116_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2116_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2116_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(thm_2Epred__set_2EGSPEC__AND) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3644 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1639_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EINTER__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3645 (all A_27a all V0f_2E0 all V1N_2E0 ((all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1N_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1N_2E0))))))))) # label(thm_2Epred__set_2EBIGUNION__IMAGE__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3646 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2116_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2116_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef2116_2_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3647 (all A_27a all V0e_2E0 all V2ps_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E1(s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2ps_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2ps_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2107_0_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2ps_2E0)))) # label(def0_2Ethm_2Epred__set_2EPOW__EQNS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3648 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 all V2b_2E0 s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27b,V2b_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2056_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27b,V2b_2E0),s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(A_27b,V2b_2E0))))))),s(A_27b,c_2Ebool_2EARB_2E0)))) # label(thm_2Epred__set_2EITSET__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3649 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2113_1_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = 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)),f2113_1_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2113_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3650 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1680_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(def0_2Ethm_2Epred__set_2EPREIMAGE__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3651 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2EPROD__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EPROD__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3652 (all A_27a all V0s_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ECHOICE__NOT__IN__REST) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3653 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3654 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2127_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2127_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2127_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3655 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2s_2E0 all V3t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) -> (exists V4u_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4u_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4u_2E0)))))))) # label(thm_2Epred__set_2EBIJ__INSERT__IMP) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3656 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3657 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3658 (all A_27a all V0s_2E0 ((exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EBIJ__NUM__COUNTABLE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3659 (all A_27a all V0s_2E0 ((exists V1x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3660 (all A_27a all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))) -> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__THM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3661 (all A_27a all V0P_2E0 all V3x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2116_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) # label(def2_2Ethm_2Epred__set_2EGSPEC__AND) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3662 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3663 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EGSPEC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EGSPEC_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3664 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2s_2E0 all V3b_2E0 ((all V4x_2E0 all V5y_2E0 all V6z_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V5y_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27b,V6z_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V5y_2E0))),s(A_27b,V6z_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V1e_2E0))),s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1e_2E0))),s(A_27b,V3b_2E0))))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(A_27b,V3b_2E0))))) # label(thm_2Epred__set_2ECOMMUTING__ITSET__RECURSES) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3665 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2ECOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3666 (all A_27a all V0R_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2Epartition__CARD) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3667 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 ((all V2x_2E0 all V3y_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) <-> s(A_27a,V3y_2E0) = s(A_27a,V2x_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2ECARD__INJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3668 (all A_27a all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2n_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3x_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__lower__bound) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3669 (all A_27a all V0s_2E0 all V1n_2E0 s(A_27a,f2169_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(def0_2Ethm_2Epred__set_2EINFINITE__EXPLICIT__ENUMERATE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3670 (all A_27a all V0s_2E0 ((exists V1f_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V3n_2E0 s(A_27a,V2x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ECOUNTABLE__ALT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3671 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2EMAX__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EMAX__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3672 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EUNION__COMM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3673 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1642_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1642_0_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1642_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3674 (all A_27a all V0n_2E0 all V1s_2E0 ((all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0)))))) & (all V3e1_2E0 all V4e2_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3e1_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4e2_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4e2_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3e1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4e2_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Epred__set_2ECARD__BIGUNION__SAME__SIZED__SETS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3675 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EDISJOINT__DELETE__SYM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3676 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)) # label(thm_2Epred__set_2EIMAGE__I) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3677 (all A_27a all V0f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))))) # label(thm_2Epred__set_2Ecountable__image__nats) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3678 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> (all V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2EIMAGE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3679 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) != s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EPOW__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3680 (all A_27a all V0x_2E0 all V1y_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0))))) # label(thm_2Epred__set_2EDIFF__SAME__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3681 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EIMAGE__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3682 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2128_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2128_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2128_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3683 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3684 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (exists V1c_2E0 exists V2n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1c_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EFINITE__BIJ__COUNT__EQ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3685 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),f1673_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f1673_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef1673_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3686 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(s(A_27a,X0_2E0))) = s(tyop_2Esum_2Esum(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),c_2Esum_2EINR_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3687 (all A_27a all A_27b all A_27c all V0P_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2ECROSS__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3688 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2116_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2116_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2116_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3689 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2ECROSS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3690 (all A_27a all V0s_2E0 all V1t_2E0 ((exists V2x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2ENOT__EQUAL__SETS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3691 (all A_27a all A_27b all V2P_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f1692_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V3x_2E0),s(A_27b,V4y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27b,V4y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V3x_2E0))),s(A_27b,V4y_2E0)))))) # label(def0_2Ethm_2Epred__set_2EPAIR__IN__GSPEC__IFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3692 (all A_27a all V0P_2E0 ((s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0) | s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)) & (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))) <-> s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0) | s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Epred__set_2EBIGUNION__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3693 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3694 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V1f_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1993_0_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) & (all V2n_2E0 all V3m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) -> (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3m_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) -> s(tyop_2Enum_2Enum,V3m_2E0) = s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Epred__set_2EFINITE__ISO__NUM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3695 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (exists V3g_2E0 ((all V5x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V5x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(A_27b,V5x_2E0) = s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(A_27b,V5x_2E0))))) & (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(A_27a,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))) = s(A_27a,V4x_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EBIJ__INV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3696 (all A_27a ((all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)) & (all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Epred__set_2EINTER__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3697 (all A_27a all V0s_2E0 ((exists V1f_2E0 exists V2b_2E0 all V3e_2E0 ((exists V4n_2E0 (s(A_27a,V3e_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EFINITE__WEAK__ENUMERATE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3698 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(A_27a,V0x_2E0)))) # label(thm_2Epred__set_2EEMPTY__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3699 (all A_27a all V0s1_2E0 all V1s2_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__DELETE__BOTH) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3700 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Eenumerate_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ECOUNTABLE__ALT__BIJ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3701 (all A_27a all V0P_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Ebool,f1661_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1661_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def1_2Ethm_2Epred__set_2EBIGUNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3702 (all A_27a all A_27b all V0x_2E0 all V3P_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),s(A_27b,V0x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V4y_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f1694_0_2E3(s(A_27b,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V4y_2E0)))) # label(def0_2Ethm_2Epred__set_2EPAIR__IN__GSPEC__1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3703 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1937_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1937_0_2E3(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1937_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3704 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) # label(thm_2Epred__set_2EUNION__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3705 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3706 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EINTER__COMM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3707 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),f1663_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(thm_2Epred__set_2ECROSS__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3708 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) # label(thm_2Epred__set_2EDISJOINT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3709 (all A_27a all V0P_2E0 all V3x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2117_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) # label(def2_2Ethm_2Epred__set_2EGSPEC__OR) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3710 (all A_27a all V0R_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2127_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))))) # label(def0_2Ethm_2Epred__set_2EKoenigsLemma) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3711 (all A_27a all V0R_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__StrongOrder__WF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3712 (all A_27a all V0R_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2Epairwise__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3713 (all A_27a all V0P_2E0 all V2x_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,f2117_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Epred__set_2EGSPEC__OR) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3714 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1692_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f1692_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef1692_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3715 (all A_27a all V0P_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))) # label(thm_2Epred__set_2EINFINITE__INHAB) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3716 (all V0x_2E0 all V1y_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))))) # label(thm_2Epred__set_2Epair__to__num__formula) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3717 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3718 (all A_27a all V0y_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2112_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0)))))) # label(def0_2Ethm_2Epred__set_2EGSPEC__ID) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3719 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3720 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E1(s(A_27a,V0x_2E0))))) # label(thm_2Epred__set_2EUNIV__applied) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3721 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))))) # label(thm_2Epred__set_2EFUNSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3722 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3723 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2EK_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3724 (all A_27a all V0X_2E0 all V1P_2E0 ((all V2Y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0)))))) # label(thm_2Epred__set_2EBIGUNION__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3725 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 ((all V2s_2E0 all V3b_2E0 ((s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))),s(A_27b,V3b_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(A_27b,V3b_2E0)))))) -> (all V4v_2E0 all V5v1_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4v_2E0))),s(A_27b,V5v1_2E0))))))) # label(thm_2Epred__set_2EITSET__IND) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3726 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2Ecountable__surj) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3727 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3728 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0)))) & (all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2Ebigunion__countable) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3729 (all A_27a all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2n_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__upper__bound) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3730 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ECARD__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3731 (all A_27a all V0x_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ECOMPONENT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3732 (all A_27a all V0s_2E0 all V1t_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__ALT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3733 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1667_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1667_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1667_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3734 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2EDIFF__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.82 3735 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3736 (all A_27a all V0x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2110_0_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(def0_2Ethm_2Epred__set_2EGSPEC__F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3737 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3738 (all A_27a all V0s_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2EMEMBER__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3739 (all A_27a all A_27b all A_27c all V0f_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1a_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),c_2Epair_2ESND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2b_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1a_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2b_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__CROSS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3740 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2EINJ__IMAGE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3741 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2ECOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ECOMPL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ECOMPL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3742 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1660_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f1660_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef1660_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3743 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))) # label(thm_2Epred__set_2EPREIMAGE__ALT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3744 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3745 (all A_27a all X0_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2111_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2111_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2111_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3746 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1689_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Epred__set_2EGSPEC__ETA) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3747 (all A_27a all V0R_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f1673_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Epred__set_2Epartition__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3748 (all A_27a all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2ESCHROEDER__CLOSE__SET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3749 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3750 (all A_27a all V2x_2E0 all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f1638_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(def0_2Ethm_2Epred__set_2EUNION__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3751 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2ECARD__UNION__EQN) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3752 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1667_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,f1667_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef1667_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3753 (all A_27a all V0x_2E0 all V1sos_2E0 ((exists V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIGUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Epred__set_2EBIGUNION__applied) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3754 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMAX_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMAX_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3755 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2EBIGUNION__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3756 (all A_27a all 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_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3757 (all A_27a all V0x_2E0 all V1f_2E0 all V2s_2E0 ((exists V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))) # label(thm_2Epred__set_2ESCHROEDER__CLOSE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3758 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3759 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3760 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3761 (all A_27a all V0s_2E0 all V1x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2EDELETE__NON__ELEMENT__RWT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3762 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2EPROD__IMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2EPROD__IMAGE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EPROD__IMAGE_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3763 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EINSERT__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3764 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EFINITE__INJ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3765 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3766 (all A_27a all V0s_2E0 all V1R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2EBIGUNION__partition) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3767 (all A_27a all A_27b all V0s2_2E0 all V1s1_2E0 all V2f_2E0 ((all V3x_2E0 all V4y_2E0 (s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0) <-> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4y_2E0))))) -> (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))))) # label(thm_2Epred__set_2EIMAGE__11) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3768 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2027_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2027_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2027_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3769 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2Ecount_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecount_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3770 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) # label(thm_2Epred__set_2ECROSS__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3771 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f1671_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f1671_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef1671_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3772 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2127_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2127_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2127_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3773 (all A_27a all V0P_2E0 ((exists V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Epred__set_2EFINITE__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3774 (all A_27a all A_27b all V0s2_2E0 all V1s1_2E0 all V2f_2E0 ((all V3x_2E0 all V4y_2E0 (s(A_27a,V4y_2E0) = s(A_27a,V3x_2E0) <-> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))))) -> s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0))))) # label(thm_2Epred__set_2EDISJOINT__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3775 (all A_27a all V0n_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EEXPLICIT__ENUMERATE__MONO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3776 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2107_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2107_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2107_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3777 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2026_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2026_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2026_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3778 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))) # label(thm_2Epred__set_2EBIJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3779 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V1y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2ECROSS__SINGS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3780 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3781 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3782 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f1642_1_2E3(s(A_27a,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f1642_1_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef1642_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3783 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EDIFF__INTER2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3784 (all A_27a all V0r_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))))) # label(thm_2Epred__set_2EDIFF__INTER__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3785 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Esum_2Esum(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Esum_2Esum(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3786 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3787 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2113_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2113_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2113_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3788 (all A_27a all V0sp_2E0 all V1s_2E0 ((all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0)))))) & s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0) != s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0)))))) # label(thm_2Epred__set_2EBIGINTER__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3789 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EDIFF__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3790 (all A_27a ((all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) & (all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EUNION__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3791 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool))),c_2Epred__set_2ECROSS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3792 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3793 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3794 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Epred__set_2ERINV_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0))) = s(A_27a,c_2Epred__set_2ERINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ERINV_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3795 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1641_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,f1641_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(def1_2Ethm_2Epred__set_2EDIFF__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3796 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__EMPTY__REFL__RWT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3797 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3798 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Epred__set_2EFINITE__CROSS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3799 (all A_27a all V0g_2E0 all V1f_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V4x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(A_27a,V4x_2E0)))))))) & (exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(A_27a,V3x_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__MONO__LESS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3800 (all A_27a all V0e_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E1(s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EPOW__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3801 (all A_27a all V0x_2E0 all V1y_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f1817_0_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1y_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(A_27a,V1y_2E0)))) # label(thm_2Epred__set_2EDELETE__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3802 (all A_27a all V0c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0c_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0c_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | (exists V1f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0c_2E0)))) # label(thm_2Epred__set_2ECOUNTABLE__ENUM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3803 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f1691_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1691_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef1691_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3804 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3805 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2EIN__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3806 (all A_27a all V0P_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,f1661_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) <-> (exists V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))) # label(def0_2Ethm_2Epred__set_2EBIGUNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3807 (all A_27a all V0R_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EREL__RESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) # label(thm_2Epred__set_2EREL__RESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3808 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EPOW_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EPOW_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3809 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFUNSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Epred__set_2EFUNSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3810 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) # label(thm_2Epred__set_2EIN__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3811 (all A_27a all V0P_2E0 all V1a_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1a_2E0)))) | (exists V4x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) <-> (exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))))) # label(thm_2Epred__set_2EEXISTS__IN__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3812 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(A_27a,V2x_2E0)))) # label(thm_2Epred__set_2EDELETE__INTER) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3813 (all A_27a all V0x_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ESING__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3814 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3815 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ECARD__POW) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3816 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EEMPTY__NOT__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3817 (all A_27a all V4y_2E0 all V1s_2E0 all V0R_2E0 all V3x_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)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f1673_3_2E4(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0)))))) # label(def0_2Ethm_2Epred__set_2Epartition__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3818 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINTER_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EINTER__applied) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3819 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3820 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Epred__set_2ELINV__OPT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2Epred__set_2ELINV__OPT_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ELINV__OPT_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3821 (all A_27a all V0x_2E0 all V1s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2t_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3822 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__INTER) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3823 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__applied) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3824 (all A_27a all V0x_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0)))))) <-> (all V2P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0)))))))) # label(thm_2Epred__set_2EIN__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3825 (all A_27a all X0_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2110_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2110_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2110_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3826 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EEMPTY_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(thm_2Epred__set_2EEMPTY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3827 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3828 (all A_27a (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) & (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))))))) # label(thm_2Epred__set_2ECARD__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3829 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3830 (all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2ESUM__SET__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3831 (all A_27a all V0s2_2E0 all V1s1_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))))))) # label(thm_2Epred__set_2EREL__RESTRICT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3832 (all A_27a all V0y_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2114_0_2E2(s(A_27a,V0y_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Ebool,f2114_1_2E2(s(A_27a,V0y_2E0),s(A_27a,V1x_2E0)))))) # label(def1_2Ethm_2Epred__set_2EGSPEC__EQ2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3833 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) # label(thm_2Epred__set_2ECOMPL__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3834 (all A_27a all V0s_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0)))))) <-> s(A_27a,V1x_2E0) != s(A_27a,V2y_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3835 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))))))) # label(thm_2Epred__set_2ECARD__DIFF__EQN) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3836 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ESUM__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3837 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),f1874_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2ESURJ__ID) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3838 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),f1847_0_2E0),s(A_27a,X0_2E0))) = s(A_27a,f1847_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef1847_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3839 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3840 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3841 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2ESING__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3842 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),f1647_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),f1647_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1647_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3843 (all A_27a all V0s_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0))) # label(thm_2Epred__set_2EPSUBSET__SING) # label(axiom) # label(non_clause). [assumption]. 107.77/107.83 3844 (all A_27a all V0s_2E0 all V1M_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) <-> (exists V3x_2E0 ((all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1M_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1M_2E0),s(A_27a,V4y_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2ESET__MINIMUM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3845 (all A_27a all V0x_2E0 all V1s_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1642_0_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Ebool,f1642_1_2E3(s(A_27a,V2y_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(def1_2Ethm_2Epred__set_2EINSERT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3846 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),f1679_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),f1679_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef1679_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3847 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2y_2E0 s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V2y_2E0))))) = s(A_27a,c_2Epred__set_2ERINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V2y_2E0)))) # label(thm_2Epred__set_2ERINV__LO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3848 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EFINITE__BIJ__CARD) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3849 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f1679_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)),f1679_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0)))) # label(arityeq2_2Ef1679_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3850 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1638_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EUNION__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3851 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2110_0_2E0)))) # label(thm_2Epred__set_2EGSPEC__F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3852 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3853 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3854 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),f1693_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),f1693_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1693_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3855 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3856 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EABS__DIFF_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EABS__DIFF_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3857 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIGINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EBIGINTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3858 (all A_27a all V1P_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1691_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) # label(def0_2Ethm_2Epred__set_2EIN__GSPEC__IFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3859 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2Einfinite__pow__uncountable) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3860 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3861 (all V0I_2E0 all V1J_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0I_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__MAX__SET) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3862 (all A_27a all V0b_2E0 all V1a_2E0 all V2P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1a_2E0),s(A_27a,V0b_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),f1696_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V1a_2E0)))) & s(A_27a,V1a_2E0) = s(A_27a,V0b_2E0))) # label(thm_2Epred__set_2EPAIR__IN__GSPEC__same) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3863 (all A_27a all A_27b all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) -> (all V1x_2E0 all V2y_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))) <-> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))))) # label(thm_2Epred__set_2EBIJ__IMP__11) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3864 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2ENOT__EMPTY__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3865 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3866 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f1661_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1661_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef1661_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3867 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1662_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f1662_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef1662_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3868 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumpair_2Enpair_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumpair_2Enpair_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3869 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__REST) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3870 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2f_27_2E0 all V3s_27_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) & (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_27_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))))) -> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0))))) # label(thm_2Epred__set_2EIMAGE__CONG) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3871 (all A_27a all V0x_2E0 all V1y_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) | s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))) # label(thm_2Epred__set_2EIN__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3872 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2ENOT__SING__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3873 (all A_27a all V0m_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0))))))) # label(thm_2Epred__set_2EFINITE__is__measure__maximal) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3874 (all A_27a all V0y_2E0 all V1x_2E0 all V2m_2E0 (s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(A_27a,V0y_2E0)))))) # label(thm_2Epred__set_2Eis__measure__maximal__SING) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3875 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),f1694_0_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1694_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1694_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3876 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EUNIV__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3877 (all A_27a all V2y_2E0 all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,f1642_1_2E3(s(A_27a,V2y_2E0),s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> s(A_27a,V0x_2E0) = s(A_27a,V2y_2E0) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(def0_2Ethm_2Epred__set_2EINSERT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3878 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3879 (all A_27a all V0y_2E0 all V1P_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V0y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1691_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Epred__set_2EIN__GSPEC__IFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3880 (all A_27a all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3881 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3882 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3883 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3884 (all A_27a all V0R_2E0 all V1s_2E0 ((all V5x_2E0 all V6y_2E0 all V7z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),V0R_2E0),s(A_27a,V6y_2E0))),s(A_27a,V7z_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)),V0R_2E0),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V7z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),V0R_2E0),s(A_27a,V5x_2E0))),s(A_27a,V7z_2E0)))))) & (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> 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)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V3x_2E0))) = 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)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0))))) & (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2Eequiv__on__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3885 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3886 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3887 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3888 (all A_27a all V0P_2E0 ((all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Epred__set_2EFINITE__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3889 (all A_27a all A_27b all V0P_2E0 all V1f_2E0 all V2s_2E0 ((exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))))))) <-> (exists V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V4x_2E0)))))))))) # label(thm_2Epred__set_2EEXISTS__IN__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3890 (all A_27a all V0f_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ECOUNTABLE__IMAGE__NUM) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3891 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3892 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EDFUNSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDFUNSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EDFUNSET_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3893 (all A_27a all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,f1874_0_2E1(s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Epred__set_2ESURJ__ID) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3894 (all A_27a all V0f_2E0 all V1s_2E0 all V2x_2E0 ((exists V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0))),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eschroeder__close_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0)))))) # label(thm_2Epred__set_2Eschroeder__close__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3895 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))))) & (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V5y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4x_2E0))) <-> s(A_27a,V4x_2E0) = s(A_27a,V5y_2E0)))))) # label(thm_2Epred__set_2EINJ__IFF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3896 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2026_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2026_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2026_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3897 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2ESUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3898 (all A_27a all V0s_2E0 -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2ENOT__PSUBSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3899 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),f1880_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EBIJ__ID) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3900 (all A_27a ((all V3s_2E0 all V4n_2E0 s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))) = s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))))))) & (all V1s_2E0 all V2n_2E0 s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))))) = s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) & (all V0s_2E0 s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Epred__set_2Echooser__def__compute) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3901 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2ESUBSET__INSERT__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3902 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3903 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3904 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2p_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f1663_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0),s(tyop_2Emin_2Ebool,f1663_1_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(def1_2Ethm_2Epred__set_2ECROSS__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3905 (all A_27a all V0t_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2ECOMPL__UNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3906 (all A_27a all V0s_2E0 all V1x_2E0 all V2x_27_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_27_2E0))))) <-> s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EIN__DELETE__EQ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3907 (all A_27a s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EI_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0)))) # label(thm_2Epred__set_2EPREIMAGE__I) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3908 (all A_27a all V0X_2E0 all V1P_2E0 ((all V2Y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3909 (all A_27a all V0s_2E0 ((exists V1f_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EINFINITE__INJ__NOT__SURJ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3910 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 ((all V2x_2E0 all V3y_2E0 all V4z_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V3y_2E0))),s(A_27b,V4z_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V3y_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,V4z_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V5x_2E0 all V6b_2E0 s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27b,V6b_2E0))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V5x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,V5x_2E0))),s(A_27b,V6b_2E0)))))))) # label(thm_2Epred__set_2ECOMMUTING__ITSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3911 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) # label(thm_2Epred__set_2EIMAGE__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3912 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) # label(thm_2Epred__set_2ESUBSET__INTER1) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3913 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EIMAGE__SURJ) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3914 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2Eschroeder__close_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Eschroeder__close_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3915 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2ESUBSET__PSUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3916 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2EREST__SING) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3917 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f1937_1_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f1937_1_2E3(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1937_1_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3918 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1639_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1639_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1639_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3919 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1680_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Epred__set_2EPREIMAGE__def) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3920 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),f1847_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EIMAGE__ID) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3921 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & (exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))) -> (exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2ESCHROEDER__BERNSTEIN__AUTO) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3922 (all A_27a all A_27b all V0f_2E0 all V1M_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1M_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1M_2E0)))))) # label(thm_2Epred__set_2EIMAGE__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3923 (all A_27a all V0x_2E0 all V1y_2E0 (s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EEQUAL__SING) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3924 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3925 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),f1647_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EIMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3926 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3927 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2127_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2127_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2127_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3928 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),f2133_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),f2133_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2133_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3929 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> (all V1f_2E0 all V2p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & (all V3q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V3q_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V2p_2E0))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V2p_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))) # label(thm_2Epred__set_2ESUM__SAME__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3930 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3931 (all A_27a all V0R_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2127_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))))))))) -> (all V3x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2127_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0)))))))) -> (exists V5f_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(A_27a,V3x_2E0) & (all V6n_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)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,V6n_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))))))))))))) # label(thm_2Epred__set_2EKoenigsLemma) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3932 (all A_27a all V0x_2E0 all V1s_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))))))) # label(thm_2Epred__set_2EELT__IN__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3933 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3934 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3935 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 all V2s_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0),s(A_27b,V3y_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))))))))) # label(thm_2Epred__set_2EIN__BIGINTER__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3936 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3937 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EINSERT_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.77/107.84 3938 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2ECOMPL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.84 3939 (all A_27a all V0y_2E0 all V1x_2E0 (s(A_27a,V0y_2E0) = s(A_27a,V1x_2E0) <-> p(s(tyop_2Emin_2Ebool,f2114_1_2E2(s(A_27a,V0y_2E0),s(A_27a,V1x_2E0)))))) # label(def0_2Ethm_2Epred__set_2EGSPEC__EQ2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.84 3940 (all A_27a all A_27b all V0P_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f1690_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0)))))))) # label(thm_2Epred__set_2EGSPEC__PAIR__ETA) # label(axiom) # label(non_clause). [assumption]. 107.88/107.84 3941 (all A_27a ((all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)) & (all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Epred__set_2EUNION__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.84 3942 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ECROSS_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Epred__set_2ECROSS__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.84 3943 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.84 3944 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3945 (all A_27a all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,f1880_0_2E1(s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Epred__set_2EBIJ__ID) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3946 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3947 (all A_27a all A_27b all V0t_2E0 all V1s0_2E0 all V2s_2E0 all V3f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s0_2E0)))))))) # label(thm_2Epred__set_2EINJ__BIJ__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3948 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f1690_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1690_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef1690_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3949 (all A_27a all A_27b all V0f_2E0 ((all V1x_2E0 all V2y_2E0 (s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) <-> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))))) -> (all V3s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))))) # label(thm_2Epred__set_2EINJECTIVE__IMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3950 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f1641_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,f1641_1_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef1641_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3951 (all A_27a all V0s_2E0 all V1t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2EINFINITE__DIFF__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3952 (all A_27a all A_27b all V0z_2E0 all V1s_2E0 all V2f_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0z_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0) & (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(A_27a,V0z_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(A_27b,V3x_2E0))))))) # label(thm_2Epred__set_2EIMAGE__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3953 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Enfst_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Enfst_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3954 (all A_27a all V0set_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f1671_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0)))))) # label(thm_2Epred__set_2EPOW__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3955 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Epred__set_2EITSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3956 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3957 (all A_27a all A_27b all V0t_2E0 all V1f_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Epred__set_2EINJ__CARD__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3958 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EINJ__CARD) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3959 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (exists V1x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2ESING__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3960 (all A_27a all V2x_2E0 all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,f1639_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(def0_2Ethm_2Epred__set_2EINTER__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3961 (all A_27a all X0_2E0 s(A_27a,f1880_0_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),f1880_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef1880_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3962 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3963 (all X0_2E0 s(tyop_2Emin_2Ebool,f2134_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2134_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef2134_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3964 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Epred__set_2ELINV_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Epred__set_2ELINV_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ELINV_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3965 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 ((exists V4g_2E0 ((all V7x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V7x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V4g_2E0),s(A_27b,V7x_2E0))))) = s(A_27b,V7x_2E0))) & (all V6x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(A_27a,V6x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V4g_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V6x_2E0))))))) & (all V5x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V5x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V4g_2E0),s(A_27b,V5x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) & (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EBIJ__IFF__INV) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3966 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3967 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1690_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f1690_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef1690_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3968 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))),s(A_27b,X2_2E0))) = s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3969 (all A_27a all V0set_2E0 all V1e_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0)))) # label(thm_2Epred__set_2EIN__POW) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3970 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINTER_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINTER_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3971 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ECHOICE__INSERT__REST) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3972 (all A_27a all A_27b all V0x_2E0 all V1b_2E0 all V2a_2E0 all V3P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2a_2E0),s(A_27b,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),f1695_0_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0)))))))) <-> s(A_27a,V2a_2E0) = s(A_27a,V0x_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0),s(A_27b,V1b_2E0)))))) # label(thm_2Epred__set_2EPAIR__IN__GSPEC__2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3973 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3974 (all A_27a all X0_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3975 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3976 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Epred__set_2Epair__to__num_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Epair__to__num_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3977 (all A_27a all V0n_2E0 all V1s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EEXPLICIT__ENUMERATE__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3978 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) # label(thm_2Epred__set_2ECROSS__INSERT__LEFT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3979 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2117_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2117_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2117_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3980 (all A_27a all V0B_2E0 all V1A_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0)) & (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))))))) # label(thm_2Epred__set_2EINTER__SUBSET__EQN) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3981 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EUNION__OVER__INTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3982 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3983 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,f2169_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),f2169_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2169_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3984 (all A_27a all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3985 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2Ecountable__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3986 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2107_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2107_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2107_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3987 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2ESUBSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3988 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3989 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Epred__set_2EIMAGE__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3990 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__COMPL) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3991 (all A_27a all V0s_2E0 all V1x_2E0 all V2y_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) <-> s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))))) # label(thm_2Epred__set_2EINSERT__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3992 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3993 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3994 (all A_27a all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3995 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3996 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))))) # label(thm_2Epred__set_2ECARD__PSUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3997 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ECOUNTABLE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3998 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ESING__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 3999 (all A_27a all V0f_2E0 all V1s_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1665_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Epred__set_2ESUM__IMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4000 (all A_27a all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ECOMPL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2ECOMPL__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4001 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EDISJOINT__SYM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4002 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4003 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) # label(thm_2Epred__set_2ESING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4004 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),f1647_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(def0_2Ethm_2Epred__set_2EIMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4005 (all A_27a all V0P_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> (all V2e1_2E0 all V3e2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_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)),V0P_2E0),s(A_27a,V2e1_2E0))),s(A_27a,V3e2_2E0)))))))) # label(thm_2Epred__set_2Epairwise__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4006 (all A_27a all A_27b all V2p_2E0 all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,f1663_1_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(def0_2Ethm_2Epred__set_2ECROSS__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4007 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4008 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4009 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f1671_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f1671_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1671_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4010 (all A_27a all A_27b all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))))) # label(thm_2Epred__set_2EIMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4011 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2112_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2112_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2112_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4012 (all A_27a all V1f_2E0 all V0g_2E0 all V3x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EABS__DIFF_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Enum_2Enum,f2073_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Epred__set_2EABS__DIFF__SUM__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4013 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EINSERT__UNION__EQ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4014 (all A_27a all V0R_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2128_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))))))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) -> (all V3x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2128_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))))))))))) # label(thm_2Epred__set_2EKoenigsLemma__WF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4015 (all A_27a all A_27b all V0P_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f1690_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0)))))) # label(def0_2Ethm_2Epred__set_2EGSPEC__PAIR__ETA) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4016 (all A_27a all V0P_2E0 ((all V1x_2E0 ((all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0))))))) -> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0)))))))) # label(thm_2Epred__set_2EFINITE__COMPLETE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4017 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2128_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2y_2E0),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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0)))))) # label(def1_2Ethm_2Epred__set_2EKoenigsLemma__WF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4018 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f1684_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f1684_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef1684_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4019 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4020 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1691_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f1691_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef1691_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4021 (all A_27a all V0s_2E0 all V1e_2E0 all V2s2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1e_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0)))))) # label(thm_2Epred__set_2EDELETE__SUBSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4022 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Epred__set_2EREL__RESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EREL__RESTRICT_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Epred__set_2EREL__RESTRICT_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4023 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4024 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,f2073_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),f2073_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2073_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4025 (all A_27a all V0x_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EDELETE__NON__ELEMENT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4026 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool))),c_2Epred__set_2ECROSS_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4027 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 ((exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))) -> (exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ESURJ__IMP__INJ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4028 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__INTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4029 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EDIFF__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4030 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4031 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))))) # label(thm_2Epred__set_2Ecountable__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4032 (all A_27a all V0e_2E0 all V1s1_2E0 all V2s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__INSERT__RIGHT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4033 (all A_27a all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EEQ__SUBSET__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4034 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4035 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2128_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2128_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2128_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4036 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2ECARD__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4037 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0)))) # label(thm_2Epred__set_2EIMAGE__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4038 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0t_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2EINJ__INL) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4039 (all A_27a ((all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) & (all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2EINTER__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4040 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),V0t_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),c_2Esum_2EINR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2EINJ__INR) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4041 (all A_27a all A_27b all V0x_2E0 all V1b_2E0 all V2a_2E0 all V3P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2a_2E0),s(A_27b,V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),f1694_0_2E2(s(A_27b,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0)))))))) <-> s(A_27b,V0x_2E0) = s(A_27b,V1b_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V2a_2E0)))))) # label(thm_2Epred__set_2EPAIR__IN__GSPEC__1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4042 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4043 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> (all V3x_2E0 all V4y_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))) = s(A_27b,V4y_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V4y_2E0))))))) # label(thm_2Epred__set_2EINJ__LINV__OPT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4044 (all A_27a all V0R_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2y_2E0),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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2127_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) # label(def1_2Ethm_2Epred__set_2EKoenigsLemma) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4045 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))))))))) # label(thm_2Epred__set_2ECARD__UNION__LE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4046 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f1684_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1684_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef1684_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4047 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESING_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ESING_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4048 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2Epartition_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Epartition_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4049 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EBIJ__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.85 4050 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) # label(thm_2Epred__set_2EFINITE__SING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4051 (all A_27a all V0P_2E0 ((all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Epred__set_2EFINITE__BIGUNION__EQ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4052 (all A_27a all A_27b all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1937_0_2E2(s(A_27b,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))))))) -> (all V3s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))))) # label(thm_2Epred__set_2EFINITELY__INJECTIVE__IMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4053 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4054 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EIMAGE__PREIMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4055 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4056 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f2169_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),f2169_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2169_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4057 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4058 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),f1665_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f1665_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef1665_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4059 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4060 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4061 (all A_27a all V2P_2E0 all V3x_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f1696_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))))) # label(def0_2Ethm_2Epred__set_2EPAIR__IN__GSPEC__same) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4062 (all A_27a all A_27b all V1s_2E0 all V3y_2E0 all V0f_2E0 all V4x_2E0 (p(s(tyop_2Emin_2Ebool,f1908_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0)))) <-> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))) = s(A_27b,V3y_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(def0_2Ethm_2Epred__set_2EBIJ__ALT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4063 (all A_27a all V0x_2E0 all V1s_2E0 all V2m_2E0 all V3e_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2m_2E0),s(A_27a,V3e_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2m_2E0),s(A_27a,V0x_2E0)))))) -> s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V4y_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(A_27a,V4y_2E0))))) # label(thm_2Epred__set_2Eis__measure__maximal__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4064 (all A_27a s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2ESING__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4065 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),f1673_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f1673_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef1673_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4066 (all A_27a all A_27b all V0a_2E0 all V3y_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0a_2E0),s(A_27b,V3y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),f2133_0_2E2(s(A_27a,V0a_2E0),s(A_27b,V3y_2E0)))) # label(def0_2Ethm_2Epred__set_2ECROSS__EQNS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4067 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EUNION__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4068 (all A_27a all V0f_2E0 all V1s_2E0 all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ESUM__IMAGE__IN__LE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4069 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 all V2Q_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V3x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EDFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0)))))))) # label(thm_2Epred__set_2EIN__DFUNSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4070 (all A_27a all A_27b all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4071 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f2056_0_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),f2056_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2056_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4072 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2u_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))))) # label(thm_2Epred__set_2EIMAGE__SUBSET__gen) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4073 (all A_27a all V0f_2E0 ((all V1e_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1e_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1e_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EPROD__IMAGE__THM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4074 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 all V3t_2E0 all V4u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))))) # label(thm_2Epred__set_2EBIJ__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4075 (all A_27a all V2x_2E0 all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f1641_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(def0_2Ethm_2Epred__set_2EDIFF__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4076 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4077 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2EFINITE__SURJ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4078 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EINTER__OVER__UNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4079 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Epred__set_2ELINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Epred__set_2ELINV_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ELINV_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4080 (all A_27a all A_27b all V0y_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EIMAGE_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V0y_2E0)))) <-> (exists V3x_2E0 (s(A_27b,V0y_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EIMAGE__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4081 (all A_27a all V0s_2E0 all V1R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EEMPTY__NOT__IN__partition) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4082 (all A_27a all V0s_2E0 all V1t_2E0 ((exists V2x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__INSERT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4083 (all A_27a all A_27b all V0a_2E0 all V1s1_2E0 all V2s2_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s2_2E0))) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),f2133_0_2E1(s(A_27a,V0a_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s2_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s2_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s2_2E0))))) # label(thm_2Epred__set_2ECROSS__EQNS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4084 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) # label(thm_2Epred__set_2EINSERT__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4085 (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1e_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V1e_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,V1e_2E0)))))))) # label(thm_2Epred__set_2ESUM__SET__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4086 (all A_27a all A_27b all V0f_2E0 all V1t_2E0 all V2sp_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2sp_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__COMPL__INTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4087 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2y_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V2y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1654_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27b,V2y_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) # label(thm_2Epred__set_2ELINV__OPT__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4088 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0))) # label(thm_2Epred__set_2ECROSS__EMPTY__EQN) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4089 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EDISJOINT__INSERT_27) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4090 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4091 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4092 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f1661_1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f1661_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef1661_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4093 (all A_27a all V1x_2E0 s(A_27a,V1x_2E0) = s(A_27a,f1847_0_2E1(s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Epred__set_2EIMAGE__ID) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4094 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4095 (all A_27a all V0s1_2E0 all V1s2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s2_2E0)))))) # label(thm_2Epred__set_2EBIGUNION__UNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4096 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EFINITE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4097 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2ECROSS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ECROSS_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ECROSS_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4098 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(A_27a,V3x_2E0) = s(A_27a,c_2Epred__set_2ELINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))))))))) # label(thm_2Epred__set_2ELINV__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4099 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2117_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2117_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2117_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4100 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Eenumerate_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Epred__set_2Eenumerate_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Eenumerate_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4101 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2Efinite__countable) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4102 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Epred__set_2ERINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V3x_2E0))))) = s(A_27b,V3x_2E0))))) # label(thm_2Epred__set_2ERINV__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4103 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EINTER__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4104 (all A_27a all V0x_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EDELETE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4105 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2P0_2E0 all V3Q0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3Q0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3Q0_2E0) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3Q0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P0_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2ECROSS__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4106 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4107 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4108 (all A_27a all X0_2E0 s(A_27a,f1874_0_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),f1874_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef1874_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4109 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumpair_2Enpair_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Epred__set_2Epair__to__num__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4110 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4111 (all A_27a all V0x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2ENOT__IN__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4112 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) # label(thm_2Epred__set_2EINTER__UNION__COMPL) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4113 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1661_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Epred__set_2EBIGUNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4114 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4115 (all A_27a all V0x_2E0 all V1y_2E0 all V2P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0)))) & s(A_27a,V0x_2E0) != s(A_27a,V1y_2E0) | s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0)))))))) # label(thm_2Epred__set_2EIN__INSERT__EXPAND) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4116 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) # label(thm_2Epred__set_2ESUBSET__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4117 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2ECARD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4118 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4119 (all A_27a all V0s_2E0 ((exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Eenumerate_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EENUMERATE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4120 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0),s(A_27a,V3x_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDFUNSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0)))))) # label(thm_2Epred__set_2EDFUNSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4121 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4122 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1642_0_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Epred__set_2EINSERT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4123 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))))) # label(thm_2Epred__set_2EPREIMAGE__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4124 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2EIN__INFINITE__NOT__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4125 (all V0s_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> (all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V1x_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EMIN__SET__LEM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4126 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4127 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EREST__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4128 (all A_27a all A_27b all V0f_2E0 all V3P_2E0 all V4x_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4x_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V4x_2E0))))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),f1693_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V4x_2E0)))) # label(def0_2Ethm_2Epred__set_2EIN__GSPEC) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4129 (all A_27a all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4130 (all A_27a all A_27b all V0S_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_2E0)))) -> (all V1t_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0S_2E0))))))) # label(thm_2Epred__set_2EFINITE__BIJ__CARD__EQ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4131 (all A_27a all V0x_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) <-> (all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(A_27a,V0x_2E0) = s(A_27a,V2y_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EUNIQUE__MEMBER__SING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4132 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) # label(thm_2Epred__set_2ESUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4133 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4134 (all A_27a all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) <-> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Epred__set_2ESUM__IMAGE__ZERO) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4135 (all A_27a all V0P_2E0 ((all V1s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2e_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) -> (all V3s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4136 (all A_27a all V0f_2E0 all V2e_2E0 all V3acc_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2e_2E0))),s(tyop_2Enum_2Enum,V3acc_2E0))) = s(tyop_2Enum_2Enum,f1667_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,V3acc_2E0)))) # label(def0_2Ethm_2Epred__set_2EPROD__IMAGE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4137 (all A_27a all A_27b (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2EINFINITE__PAIR__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4138 (all A_27a all V0sp_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0) & (all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0)))))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2027_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0sp_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))))))) # label(thm_2Epred__set_2EDIFF__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4139 (all A_27a all V0x_2E0 all V1y_2E0 all V2z_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2z_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2z_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0)))) # label(thm_2Epred__set_2EDIFF__COMM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4140 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4141 (all A_27a all V0s_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EINSERT__SING__UNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4142 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EPHP) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4143 (all A_27a all A_27b all V0a_2E0 all V1b_2E0 all V2c_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1b_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2c_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1b_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0a_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2c_2E0)))))) # label(thm_2Epred__set_2EFUNSET__INTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4144 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 all V3t_2E0 all V4u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))))) # label(thm_2Epred__set_2ESURJ__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4145 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4146 (all V0n_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2134_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2134_1_2E0),s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Epred__set_2Ecount__EQN) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4147 (all A_27a all V0s2_2E0 all V1s1_2E0 all V2f2_2E0 all V3f1_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))) -> s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f2_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f1_2E0),s(A_27a,V4x_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0))))) # label(thm_2Epred__set_2ESUM__IMAGE__CONG) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4148 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1641_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1641_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1641_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4149 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4150 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1680_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1680_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1680_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.86 4151 (all A_27a ((all V0e_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2107_0_2E1(s(A_27a,V0e_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EPOW__EQNS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4152 (all A_27a all V0x_2E0 all V1P_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1684_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))))) # label(thm_2Epred__set_2EIN__ABS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4153 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4154 (all A_27a all V0X_2E0 all V1Y_2E0 all V2P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Y_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2P_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0X_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4155 (all A_27a all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4156 (all A_27a all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Epred__set_2EINSERT__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4157 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Epred__set_2EIN__COUNT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4158 (all A_27a all V0f_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Eschroeder__close_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ESCHROEDER__CLOSE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4159 (all A_27a all V0s_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2EDELETE__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4160 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4161 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> p(s(tyop_2Emin_2Ebool,f2056_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(def0_2Ethm_2Epred__set_2EITSET__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4162 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EPREIMAGE_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EPREIMAGE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4163 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (all V1P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) & (all V2s_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> (all V3e_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EFINITE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4164 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4165 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EFUNSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFUNSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EFUNSET_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4166 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & (exists V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EPSUBSET__MEMBER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4167 (all A_27a all V0x_2E0 all V1sos_2E0 ((exists V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0)))))))) # label(thm_2Epred__set_2EIN__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4168 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1689_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f1689_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef1689_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4169 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))))))) # label(thm_2Epred__set_2Ecross__countable__IFF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4170 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1680_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1680_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1680_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4171 (all A_27a all V0y_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2112_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0y_2E0)) # label(thm_2Epred__set_2EGSPEC__ID) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4172 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4173 (all A_27a all V0s_2E0 -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2ENOT__UNIV__PSUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4174 (all A_27a all V0g_2E0 all V1f_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(A_27a,V3x_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__MONO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4175 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2EMIN__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EMIN__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4176 (all A_27a all V0P_2E0 all V1a_2E0 all V2s_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1a_2E0)))) & (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))))))) # label(thm_2Epred__set_2EFORALL__IN__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4177 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f1638_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,f1638_1_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef1638_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4178 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eprim__rec_2EPRE_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4179 (all A_27a all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(A_27a,V0x_2E0) != s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EIN__REST) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4180 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1661_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f1661_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef1661_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4181 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f1696_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f1696_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef1696_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4182 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4183 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 ((exists V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))) & (exists V3g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V3g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))) -> (exists V4h_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V4h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))))) # label(thm_2Epred__set_2EBIJ__INJ__SURJ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4184 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4185 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) # label(thm_2Epred__set_2EDIFF__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4186 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2Epairwise_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Epairwise_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4187 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Epred__set_2ELINV_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EBIJ__LINV__BIJ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4188 (all V0e_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2EMAX__SET__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4189 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2117_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2117_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2117_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4190 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4191 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4192 (all V0n_2E0 s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2ESUM__SET__SING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4193 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EPREIMAGE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4194 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDIFF_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EDIFF__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4195 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDIFF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4196 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EINJ__CARD__IMAGE__EQ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4197 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EEQ__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4198 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f1694_0_2E3(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f1694_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1694_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4199 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2ENOT__INSERT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4200 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) # label(thm_2Epred__set_2EINTER__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4201 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 ((all V2s_2E0 all V3b_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))),s(A_27b,V3b_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(A_27b,V3b_2E0)))))) -> (all V4v_2E0 all V5v1_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4v_2E0))),s(A_27b,V5v1_2E0))))))) # label(thm_2Epred__set_2EITSET__ind) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4202 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4203 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1638_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1638_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1638_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4204 (all A_27a all V0s_2E0 ((exists V1x_2E0 exists V2t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) | s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2ESET__CASES) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4205 (all A_27a all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EREST_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) != s(A_27a,V0x_2E0))) # label(thm_2Epred__set_2EREST__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4206 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4207 (all A_27a all X0_2E0 s(A_27a,f1865_0_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),f1865_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef1865_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4208 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4209 (all V0n_2E0 all V1m_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f1660_0_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(def0_2Ethm_2Epred__set_2Ecount__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4210 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1673_3_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,f1673_3_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef1673_3_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4211 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)) # label(thm_2Epred__set_2EBIGUNION__SING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4212 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4213 (all A_27a all V0R_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2128_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) # label(def0_2Ethm_2Epred__set_2EKoenigsLemma__WF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4214 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4215 (all V0P_2E0 all V1Q_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & (all V2x_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Epred__set_2EMIN__SET__ELIM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4216 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2Esubset__countable) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4217 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4218 (all A_27a all A_27b all A_27c all V0s_2E0 all V1t_2E0 all V2u_2E0 ((exists V3f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V1t_2E0))))) & (exists V4g_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),V4g_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0))))) -> (exists V5h_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V5h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0))))))) # label(thm_2Epred__set_2EBIJ__TRANS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4219 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2Einter__countable) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4220 (all A_27a all V0s_2E0 all V1f_2E0 s(tyop_2Emin_2Ebool,f1679_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(def0_2Ethm_2Epred__set_2Eenumerate__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4221 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1673_2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),f1673_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef1673_2_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4222 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(A_27a,V0x_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4223 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2114_1_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = 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)),f2114_1_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2114_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4224 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4225 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2Ecross__countable) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4226 (all A_27a all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Epred__set_2EABSORPTION__RWT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4227 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),f1679_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Eenumerate_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2Eenumerate__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4228 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4229 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2E_2B_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4230 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EEMPTY__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4231 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EBIJ__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4232 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) # label(thm_2Epred__set_2EFINITE__BIJ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4233 (all A_27a all V0R_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2Epartition__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4234 (all A_27a all V0s_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (exists V2t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EDECOMPOSITION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4235 (all A_27a s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EI_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0)))) # label(thm_2Epred__set_2EIMAGE__II) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4236 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EPREIMAGE__DISJOINT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4237 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumpair_2Ensnd_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumpair_2Ensnd_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4238 (all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epred__set_2Enum__to__pair_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2Enum__to__pair_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Enum__to__pair_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4239 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EEXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EEXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EEXP_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4240 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2ESUM__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4241 (all A_27a all A_27b all V0f_2E0 all V1P_2E0 all V2Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFUNSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0)))))))) # label(thm_2Epred__set_2EFUNSET__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4242 (all A_27a all V0s_2E0 all V1t_2E0 all V2u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0)))))) # label(thm_2Epred__set_2EUNION__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4243 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 all V2b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27b,V2b_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2057_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27b,V2b_2E0),s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(A_27b,V2b_2E0))))))))) # label(thm_2Epred__set_2EITSET__THM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4244 (all A_27a all V0s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),f1865_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2EINJ__ID) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4245 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4246 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),f1693_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),f1693_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1693_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4247 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EPREIMAGE_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Epred__set_2EPREIMAGE__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4248 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4249 (all A_27a all V0s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EFINITE__REST__EQ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4250 (all V0A_2E0 all V1B_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMAX_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0A_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0))))))) # label(thm_2Epred__set_2EMAX__SET__UNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4251 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2ESURJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4252 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 all V3s0_2E0 all V4t0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4t0_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4t0_2E0)))))) # label(thm_2Epred__set_2EINJ__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4253 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 ((exists V2t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EINJ__IMAGE__BIJ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4254 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIGUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EBIGUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4255 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EDFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1y_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1y_2E0)))) # label(thm_2Epred__set_2EFUNSET__DFUNSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4256 (all A_27a all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINSERT_2E3(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(A_27a,V0x_2E0)))) <-> s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0))) # label(thm_2Epred__set_2ESING__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4257 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4258 (all A_27a all V0P_2E0 all V1Q_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))) # label(thm_2Epred__set_2EBIGINTER__INTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4259 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Eschroeder__close_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2Eschroeder__close_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2Eschroeder__close_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.87 4260 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4261 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EFUNSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EFUNSET_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4262 (all A_27a (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) <-> (exists V0f_2E0 ((exists V3y_2E0 all V4x_2E0 s(A_27a,V3y_2E0) != s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V4x_2E0)))) & (all V1x_2E0 all V2y_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(A_27a,V2y_2E0))) -> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))))))) # label(thm_2Epred__set_2EINFINITE__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4263 (all A_27a all V0R_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2EFINITE__WF__noloops) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4264 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4265 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4266 (all A_27a all A_27b all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2f_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))))) # label(thm_2Epred__set_2EIMAGE__IN) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4267 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4268 (all A_27a all A_27b (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2Ecountable__Usum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4269 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2Einv_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4270 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EFINITE__UNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4271 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4272 (all A_27a all V0P_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1689_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Epred__set_2EGSPEC__ETA) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4273 (all A_27a all A_27b all V0f_2E0 ((all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))) & (all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2EBIJ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4274 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Epred__set_2EIN__PREIMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4275 (all A_27a all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4276 (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) & s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2EMIN__SET__LEQ__MAX__SET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4277 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) # label(thm_2Epred__set_2EUNIV__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4278 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2t_2E0 all V3s_2E0 all V4b_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V4b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EUPDATE_2E3(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EINJ__EXTEND) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4279 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4280 (all A_27a ((all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V1x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) # label(thm_2Epred__set_2ENOT__IN__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4281 (all A_27a all A_27b all V0f_2E0 all V1v_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EGSPEC_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27a,V1v_2E0)))) <-> (exists V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27b,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1v_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))))) # label(thm_2Epred__set_2EGSPECIFICATION__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4282 (all A_27a all V0s_2E0 all V1t_2E0 all V2g_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0)))) # label(thm_2Epred__set_2EDIFF__INTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4283 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2EBIGINTER__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4284 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDIFF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDIFF_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EDIFF_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4285 (all A_27a all V0s_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & s(A_27a,V1x_2E0) != s(A_27a,V2y_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2y_2E0),s(A_27a,V1x_2E0)))))) # label(thm_2Epred__set_2EDELETE__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4286 (all A_27a all V0s_2E0 all V1t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EUNION__DIFF__2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4287 (all A_27a all V0m_2E0 all V1s_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eis__measure__maximal_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0)))) <-> (all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0),s(A_27a,V3y_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0m_2E0),s(A_27a,V2x_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2Eis__measure__maximal__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4288 (all A_27a all V0s_2E0 all V1R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) -> (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_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)),V1R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))))))) # label(thm_2Epred__set_2Epartition__elements__interrelate) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4289 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2EPROD__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EPROD__IMAGE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4290 (all A_27a all V1s_2E0 all V2t_2E0 all V0R_2E0 (p(s(tyop_2Emin_2Ebool,f1673_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1673_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) # label(def2_2Ethm_2Epred__set_2Epartition__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4291 (all A_27a all V0s_2E0 all V1t_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1639_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,f1639_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(def1_2Ethm_2Epred__set_2EINTER__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4292 (all A_27a all V0s1_2E0 all V1s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))))))) # label(thm_2Epred__set_2EFINITE__INTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4293 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f1696_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),f1696_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef1696_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4294 (all A_27a all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) <-> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0))) # label(thm_2Epred__set_2EIN__SING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4295 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2117_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2117_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2117_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4296 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_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_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4297 (all A_27a all V0s_2E0 all V1P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))))) # label(thm_2Epred__set_2EBIGUNION__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4298 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4299 (all V0n2_2E0 all V1n1_2E0 (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1n1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n2_2E0))) <-> s(tyop_2Enum_2Enum,V1n1_2E0) = s(tyop_2Enum_2Enum,V0n2_2E0))) # label(thm_2Epred__set_2ECOUNT__11) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4300 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EIMAGE_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EIMAGE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4301 (all A_27a all V0x_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1P_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__BIGUNION__I) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4302 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) -> s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2Einj__image__countable__IFF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4303 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecount_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2Ecount_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Ecount_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4304 (all A_27a all A_27b all V0f_2E0 ((all V2s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) & (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2ESURJ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4305 (all A_27a all V0x_2E0 all V1y_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Epred__set_2EINSERT__COMM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4306 (all A_27a all A_27b all V0x_2E0 all V3P_2E0 all V4y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V4y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0),s(A_27b,V4y_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f1695_0_2E3(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0),s(A_27b,V4y_2E0)))) # label(def0_2Ethm_2Epred__set_2EPAIR__IN__GSPEC__2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4307 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4308 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(A_27a,V0x_2E0)))) # label(thm_2Epred__set_2ESING__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4309 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4310 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2116_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2116_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2116_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4311 (all A_27a all V0f_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) & (all V1e_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1e_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1e_2E0))))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__THM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4312 (all A_27a all A_27b all V1x_2E0 all V0f_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Ebool,f1937_1_2E3(s(A_27b,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1937_0_2E3(s(A_27b,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0)))) # label(def1_2Ethm_2Epred__set_2EFINITELY__INJECTIVE__IMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4313 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Eequiv__on_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2Eequiv__on_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Eequiv__on_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4314 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4315 (all A_27a all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2ESUM__IMAGE__SUBSET__LE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4316 (all A_27a all A_27b all V0y_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) <-> (exists V3x_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))) = s(A_27b,V0y_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EIN__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4317 (all A_27a all V0B_2E0 all V1A_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0B_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0))) # label(thm_2Epred__set_2EINTER__UNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4318 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))))))) # label(thm_2Epred__set_2ECARD__CROSS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4319 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2EFINITE__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4320 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f1654_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27b,X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1654_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27b,X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef1654_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4321 (all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,V0x_2E0))))))))) # label(thm_2Epred__set_2ESUM__SET__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4322 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EDIFF_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4323 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4324 (all A_27a all V0s_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2Ecompl__insert) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4325 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4326 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2EPSUBSET__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4327 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Epred__set_2ELINV__OPT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EINJ__LINV__OPT__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4328 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4329 (all A_27a all A_27b all V0f_2E0 ((all V1x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27a,V1x_2E0))))))) -> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2EGSPEC__F__COND) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4330 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4331 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4332 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Epred__set_2EUNION__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4333 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1993_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1993_0_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1993_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4334 (all A_27a all V0x_2E0 all V1P_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) # label(thm_2Epred__set_2EIN__APP) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4335 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f1673_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),f1673_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0)))) # label(arityeq3_2Ef1673_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4336 (all A_27a all V0f_2E0 all V1s_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))))) # label(thm_2Epred__set_2EPROD__SET__IMAGE__REDUCTION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4337 (all A_27a all V0x_2E0 all V1s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EIN__COMPL) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4338 (all A_27a all A_27b all V0P_2E0 all V1f_2E0 all V2s_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3y_2E0)))))) <-> (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V4x_2E0)))))))))) # label(thm_2Epred__set_2EFORALL__IN__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4339 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4340 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) -> (all V3e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V3e_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3e_2E0)))))))))))) # label(thm_2Epred__set_2EINJ__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4341 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) | s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Epred__set_2EFINITE__CROSS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4342 (all A_27a all A_27b all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1g_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) -> (all V2f_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0)))))))))) # label(thm_2Epred__set_2ESUM__IMAGE__INJ__o) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4343 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1654_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f1654_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef1654_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4344 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 all V2s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(A_27a,V1x_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) # label(thm_2Epred__set_2EIMAGE__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4345 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (exists V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2Einfinite__num__inj) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4346 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) # label(thm_2Epred__set_2Ecountable__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4347 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))))))) # label(thm_2Epred__set_2Eunion__countable__IFF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4348 (all A_27a ((all V2s_2E0 all V3t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))) & (all V0s_2E0 all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2ESUBSET__UNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4349 (all A_27a all V0y_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2113_0_2E2(s(A_27a,V0y_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Ebool,f2113_1_2E2(s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))))) # label(def1_2Ethm_2Epred__set_2EGSPEC__EQ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4350 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2ESURJ__CARD) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4351 (all A_27a all A_27b all V0f_2E0 all V1b_2E0 s(A_27b,V1b_2E0) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(A_27b,V1b_2E0)))) # label(thm_2Epred__set_2EITSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4352 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4353 (all A_27a all V0x_2E0 all V1s_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Epred__set_2EFINITE__DELETE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4354 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4355 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4356 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Epred__set_2ESUBSET__DIFF__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4357 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4358 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4359 (all A_27a all V0s_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0)))) # label(thm_2Epred__set_2EDELETE__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4360 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4361 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2116_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2116_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2116_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4362 (all A_27a all V0x_2E0 all V1s_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Epred__set_2ESUBSET__OF__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4363 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Epred__set_2EPREIMAGE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4364 (all A_27a all X0_2E0 all X1_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4365 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))))) # label(thm_2Epred__set_2EIN__CROSS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4366 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2EUNIV__FUNSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4367 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4368 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))))) # label(thm_2Epred__set_2EFINITE__PSUBSET__INFINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4369 (all A_27a all V0f_2E0 all V1n_2E0 all V2d_2E0 ((all V3n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2d_2E0)))))))))) # label(thm_2Epred__set_2ESUBSET__ADD) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4370 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1638_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1638_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef1638_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4371 (all A_27a all A_27b all V0s_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) # label(thm_2Epred__set_2EIMAGE__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4372 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f1663_1_2E3(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f1663_1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef1663_1_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4373 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4374 (all A_27a all V0P_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Ebool,f1662_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1662_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) # label(def1_2Ethm_2Epred__set_2EBIGINTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4375 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4376 (all A_27a all X0_2E0 s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epred__set_2ECHOICE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.88 4377 (all V0n_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f1660_0_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Epred__set_2Ecount__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4378 (all A_27a all V1f_2E0 all V0s_2E0 all V4n_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1993_0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))) # label(def0_2Ethm_2Epred__set_2EFINITE__ISO__NUM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4379 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Epred__set_2EIMAGE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4380 (all A_27a all V0s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2EINFINITE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4381 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V2x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V2x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(thm_2Epred__set_2ECROSS__INSERT__RIGHT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4382 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ESING__IFF__CARD1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4383 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 all V2s_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) <-> (all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))) -> s(A_27a,V4y_2E0) = s(A_27a,V1x_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))))) # label(thm_2Epred__set_2EINJ__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4384 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4385 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2112_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2112_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2112_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4386 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EREST__PSUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4387 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERTC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERTC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4388 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),f1908_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,f1908_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef1908_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4389 (all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 ((all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3y_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) & (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Epred__set_2EMAX__SET__ELIM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4390 (all A_27a all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Epred__set_2EABSORPTION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4391 (all A_27a all V0f_2E0 all V1e_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1e_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2ESUM__IMAGE__SING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4392 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDELETE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EDELETE_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4393 (all V0n_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Epred__set_2ECOUNT__SUC) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4394 (all A_27a all V0x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2111_0_2E1(s(A_27a,V0x_2E0)))) # label(def0_2Ethm_2Epred__set_2EGSPEC__T) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4395 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4396 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) # label(thm_2Epred__set_2EPREIMAGE__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4397 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EPREIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EPREIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4398 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))))) # label(thm_2Epred__set_2ECARD__INTER__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4399 (all V1s_2E0 all V2e1_2E0 all V3e2_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,V2e1_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V3e2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V2e1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V3e2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EMIN__SET__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4400 (all V0e_2E0 s(tyop_2Enum_2Enum,V0e_2E0) = s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2EMIN__SET__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4401 (all A_27a all V1s_2E0 all V0R_2E0 all V2t_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Ebool,f1673_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f1673_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) # label(def3_2Ethm_2Epred__set_2Epartition__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4402 (all V0m_2E0 all V1n_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecount_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0)))) # label(thm_2Epred__set_2ECOUNT__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4403 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,c_2Epred__set_2Echooser_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Epred__set_2Echooser_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2Echooser_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4404 (all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0)))))))) # label(thm_2Epred__set_2ESUM__SET__SUBSET__LE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4405 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f1639_1_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f1639_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef1639_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4406 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2y_2E0 ((exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27a,V3x_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))))) # label(thm_2Epred__set_2EIN__BIGUNION__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4407 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V1f_2E0 exists V2b_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Epred__set_2EFINITE__BIJ__COUNT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4408 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Epred__set_2EINSERT__UNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4409 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4410 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2Eimage__countable) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4411 (all A_27a all V0x_2E0 all V1B_2E0 ((all V2P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIGINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1B_2E0),s(A_27a,V0x_2E0)))))) # label(thm_2Epred__set_2EBIGINTER__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4412 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2ESURJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4413 (all V0n_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Epred__set_2Ecount__add1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4414 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1662_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Epred__set_2EBIGINTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4415 (all A_27a all V0s_2E0 all V1t_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2ESUBSET__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4416 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Epred__set_2EINJ__IMAGE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4417 (all A_27a all V0s1_2E0 all V1s2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0s1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s2_2E0)))))) # label(thm_2Epred__set_2EBIGINTER__UNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4418 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4419 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2s_2E0 all V3t_2E0 all V4u_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4u_2E0)))))) # label(thm_2Epred__set_2EINJ__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4420 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4421 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f1817_0_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = 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)),f1817_0_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef1817_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4422 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2EDISJOINT__EMPTY__REFL) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4423 (all A_27a all V0set_2E0 all V1s_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f1671_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0set_2E0)))))) # label(def0_2Ethm_2Epred__set_2EPOW__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4424 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epred__set_2EITSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4425 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Epred__set_2ECARD__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4426 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2y_2E0 s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Epred__set_2ELINV__OPT_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V2y_2E0))))) = s(A_27a,c_2Epred__set_2ELINV_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V2y_2E0)))) # label(thm_2Epred__set_2ELINV__LO) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4427 (all A_27a all V0s_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Epred__set_2ESUBSET__INTER2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4428 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1937_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1937_0_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef1937_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4429 (all A_27a all A_27b all V1x_2E0 all V0f_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,f1937_1_2E3(s(A_27b,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0)))) <-> s(A_27b,V1x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))))) # label(def0_2Ethm_2Epred__set_2EFINITELY__INJECTIVE__IMAGE__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4430 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1t_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))))))))) # label(thm_2Epred__set_2EINTER__FINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4431 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1642_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1642_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1642_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4432 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2027_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2027_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2027_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4433 (all A_27a (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) <-> (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EPSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))))) # label(thm_2Epred__set_2EFINITE__PSUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4434 (all A_27b all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4435 (all A_27a all A_27b all V0x_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))))) # label(thm_2Epred__set_2ECARD__SING__CROSS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4436 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0)))) -> (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0t_2E0))))))))))))) # label(thm_2Epred__set_2ELESS__CARD__DIFF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4437 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f1689_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f1689_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef1689_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4438 (all A_27a all V0x_2E0 all V1y_2E0 (p(s(tyop_2Emin_2Ebool,V1y_2E0)) | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,V1y_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__K) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4439 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4440 (all A_27a all V0x_2E0 all V1s_2E0 all V2t_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) # label(thm_2Epred__set_2EINSERT__INTER) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4441 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) # label(thm_2Epred__set_2EBIGINTER__SING) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4442 (all V0x_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Enum_2Enum,V0x_2E0))))))))) # label(thm_2Epred__set_2EPROD__SET__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4443 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Epred__set_2EREL__RESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EREL__RESTRICT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4444 (all A_27a all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EEMPTY_2E1(s(A_27a,V0x_2E0)))) # label(thm_2Epred__set_2EEMPTY__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4445 (all A_27a all A_27b all V0f_2E0 ((all V1x_2E0 all V2y_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2y_2E0))) -> s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0))) -> (all V3s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))))))) # label(thm_2Epred__set_2EIMAGE__11__INFINITE) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4446 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4447 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 all V2f_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EFUNSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2EFUNSET__THM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4448 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f1641_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f1641_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef1641_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4449 (all A_27a all V1P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f1684_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) # label(def0_2Ethm_2Epred__set_2EIN__ABS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4450 (all A_27a all A_27b all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) <-> (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))) & (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))) -> (exists V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(A_27b,V4x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))))))))) # label(thm_2Epred__set_2ESURJ__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4451 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Epred__set_2ESING__IFF__EMPTY__REST) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4452 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4453 (all A_27a all V0s2_2E0 all V1s1_2E0 all V2R_2E0 ((all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_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)),V2R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V3x_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)),V2R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Epairwise_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))))))) # label(thm_2Epred__set_2Epairwise__UNION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4454 (all A_27a all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0)))))) # label(thm_2Epred__set_2ESUBSET__INTER__ABSORPTION) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4455 (all A_27a all V0s1_2E0 all V1s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0)))))))) # label(thm_2Epred__set_2ESUBSET__POW) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4456 (all A_27a s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2111_0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)) # label(thm_2Epred__set_2EGSPEC__T) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4457 (all A_27a all A_27b all V0t_2E0 all V1s_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESURJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))) & s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0t_2E0)))))) # label(thm_2Epred__set_2EFINITE__SURJ__BIJ) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4458 (all A_27a all V0P_2E0 all V1Q_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2116_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,f2116_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) # label(def1_2Ethm_2Epred__set_2EGSPEC__AND) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4459 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4460 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4461 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4462 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4463 (all A_27a all V0g_2E0 all V1f_2E0 all V2m_2E0 all V3n_2E0 ((all V4n_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))))))) & (all V5n_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0g_2E0),s(tyop_2Enum_2Enum,V5n_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V5n_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,V5n_2E0)))))) & s(tyop_2Enum_2Enum,V2m_2E0) != s(tyop_2Enum_2Enum,V3n_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0g_2E0),s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0g_2E0),s(tyop_2Enum_2Enum,V3n_2E0)))))))) # label(thm_2Epred__set_2EDISJOINT__DIFFS) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4464 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EfixedPoint_2Emonotone_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2EfixedPoint_2Emonotone_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4465 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4466 (all A_27a all A_27b all V0x_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2EfixedPoint_2Eempty_2E1(s(A_27a,V0x_2E0)))) # label(thm_2EfixedPoint_2Eempty__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4467 (all A_27a all A_27b p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Eempty_2E0))))) # label(thm_2EfixedPoint_2Eempty__monotone) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4468 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4469 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4470 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2219_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2219_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2219_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4471 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4472 (all A_27a all A_27b all V0f_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Eempty_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Eempty_2E0))))) # label(thm_2EfixedPoint_2Efnsum__empty) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4473 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) & p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4474 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4475 (all A_27a all A_27b all V0f1_2E0 all V1f2_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1f2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1f2_2E0)))))))) # label(thm_2EfixedPoint_2Efnsum__monotone) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4476 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4477 (all A_27a all A_27b all V0f1_2E0 all V1f2_2E0 all V2X_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(A_27b,V2X_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0),s(A_27b,V2X_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Efnsum_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0),s(A_27b,V2X_2E0)))) # label(thm_2EfixedPoint_2Efnsum__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4478 (all A_27a all A_27b all V0f_2E0 ((all V1X_2E0 all V2Y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0)))))) # label(thm_2EfixedPoint_2Emonotone__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4479 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.88/107.89 4480 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0)))) # label(thm_2EfixedPoint_2Efnsum__COMM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4481 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2EfixedPoint_2Efnsum_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2EfixedPoint_2Efnsum_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2EfixedPoint_2Efnsum_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4482 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Egfp_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2EfixedPoint_2Egfp_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4483 (all A_27a all V0f_2E0 all V1X_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2218_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))) # label(def0_2Ethm_2EfixedPoint_2Elfp__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4484 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4485 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Edense_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))) & (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Edense_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))))) # label(thm_2EfixedPoint_2Egfp__greatest__dense) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4486 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4487 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__induction) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4488 (all A_27a all V0f_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__empty) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4489 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4490 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Efnsum_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2EfixedPoint_2Efnsum_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2EfixedPoint_2Efnsum_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4491 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4492 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4493 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Edense_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EfixedPoint_2Edense_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2EfixedPoint_2Edense_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4494 (all A_27a all V0f_2E0 all V1X_2E0 s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Eclosed_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) # label(thm_2EfixedPoint_2Eclosed__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4495 (all A_27a all V0f1_2E0 all V1f2_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f2_2E0)))))))))) # label(thm_2EfixedPoint_2Elfp__fnsum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4496 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2EfixedPoint_2Emonotone_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2EfixedPoint_2Emonotone_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4497 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4498 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4499 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4500 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4501 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4502 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))))) # label(thm_2EfixedPoint_2Egfp__coinduction) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4503 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Eclosed_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EfixedPoint_2Eclosed_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2EfixedPoint_2Eclosed_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4504 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2218_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2218_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2218_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4505 (all A_27a all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4506 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))))) # label(thm_2EfixedPoint_2Egfp__strong__coinduction) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4507 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Elfp_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2EfixedPoint_2Elfp_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4508 (all A_27a all V0f_2E0 all V1X_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__rule__applied) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4509 (all A_27a all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2218_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4510 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4511 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))))) # label(thm_2EfixedPoint_2Egfp__greatest__fixedpoint) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4512 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4513 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2EfixedPoint_2Efnsum_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2EfixedPoint_2Efnsum_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4514 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4515 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4516 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__strong__induction) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4517 (all A_27a all V0f_2E0 all V1X_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2219_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))))) # label(def0_2Ethm_2EfixedPoint_2Egfp__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4518 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2EfixedPoint_2Efnsum_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2EfixedPoint_2Efnsum_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4519 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4520 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2h_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2h_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2h_2E0)))))) # label(thm_2EfixedPoint_2Efnsum__ASSOC) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4521 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4522 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2EfixedPoint_2Efnsum_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Efnsum_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2EfixedPoint_2Efnsum_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4523 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4524 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> (all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Eclosed_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Eclosed_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__least__closed) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4525 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2EfixedPoint_2Eempty_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2EfixedPoint_2Eempty_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2EfixedPoint_2Eempty_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4526 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4527 (all A_27a all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2219_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) # label(thm_2EfixedPoint_2Egfp__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4528 (all A_27a all V0f_2E0 all V1X_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))))) = s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Edense_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) # label(thm_2EfixedPoint_2Edense__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4529 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4530 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2219_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2219_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2219_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4531 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27a,V2X_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2EfixedPoint_2Efnsum_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0),s(A_27a,V2X_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0),s(A_27a,V2X_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2EfixedPoint_2Efnsum_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1g_2E0),s(A_27a,V2X_2E0)))))))) # label(thm_2EfixedPoint_2Efnsum__SUBSET) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4532 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4533 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))) & (all V1X_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EfixedPoint_2Elfp_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))))) # label(thm_2EfixedPoint_2Elfp__fixedpoint) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4534 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2218_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2218_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2218_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4535 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4536 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4537 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4538 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f2241_1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2241_1_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2241_1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4539 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2EMAX__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EMAX__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4540 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4541 (all V0s_2E0 all V1g_2E0 ((all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V2e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1g_2E0),s(tyop_2Enum_2Enum,V2e_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V1g_2E0),s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Egcdset_2Egcdset__greatest) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4542 (all V0s_2E0 (p(s(tyop_2Emin_2Ebool,f2241_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) <-> s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0) | s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))) # label(def0_2Ethm_2Egcdset_2Egcdset__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4543 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4544 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4545 (all V0s_2E0 all V2d_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Emin_2Ebool,f2241_3_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,V2d_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2241_2_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,V2d_2E0)))) # label(def3_2Ethm_2Egcdset_2Egcdset__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4546 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Edivides_2Edivides_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Edivides_2Edivides_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4547 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4548 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4549 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X0_2E0) = s(A_27a,X1_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4550 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4551 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4552 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4553 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2241_2_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f2241_2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2241_2_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4554 (all V0x_2E0 all V1s_2E0 s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Egcdset_2Egcdset__INSERT) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4555 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4556 (all V0s_2E0 all V1e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,V1e_2E0)))))) # label(thm_2Egcdset_2Egcdset__divides) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4557 (all X0_2E0 s(tyop_2Emin_2Ebool,f2241_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2241_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2241_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4558 (all V0s_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2241_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2241_1_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2241_2_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Egcdset_2Egcdset__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4559 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4560 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4561 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4562 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2241_1_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f2241_1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2241_1_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4563 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Egcd_2Egcd_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Egcd_2Egcd_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Egcd_2Egcd_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4564 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4565 (all V0s_2E0 all V2d_2E0 (p(s(tyop_2Emin_2Ebool,f2241_3_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,V2d_2E0)))) <-> (all V3e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V3e_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Edivides_2Edivides_2E2(s(tyop_2Enum_2Enum,V2d_2E0),s(tyop_2Enum_2Enum,V3e_2E0)))))))) # label(def2_2Ethm_2Egcdset_2Egcdset__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4566 (all V0s_2E0 all V1n_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2241_1_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(def1_2Ethm_2Egcdset_2Egcdset__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4567 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4568 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2241_3_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2241_3_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2241_3_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4569 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2EMIN__SET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EMIN__SET_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4570 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4571 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4572 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4573 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4574 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4575 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4576 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4577 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4578 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4579 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Egcdset_2Egcdset_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Egcdset_2Egcdset_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Egcdset_2Egcdset_2E1) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4580 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4581 (all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f2241_2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2241_2_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2241_2_2E2) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4582 (all V6p_2E0 all V4n_2E0 (p(s(tyop_2Emin_2Ebool,f2588_0_2E2(s(tyop_2Enum_2Enum,V6p_2E0),s(tyop_2Enum_2Enum,V4n_2E0)))) <-> s(tyop_2Enum_2Enum,V4n_2E0) = s(tyop_2Enum_2Enum,V6p_2E0))) # label(def0_2Ethm_2Elist_2ELUPDATE__SEM) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4583 (all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f2670_1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(A_27c,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,f2670_1_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(A_27c,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef2670_1_2E4_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4584 (all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4585 (all A_27a all X0_2E0 all X1_2E0 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)),f2295_1_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2295_1_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2295_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4586 (all A_27a all V0P_2E0 all V1x_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))))) # label(thm_2Elist_2EEVERY__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4587 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),f2405_0_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),f2405_0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0)))) # label(arityeq1_2Ef2405_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4588 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f2675_0_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),f2675_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2675_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4589 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2639_0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2639_0_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ef2639_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4590 (all A_27a all V0y_2E0 all V1x_2E0 all V2n_2E0 all V3R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) <-> (exists V4ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V4ls_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4ls_2E0))) = s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Elist_2ENRC__LRC) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4591 (all A_27a all V0h_2E0 all V1t_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2261_0_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(A_27a,V0h_2E0),s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) # label(thm_2Elist_2ELAST__DEF) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4592 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4593 (all A_27a all V0ls_2E0 all V1n_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))))) # label(thm_2Elist_2EDROP__NIL) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4594 (all A_27a all V0P_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f2491_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Elist_2EFILTER__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4595 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4596 (all A_27a all A_27b ((all V2a0_2E0 all V3a1_2E0 all V4v_2E0 all V5f_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V5f_2E0),s(A_27a,V2a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V3a1_2E0))) = s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_2E0))),s(A_27b,V4v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V5f_2E0)))) & (all V0v_2E0 all V1f_2E0 s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(A_27b,V0v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V1f_2E0))) = s(A_27b,V0v_2E0)))) # label(thm_2Elist_2Elist__case__def) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4597 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.88/107.90 4598 (all A_27a all A_27b all X0_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EUNZIP_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EUNZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4599 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),f2312_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),f2312_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ef2312_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4600 (all A_27a all V0L_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0L_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),V0L_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Elist_2ELENGTH__LEN) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4601 (all A_27a all A_27b all A_27c all V0P_2E0 ((all V1f_2E0 all V2a_2E0 all V3b_2E0 all V4bs_2E0 all V5c_2E0 all V6cs_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0),s(A_27a,V2a_2E0))),s(A_27b,V3b_2E0))),s(A_27c,V5c_2E0))))),s(tyop_2Elist_2Elist(A_27b),V4bs_2E0))),s(tyop_2Elist_2Elist(A_27c),V6cs_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0))),s(A_27a,V2a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3b_2E0),s(tyop_2Elist_2Elist(A_27b),V4bs_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V5c_2E0),s(tyop_2Elist_2Elist(A_27c),V6cs_2E0)))))))) & (all V7f_2E0 all V8a_2E0 all V9cs_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V7f_2E0))),s(A_27a,V8a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27c),V9cs_2E0))))) & (all V10f_2E0 all V11a_2E0 all V12v6_2E0 all V13v7_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V10f_2E0))),s(A_27a,V11a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V12v6_2E0),s(tyop_2Elist_2Elist(A_27b),V13v7_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))))) -> (all V14v_2E0 all V15v1_2E0 all V16v2_2E0 all V17v3_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V14v_2E0))),s(A_27a,V15v1_2E0))),s(tyop_2Elist_2Elist(A_27b),V16v2_2E0))),s(tyop_2Elist_2Elist(A_27c),V17v3_2E0))))))) # label(thm_2Elist_2EFOLDL2__ind) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4602 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4603 (all A_27a all V0l_2E0 all V1x_2E0 all V2y_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2y_2E0),s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) & s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0) | (exists V4j_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4j_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) & s(tyop_2Enum_2Enum,V3i_2E0) != s(tyop_2Enum_2Enum,V4j_2E0) & s(A_27a,V1x_2E0) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4j_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2EMEM__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4604 (all A_27c all X0_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4605 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),f2656_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),f2656_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ef2656_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4606 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4607 (all A_27a all V0x_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) # label(thm_2Elist_2ESNOC__APPEND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4608 (all A_27a all A_27b all V1f_2E0 all V3x_2E0 all V4y_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),V1f_2E0),s(A_27b,V3x_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),s(A_27a,V4y_2E0))))) = s(A_27b,f2311_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),V1f_2E0),s(A_27b,V3x_2E0),s(A_27a,V4y_2E0)))) # label(def0_2Ethm_2Elist_2EFOLDL__ZIP__SAME) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4609 (all A_27a ((all V1P_2E0 all V2h_2E0 all V3t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))) & (all V0P_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EdropWhile__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4610 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4611 (all A_27a all V0l_2E0 all V1x_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) & s(tyop_2Elist_2Elist(A_27a),V0l_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2ECONS__ACYCLIC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4612 (all A_27a all V0e_2E0 all V1L_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0e_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))) # label(thm_2Elist_2EUNIQUE__LENGTH__FILTER) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4613 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2466_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2466_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2466_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4614 (all A_27a all V0P_2E0 all V1l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EFILTER__EQ__ID) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4615 (all A_27a ((all V0h_2E0 all V1t_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) & s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2ELENGTH) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4616 (all A_27a ((all V0R_2E0 all V1x_2E0 all V2y_2E0 (s(A_27a,V2y_2E0) = s(A_27a,V1x_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))))) & (all V3R_2E0 all V4h_2E0 all V5t_2E0 all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))),s(A_27a,V6x_2E0),s(A_27a,V7y_2E0)))) <-> (exists V8z_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)),V3R_2E0),s(A_27a,V6x_2E0))),s(A_27a,V8z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0),s(A_27a,V8z_2E0),s(A_27a,V7y_2E0)))))) & s(A_27a,V6x_2E0) = s(A_27a,V4h_2E0))))) # label(thm_2Elist_2ELRC__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4617 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2EUNION__APPEND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4618 (all A_27a all V0P_2E0 all V1l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) != s(tyop_2Elist_2Elist(A_27a),V1l_2E0) <-> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Elist_2EFILTER__NEQ__ID) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4619 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4620 (all A_27a all V0P_2E0 all V1ls_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))) # label(thm_2Elist_2ELENGTH__dropWhile__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4621 (all A_27a all A_27b all A_27c all V0x_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V0x_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) # label(thm_2Elist_2EMAP2__NIL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4622 (all A_27a all V3a_2E0 (p(s(tyop_2Emin_2Ebool,f2255_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0)))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))) # label(def0_2Ethm_2Elist_2ESET__TO__LIST__primitive__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4623 (all A_27a all A_27b all V0xs2_2E0 all V1P_2E0 all V2xs1_2E0 all V3zs_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0))),s(tyop_2Elist_2Elist(A_27b),V3zs_2E0)))) <-> (exists V4ys1_2E0 exists V5ys2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0),s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0)))) & s(tyop_2Elist_2Elist(A_27b),V3zs_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0))))))) # label(thm_2Elist_2ELIST__REL__SPLIT1) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4624 (all A_27a all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) # label(thm_2Elist_2EdropWhile__APPEND__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4625 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4626 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2ECONS_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4627 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2466_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2466_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef2466_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4628 (all A_27a all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))) # label(thm_2Elist_2EEXISTS__APPEND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4629 (all A_27a all A_27b all V0pl_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0))))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0pl_2E0))))) # label(thm_2Elist_2ELENGTH__UNZIP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4630 (all A_27a all A_27b ((all V1f_2E0 all V2h_2E0 all V3t_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2h_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))) & (all V0f_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EMAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4631 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4632 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4633 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2371_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2371_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2371_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4634 (all A_27a ((all V1x_2E0 all V2y_2E0 all V3z_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3z_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3z_2E0)))))))) & (all V0x_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EFRONT__CONS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4635 (all A_27a all V0l1_2E0 all V1x_2E0 all V2l2_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(A_27a,V1x_2E0)) # label(thm_2Elist_2Eel__append3) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4636 (all A_27a all A_27b all V0h_2E0 all V1g_2E0 all V2f_2E0 all V3ls1_2E0 all V4ls2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3ls1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V4ls2_2E0))) & (all V5x_2E0 all V6y_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27b,V6y_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(A_27a,V5x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V0h_2E0),s(A_27b,V6y_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(tyop_2Elist_2Elist(A_27a),V3ls1_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V0h_2E0),s(tyop_2Elist_2Elist(A_27b),V4ls2_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V3ls1_2E0),s(tyop_2Elist_2Elist(A_27b),V4ls2_2E0))))))))))) # label(thm_2Elist_2ESUM__MAP__PLUS__ZIP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4637 (all A_27a all V0l_2E0 ((s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) & (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Elist_2ELIST__TO__SET__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4638 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),f2314_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f2314_0_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2314_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4639 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),f2294_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),f2294_0_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2294_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4640 (all A_27a all A_27b all V0x_2E0 all V1v_27_2E0 all V2v_2E0 all V3f_2E0 ((exists V4a_2E0 exists V5l_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3f_2E0),s(A_27a,V4a_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) = s(A_27b,V1v_27_2E0) & s(tyop_2Elist_2Elist(A_27a),V0x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4a_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) | s(tyop_2Elist_2Elist(A_27a),V0x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & s(A_27b,V2v_2E0) = s(A_27b,V1v_27_2E0) <-> s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V0x_2E0),s(A_27b,V2v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3f_2E0))) = s(A_27b,V1v_27_2E0))) # label(thm_2Elist_2Elist__case__eq) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4641 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4642 (all A_27a all V0P_2E0 all V1xs_2E0 all V2h_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2h_2E0),s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0)))))))) # label(thm_2Elist_2EIMP__EVERY__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4643 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4644 (all A_27a all A_27b all V0n_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> (all V2f_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EEL__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4645 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4646 (all A_27a all V0l_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) <-> (all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))))) # label(thm_2Elist_2EEVERY__EL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4647 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4648 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4649 (all A_27a all V0P_2E0 ((exists V2n_2E0 exists V3f_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))) <-> (exists V1ls_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))) # label(thm_2Elist_2Eexists__list__GENLIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4650 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) | (exists V1h_2E0 exists V2t_2E0 s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0)))))) # label(thm_2Elist_2Elist__CASES) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4651 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27a,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4652 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Elist_2ESET__TO__LIST__CARD) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4653 (all A_27a all A_27b all A_27d all V3f2_2E0 all V5p_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27d),f2448_1_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V5p_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27d),c_2Epair_2E_2C_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V5p_2E0))),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V5p_2E0)))))))) # label(def0_2Ethm_2Elist_2EZIP__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4654 (all A_27a all X0_2E0 s(A_27a,f2548_0_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),f2548_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2548_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4655 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f2254_0_2E4(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(A_27a,X2_2E0),s(tyop_2Elist_2Elist(A_27a),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),f2254_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(A_27a,X2_2E0))),s(tyop_2Elist_2Elist(A_27a),X3_2E0)))) # label(arityeq4_2Ef2254_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4656 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4657 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4658 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4659 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2635_0_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2635_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2635_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4660 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2491_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2491_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2491_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4661 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f2267_0_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),f2267_0_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0)))) # label(arityeq1_2Ef2267_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4662 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4663 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4664 (all A_27a all A_27b ((all V2P_2E0 all V3k_2E0 all V4h_2E0 all V5t_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(A_27b,V4h_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_2E0))))),s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),f2288_0_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(A_27b,V4h_2E0))),s(tyop_2Elist_2Elist(A_27b),V5t_2E0))))) = s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_2E0)))))) & (all V0P_2E0 all V1k_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EsplitAtPki__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4665 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) # label(thm_2Elist_2EREVERSE__APPEND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4666 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4667 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4668 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2Ecount_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecount_2E1) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4669 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Epred__set_2EITSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4670 (all A_27a all V0ll_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0ll_2E0) | (exists V1x_2E0 exists V2l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0ll_2E0)))) # label(thm_2Elist_2ESNOC__CASES) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4671 (all A_27a s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f2255_0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),f2255_1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ESET__TO__LIST_2E0)) # label(thm_2Elist_2ESET__TO__LIST__primitive__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4672 (all A_27a all A_27b all A_27c all A_27d ((all V0x1_2E0 all V1l1_2E0 all V2x2_2E0 all V3l2_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2x2_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x1_2E0),s(A_27b,V2x2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0)))))))) & s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2ENIL_2E0))))))) # label(thm_2Elist_2EZIP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4673 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EsplitAtPki_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EsplitAtPki_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4674 (all A_27b all A_27c all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4675 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EdropWhile_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EdropWhile_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4676 (all A_27a all V0c_2E0 all V1n_2E0 all V2s_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2s_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V2s_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__LEFT_2E3(s(A_27a,V0c_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2s_2E0)))) # label(thm_2Elist_2EPAD__LEFT) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4677 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4678 (all A_27a all V0n_2E0 all V1f_2E0 s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Elist_2EHD__GENLIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4679 (all A_27a s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) # label(thm_2Elist_2ESET__TO__LIST__EMPTY) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4680 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4681 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4682 (all A_27a all A_27b all V0f1_2E0 all V1f2_2E0 all V2l_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) <-> (all V3e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(A_27a,V3e_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f2_2E0),s(A_27a,V3e_2E0))))))) # label(thm_2Elist_2EMAP__EQ__f) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4683 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4684 (all A_27a all A_27b all V0f_2E0 all V1ls_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2313_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))) # label(thm_2Elist_2EFOLDL__UNION__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4685 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__LIFT2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Elist_2Elist(A_27c),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2ELIST__LIFT2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Elist_2Elist(A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__LIFT2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4686 (all A_27a ((all V1h_2E0 all V2t_2E0 all V3n_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Enum_2Enum,V3n_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) & (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Elist_2ELEN__DEF) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4687 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4688 (all A_27a all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))) # label(thm_2Elist_2EEVERY__APPEND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.91 4689 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4690 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4691 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EREV_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EREV_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4692 (all A_27a all A_27b all V0P_2E0 all V1f_2E0 all V2l_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2534_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EEVERY__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4693 (all A_27a all V0f_2E0 all V1n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Elist_2EGENLIST__GENLIST__AUX) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4694 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2294_1_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),f2294_1_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ef2294_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4695 (all A_27a all V1f_2E0 all V0n_2E0 all V2m_2E0 s(A_27a,f2314_0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V2m_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V2m_2E0)))))) # label(def0_2Ethm_2Elist_2EREVERSE__GENLIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4696 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4697 (all A_27a all V0n_2E0 all V1l_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))) # label(thm_2Elist_2ELENGTH__DROP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4698 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f2468_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,f2468_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef2468_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4699 (all A_27a all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4700 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2371_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2371_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2371_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4701 (all A_27a all A_27b all A_27c ((all V0f_2E0 all V1cs_2E0 all V2c_2E0 all V3bs_2E0 all V4b_2E0 all V5a_2E0 s(A_27a,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V0f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V0f_2E0),s(A_27a,V5a_2E0))),s(A_27b,V4b_2E0))),s(A_27c,V2c_2E0))),s(tyop_2Elist_2Elist(A_27b),V3bs_2E0),s(tyop_2Elist_2Elist(A_27c),V1cs_2E0))) = s(A_27a,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V0f_2E0),s(A_27a,V5a_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4b_2E0),s(tyop_2Elist_2Elist(A_27b),V3bs_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V2c_2E0),s(tyop_2Elist_2Elist(A_27c),V1cs_2E0)))))) & (all V6f_2E0 all V7cs_2E0 all V8a_2E0 s(A_27a,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V6f_2E0),s(A_27a,V8a_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27c),V7cs_2E0))) = s(A_27a,V8a_2E0)) & (all V9v7_2E0 all V10v6_2E0 all V11f_2E0 all V12a_2E0 s(A_27a,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V11f_2E0),s(A_27a,V12a_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V10v6_2E0),s(tyop_2Elist_2Elist(A_27b),V9v7_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))) = s(A_27a,V12a_2E0)))) # label(thm_2Elist_2EFOLDL2__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4702 (all A_27a all V0l1_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f2636_0_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(A_27a,V2x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))))) # label(def0_2Ethm_2Elist_2Elist__to__set__diff) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4703 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4704 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2536_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2536_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2536_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4705 (all A_27a ((all V0h_2E0 all V1t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V1t_2E0)) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2ETL__DEF) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4706 (all A_27a all A_27b ((all V0l2_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))))) & (all V1l1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)) & (all V2x1_2E0 all V3l1_2E0 all V4x2_2E0 all V5l2_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4x2_2E0),s(tyop_2Elist_2Elist(A_27b),V5l2_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x1_2E0),s(A_27b,V4x2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27b),V5l2_2E0)))))))))) # label(thm_2Elist_2EZIP__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4707 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2370_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Elist_2ESET__TO__LIST__THM) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4708 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ERC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4709 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4710 (all A_27a ((all V1n_2E0 all V2x_2E0 all V3xs_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2259_0_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0)))))) & (all V0n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ETAKE__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4711 (all A_27a all V1x_2E0 s(tyop_2Elist_2Elist(A_27a),f2610_0_2E1(s(A_27a,V1x_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(def0_2Ethm_2Elist_2ESINGL__LIST__APPLY__R) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4712 (all A_27a all V0l_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2EDROP__LENGTH__TOO__LONG) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4713 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2529_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2529_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef2529_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4714 (all A_27b all X0_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EFLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4715 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Elist_2Elist(A_27c),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EMAP2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Elist_2Elist(A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4716 (all A_27a all A_27b all V0l_2E0 all V1k_2E0 all V2P_2E0 s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))) = s(A_27a,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2598_0_2E2(s(tyop_2Elist_2Elist(A_27b),V0l_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f2598_1_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0)))))) # label(thm_2Elist_2EsplitAtPki__EQN) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4717 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4718 (all A_27a ((all V1n_2E0 all V2x_2E0 all V3xs_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2301_0_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0)))))) & (all V0n_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EoEL__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4719 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4720 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4721 (all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Elist_2Elist(A_27d),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Elist_2Elist(A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4722 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4723 (all A_27b all X0_2E0 all X1_2E0 s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4724 (all A_27a all A_27b all A_27c all A_27d all A_27e all A_27f ((all V1f_2E0 all V2h1_2E0 all V3t1_2E0 all V4h2_2E0 all V5t2_2E0 s(tyop_2Elist_2Elist(A_27f),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2ECONS_2E2(s(A_27d,V2h1_2E0),s(tyop_2Elist_2Elist(A_27d),V3t1_2E0))),s(tyop_2Elist_2Elist(A_27e),c_2Elist_2ECONS_2E2(s(A_27e,V4h2_2E0),s(tyop_2Elist_2Elist(A_27e),V5t2_2E0))))) = s(tyop_2Elist_2Elist(A_27f),c_2Elist_2ECONS_2E2(s(A_27f,app_2E2(s(tyop_2Emin_2Efun(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(A_27d,V2h1_2E0))),s(A_27e,V4h2_2E0))),s(tyop_2Elist_2Elist(A_27f),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V1f_2E0),s(tyop_2Elist_2Elist(A_27d),V3t1_2E0),s(tyop_2Elist_2Elist(A_27e),V5t2_2E0)))))) & (all V0f_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EMAP2) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4725 (all A_27a all V0P_2E0 all V1l_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2526_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EEXISTS__NOT__EVERY) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4726 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4727 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4728 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))))) # label(thm_2Elist_2EMEM__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4729 (all A_27a all V0l2_2E0 all V1l1_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))) # label(thm_2Elist_2ETAKE__APPEND1) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4730 (all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4731 (all A_27a all V0x_2E0 all V1ls_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4732 (all A_27a all A_27b all V0f_2E0 all V1l_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4733 (all A_27a ((all V1h_2E0 all V2t_2E0 all V3l_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V3l_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),f2254_0_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))) & (all V0l_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EisPREFIX) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4734 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2259_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f2259_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef2259_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4735 (all A_27a all V0n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EDROP__nil) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4736 (all A_27a all V1a0_27_2E0 ((all V2_27list_27_2E0 ((all V3a0_27_2E0 ((exists V5a0_2E0 exists V6a1_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27list_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V6a1_2E0)))) & s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(A_27a,V5a0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(A_27a),V6a1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),f2267_2_2E0))))))) | s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(A_27a,c_2Ebool_2EARB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),f2267_1_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27list_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_27_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27list_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_27_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,f2267_0_2E1(s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_27_2E0)))))) # label(def2_2Ethm_2Elist_2Elist__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4737 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EFILTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4738 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),A_27b))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4739 (all A_27a all A_27b all V0R_2E0 all V1LIST__REL_27_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) & (all V2h1_2E0 all V3h2_2E0 all V4t1_2E0 all V5t2_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2h1_2E0))),s(A_27b,V3h2_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h2_2E0),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))))))) -> (all V6a0_2E0 all V7a1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0))),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))))))) # label(thm_2Elist_2ELIST__REL__ind) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4740 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4741 (all A_27a all V0s_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))))) # label(thm_2Elist_2ESUM__IMAGE__eq__SUM__MAP__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4742 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V1l_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) -> (all V2x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))))) -> (all V3l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))) # label(thm_2Elist_2ESNOC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4743 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4744 (all A_27e all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27e),c_2Elist_2ECONS_2E2(s(A_27e,X0_2E0),s(tyop_2Elist_2Elist(A_27e),X1_2E0))) = s(tyop_2Elist_2Elist(A_27e),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27e)),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27e))),c_2Elist_2ECONS_2E0),s(A_27e,X0_2E0))),s(tyop_2Elist_2Elist(A_27e),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27e) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4745 (all A_27g all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27g),c_2Elist_2ECONS_2E2(s(A_27g,X0_2E0),s(tyop_2Elist_2Elist(A_27g),X1_2E0))) = s(tyop_2Elist_2Elist(A_27g),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Elist_2Elist(A_27g)),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Elist_2Elist(A_27g))),c_2Elist_2ECONS_2E0),s(A_27g,X0_2E0))),s(tyop_2Elist_2Elist(A_27g),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4746 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4747 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ESNOC_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4748 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)))),f2288_0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))),s(tyop_2Elist_2Elist(A_27b),X3_2E0))) = s(A_27a,f2288_0_2E4(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0),s(tyop_2Elist_2Elist(A_27b),X3_2E0)))) # label(arityeq4_2Ef2288_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4749 (all A_27a all A_27b all V0ls_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2639_0_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) -> (exists V4l_2E0 s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V4l_2E0)))))) # label(thm_2Elist_2EEXISTS__LIST__EQ__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4750 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,f2656_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),f2656_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef2656_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4751 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1f_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1f_2E0),s(A_27b,V0x_2E0)))) # label(thm_2Elist_2ESINGL__LIST__APPLY__L) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4752 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2468_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2468_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2468_2_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4753 (all A_27a all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) & (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) <-> s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) # label(thm_2Elist_2ELIST__EQ__REWRITE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4754 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4755 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2468_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2468_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef2468_2_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4756 (all A_27a all V0n_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0))),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Elist_2EGENLIST__CONS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4757 (all V0x_2E0 all V1n_2E0 all V2b_2E0 all V3a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V3a_2E0))))),s(tyop_2Enum_2Enum,V2b_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V3a_2E0)))))))))) # label(thm_2Elist_2EDISJOINT__GENLIST__PLUS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4758 (all A_27a all V0l_2E0 p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2Eall__distinct__nub) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4759 (all A_27a all V0x_2E0 all V1L_2E0 ((exists V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V2l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1L_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1L_2E0)))))))))) # label(thm_2Elist_2EMEM__FLAT) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4760 (all A_27a all V0l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2ELENGTH__TL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4761 (all A_27a all V0ls_2E0 all V1R_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_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)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) # label(thm_2Elist_2EEVERY2__refl) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4762 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 all V2p_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))))) <-> (exists V3n_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V2p_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))))))))) # label(thm_2Elist_2EMEM__ZIP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4763 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4764 (all A_27a all V4n_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),f2267_1_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))) # label(def1_2Ethm_2Elist_2Elist__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4765 (all A_27a all V0l_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2EFINITE__LIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4766 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4767 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f2312_1_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))))),f2312_1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef2312_1_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4768 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2637_0_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))))) # label(thm_2Elist_2Elength__nub__append) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4769 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4770 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELUPDATE_2E3(s(A_27b,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),c_2Elist_2ELUPDATE_2E0),s(A_27b,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4771 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))))) # label(thm_2Elist_2EALL__DISTINCT__ZIP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4772 (all A_27a all A_27b ((all V0f_2E0 all V1e_2E0 s(A_27b,V1e_2E0) = s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27b,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V2f_2E0 all V3e_2E0 all V4x_2E0 all V5l_2E0 s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0),s(A_27b,V3e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0),s(A_27a,V4x_2E0))),s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2f_2E0),s(A_27b,V3e_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0)))))))) # label(thm_2Elist_2EFOLDR) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4773 (all A_27a all A_27b all V0f_2E0 all V1ls_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),f2656_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))) # label(thm_2Elist_2EIMAGE__EL__count__LENGTH) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4774 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))))) # label(thm_2Elist_2ELLEX__total) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4775 (all A_27a all V0R_2E0 all V1l1_2E0 all V2l2_2E0 all V3R_27_2E0 all V4l1_27_2E0 all V5l2_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0) & (all V6a_2E0 all V7b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V7b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V5l2_27_2E0)))))) -> 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)),V3R_27_2E0),s(A_27a,V6a_2E0))),s(A_27a,V7b_2E0))) = 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)),V0R_2E0),s(A_27a,V6a_2E0))),s(A_27a,V7b_2E0))))) & s(tyop_2Elist_2Elist(A_27a),V5l2_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) -> s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) # label(thm_2Elist_2ELLEX__CONG) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4776 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,f2317_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),f2317_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2317_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4777 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4778 (all A_27a all A_27b all V0P_2E0 all V1f_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Emin_2Ebool,f2530_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Elist_2EEXISTS__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4779 (all A_27a all A_27b all V0x_2E0 all V1n_2E0 all V2l_2E0 all V3f_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELUPDATE_2E3(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V0x_2E0))),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2ELUPDATE__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4780 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2636_0_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2Elist__to__set__diff) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4781 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4782 (all A_27a all A_27b all V0R_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))) # label(thm_2Elist_2ELIST__REL__EVERY__ZIP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4783 (all A_27a all V0h_2E0 all V1t_2E0 s(tyop_2Elist_2Elist(A_27a),V1t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) # label(thm_2Elist_2ETL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.92 4784 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4785 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),f2675_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,f2675_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef2675_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4786 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4787 (all A_27a all V0l_2E0 all V1P_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2371_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__FILTER) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4788 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),f2565_0_2E2(s(A_27b,V0x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),V1f_2E0))))))) # label(thm_2Elist_2Elist__Axiom__old) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4789 (all A_27a all A_27b all A_27c all A_27d all V0l2_2E0 all V1l1_2E0 all V2g_2E0 all V3f_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) -> s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) & s(tyop_2Elist_2Elist(A_27b),V0l2_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) & s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) & s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) = s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))))) # label(thm_2Elist_2EMAP__ZIP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4790 (all A_27a all A_27b all A_27c all V0t2_2E0 all V1t1_2E0 all V2t_2E0 all V3h_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V2t_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V2t_2E0))) & s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V3h_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27c),V1t1_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),V0t2_2E0))))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V3h_2E0),s(tyop_2Elist_2Elist(A_27c),V1t1_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),V0t2_2E0))))))) # label(thm_2Elist_2EFLAT__compute) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4791 (all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EoHD_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EoHD_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4792 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EPAD__RIGHT_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__RIGHT_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EPAD__RIGHT_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4793 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4794 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),f2676_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,f2676_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef2676_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4795 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4796 (all A_27a all A_27b all A_27c all V0l1_2E0 all V1l1_27_2E0 all V2l2_2E0 all V3l2_27_2E0 all V4a_2E0 all V5a_27_2E0 all V6f_2E0 all V7f_27_2E0 (s(A_27c,V4a_2E0) = s(A_27c,V5a_27_2E0) & (all V8z_2E0 all V9b_2E0 all V10c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V10c_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V9b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0)))))) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V7f_27_2E0),s(A_27c,V8z_2E0))),s(A_27a,V9b_2E0))),s(A_27b,V10c_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V6f_2E0),s(A_27c,V8z_2E0))),s(A_27a,V9b_2E0))),s(A_27b,V10c_2E0))))) & s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0) = s(tyop_2Elist_2Elist(A_27b),V2l2_2E0) & s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) -> s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V6f_2E0),s(A_27c,V4a_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V7f_27_2E0),s(A_27c,V5a_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))))) # label(thm_2Elist_2EFOLDL2__cong) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4797 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27c_29_2Ctyop_2Emin_2Efun_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4798 (all A_27a all V0m2_2E0 all V1m1_2E0 all V2l2_2E0 all V3l1_2E0 all V4e_2E0 ((exists V6l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V6l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0m2_2E0) & s(tyop_2Elist_2Elist(A_27a),V3l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V6l_2E0))))) | (exists V5l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1m1_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5l_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) # label(thm_2Elist_2EAPPEND__EQ__APPEND__MID) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4799 (all A_27a all V0xs_2E0 all V1n_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0)))))) & s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(A_27a,V2y_2E0) <-> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2y_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) # label(thm_2Elist_2EoEL__EQ__EL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4800 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4801 (all A_27a all A_27b all V0fs_2E0 all V1xs_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V0fs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Elist_2Elist(A_27b),V1xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V0fs_2E0),s(tyop_2Elist_2Elist(A_27b),V1xs_2E0)))) # label(thm_2Elist_2ELIST__APPLY__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4802 (all A_27a all A_27b all V0l_2E0 all V1l_27_2E0 all V2b_2E0 all V3b_27_2E0 all V4f_2E0 all V5f_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0) & s(A_27b,V3b_27_2E0) = s(A_27b,V2b_2E0) & (all V6x_2E0 all V7a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0)))))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V5f_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V4f_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7a_2E0))))) -> s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V4f_2E0),s(A_27b,V2b_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V5f_27_2E0),s(A_27b,V3b_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0))))) # label(thm_2Elist_2EFOLDR__CONG) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4803 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4804 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EdropWhile_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EdropWhile_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EdropWhile_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4805 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4806 (all A_27a all A_27b all A_27c all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> (all V2f_2E0 all V3a_2E0 s(A_27c,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),f2405_0_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0))),s(A_27c,V3a_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0),s(A_27c,V3a_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))) # label(thm_2Elist_2EFOLDL2__FOLDL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4807 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ESNOC_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ESNOC_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4808 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4809 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4810 (all A_27a all V0n_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) # label(thm_2Elist_2ETAKE__splitAtPki) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4811 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4812 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27c_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4813 (all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4814 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2468_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f2468_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef2468_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4815 (all A_27a all V0n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) # label(thm_2Elist_2ETAKE__nil) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4816 (all A_27a ((all V0l1_2E0 all V1l2_2E0 all V2l1_27_2E0 all V3l2_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_27_2E0))) -> (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V2l1_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) & s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0)))) & (all V4l1_2E0 all V5l2_2E0 all V6l1_27_2E0 all V7l2_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V7l2_27_2E0))) -> (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V6l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V7l2_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V7l2_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V5l2_2E0) & s(tyop_2Elist_2Elist(A_27a),V4l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V6l1_27_2E0)))))) # label(thm_2Elist_2EAPPEND__11__LENGTH) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4817 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2635_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2635_0_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ef2635_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4818 (all V1i_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,f2709_0_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) <-> s(tyop_2Enum_2Enum,V2n_2E0) != s(tyop_2Enum_2Enum,V1i_2E0))) # label(def0_2Ethm_2Elist_2EoEL__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4819 (all A_27a all V0l_2E0 all V1x_2E0 ((exists V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) & s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,V1x_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) # label(thm_2Elist_2EMEM__EL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4820 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 s(tyop_2Emin_2Ebool,f2294_0_2E5(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0),s(tyop_2Elist_2Elist(A_27a),X4_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),f2294_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))),s(tyop_2Elist_2Elist(A_27a),X4_2E0)))) # label(arityeq5_2Ef2294_0_2E5_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4821 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4822 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4823 (all A_27a all V0n_2E0 all V1f_2E0 all V2g_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0),s(tyop_2Enum_2Enum,V3x_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3x_2E0))))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2Elist_2EGENLIST__FUN__EQ) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4824 (all A_27a all V0y_2E0 all V1x_2E0 all V2ls_2E0 all V3e_2E0 all V4R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2ls_2E0)))))) -> (exists V5z_2E0 exists V6t_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)),V4R_2E0),s(A_27a,V3e_2E0))),s(A_27a,V5z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V6t_2E0),s(A_27a,V5z_2E0),s(A_27a,V0y_2E0)))))))) # label(thm_2Elist_2ELRC__MEM) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4825 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a))))),c_2Elist_2ELUPDATE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4826 (all A_27a all A_27b all V0x_2E0 all V1l_2E0 all V2f_2E0 ((exists V3x0_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x0_2E0))) = s(A_27b,V0x_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x0_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EMAP__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4827 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__TO__SET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4828 (all A_27a all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) # label(thm_2Elist_2ESWAP__REVERSE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4829 (all A_27a ((all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) & (all V1h_2E0 all V2t_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(A_27a,V3x_2E0)))) | s(A_27a,V3x_2E0) = s(A_27a,V1h_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__TO__SET_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(A_27a,V3x_2E0)))))))) # label(thm_2Elist_2ELIST__TO__SET__DEF) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4830 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),f2261_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,f2261_0_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ef2261_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4831 (all A_27a all A_27b all V0t_2E0 all V1h_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & s(tyop_2Eoption_2Eoption(A_27b),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1h_2E0))))) # label(thm_2Elist_2EoHD__thm) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4832 (all A_27a all V1h_2E0 all V2t_2E0 all V4h_27_2E0 all V5t_27_2E0 (p(s(tyop_2Emin_2Ebool,f2254_0_2E4(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(A_27a,V4h_27_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0)))) & s(A_27a,V4h_27_2E0) = s(A_27a,V1h_2E0))) # label(def0_2Ethm_2Elist_2EisPREFIX) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4833 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 all V2P_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f2676_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) # label(thm_2Elist_2Eevery__zip__fst) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4834 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2592_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),f2592_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ef2592_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4835 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EdropWhile_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EsplitAtPki_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0)))))) # label(thm_2Elist_2EdropWhile__splitAtPki) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4836 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4837 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 all V2P_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f2675_0_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))))) # label(thm_2Elist_2Eevery__zip__snd) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4838 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4839 (all A_27a all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27a,A_27d))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27d,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27d),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27d,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4840 (all A_27a all V0t2_2E0 all V1t1_2E0 all V2t_2E0 all V3l_2E0 all V4h2_2E0 all V5h1_2E0 all V6h_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V1t1_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))) & s(A_27a,V5h1_2E0) = s(A_27a,V4h2_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))))))) & s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))) # label(thm_2Elist_2EisPREFIX__THM) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4841 (all A_27a ((all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & (all V9l_2E0 all V10n1_2E0 all V11n2_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V10n1_2E0),s(tyop_2Enum_2Enum,V11n2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V9l_2E0))) <-> (exists V12l1_2E0 exists V13l2_2E0 (s(tyop_2Enum_2Enum,V10n1_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V12l1_2E0))) & s(tyop_2Enum_2Enum,V11n2_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V13l2_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V12l1_2E0),s(tyop_2Elist_2Elist(A_27a),V13l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V9l_2E0))))) & (all V5l_2E0 all V6n_2E0 ((exists V7h_2E0 exists V8l_27_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7h_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),V5l_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V8l_27_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) & (all V1l_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))) <-> (exists V3h_2E0 exists V4l_27_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) & s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))))))))) # label(thm_2Elist_2ELENGTH__EQ__NUM__compute) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4842 (all A_27a all A_27b all V0v_2E0 all V1l1_2E0 all V2x_2E0 all V3l2_2E0 all V4l3_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0v_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0v_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0)))) # label(thm_2Elist_2Elupdate__append2) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4843 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4844 (all A_27a all V0P_2E0 ((all V2h_2E0 all V3t_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) <-> (all V1l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))) # label(thm_2Elist_2EFORALL__LIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4845 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EUNIQUE_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EUNIQUE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4846 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4847 (all A_27a all V0n_2E0 all V1ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) # label(thm_2Elist_2ELUPDATE__SAME) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4848 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b))),f2448_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27b),f2448_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef2448_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4849 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2530_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2530_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2530_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4850 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4851 (all A_27a all V0P_2E0 all V1ls_2E0 all V2k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))),s(tyop_2Enum_2Enum,V2k_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2k_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))) # label(thm_2Elist_2EEL__LENGTH__dropWhile__REVERSE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4852 (all A_27a all V0x_2E0 all V1l_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,V0x_2E0)) # label(thm_2Elist_2ELAST__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4853 (all A_27a all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0)))))) <-> s(tyop_2Elist_2Elist(A_27a),V0x_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2ENOT__NIL__EQ__LENGTH__NOT__0) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4854 (all A_27a all A_27b all V0e_2E0 all V1f_2E0 exists V2fn_2E0 (s(A_27b,V0e_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & (all V3x_2E0 all V4l_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),V1f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0)))))))) # label(thm_2Elist_2ESNOC__Axiom) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4855 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4856 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27d))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27d),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4857 (all A_27a all V0l1_2E0 all V1l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))) & (all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__APPEND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4858 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4859 (all A_27a all A_27b all X0_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4860 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 all V2x_27_27_2E0 s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))),s(A_27b,V1x_27_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V2x_27_27_2E0),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))))) = s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V0x_2E0),s(A_27b,V1x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V2x_27_27_2E0)))) # label(thm_2Elist_2Elazy__list__case__compute) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4861 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2E_2B_2E1) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4862 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4863 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4864 (all A_27a all V0x_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EREVERSE__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.93 4865 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EisPREFIX_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EisPREFIX_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4866 (all A_27a all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2ENOT__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4867 (all A_27a all A_27b all V0R_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))))) # label(thm_2Elist_2EEVERY2__REVERSE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4868 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0)) # label(thm_2Elist_2EDROP__0) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4869 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4870 (all A_27a all A_27b all A_27c all V0l_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0)))) # label(thm_2Elist_2ELIST__BIND__LIST__BIND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4871 (all A_27a all A_27b all X0_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b)),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4872 (all A_27a all A_27b all A_27c all A_27d all V0l1_2E0 all V1l2_2E0 all V2f1_2E0 all V3f2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),f2448_1_2E1(s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V3f2_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) & s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),f2448_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) # label(thm_2Elist_2EZIP__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4873 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)))),c_2Elist_2EMAP2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4874 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2ENRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Earithmetic_2ENRC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Earithmetic_2ENRC_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4875 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))))) # label(thm_2Elist_2EEL__ZIP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4876 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2636_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2636_0_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ef2636_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4877 (all A_27a all X0_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4878 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4879 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4880 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4881 (all A_27a all V0P_2E0 all V1l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))))) # label(thm_2Elist_2EFILTER__NEQ__NIL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4882 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 all V2fn1_2E0 (s(A_27b,V0x_2E0) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & (all V3h_2E0 all V4t_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4t_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),V1f_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t_2E0))))),s(A_27a,V3h_2E0))),s(tyop_2Elist_2Elist(A_27a),V4t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2565_0_2E3(s(A_27b,V0x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn1_2E0)))))) # label(def0_2Ethm_2Elist_2Elist__Axiom__old) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4883 (all A_27a all V0P_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f2526_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Elist_2EEXISTS__NOT__EVERY) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4884 (all A_27a all V0l_2E0 all V1Q_2E0 all V2P_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2EMONO__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4885 (all A_27a all V0h1_2E0 all V1h2_2E0 (s(A_27a,V0h1_2E0) != s(A_27a,V1h2_2E0) -> (all V2l1_2E0 all V3l2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0)))))) # label(thm_2Elist_2ENOT__EQ__LIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4886 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2597_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2597_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2597_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4887 (all A_27a ((all V1P_2E0 all V2h_2E0 all V3t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))) & (all V0P_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EFILTER) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4888 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4889 (all A_27a all V0l_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2ELENGTH__REVERSE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4890 (all A_27a all A_27b all A_27c ((all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (all V6n_2E0 all V7h_2E0 all V8t_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V7h_2E0),s(tyop_2Elist_2Elist(A_27c),V8t_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V7h_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27c),V8t_2E0)))))) & (all V3n_2E0 all V4h_2E0 all V5t_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27c),V5t_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h_2E0),s(tyop_2Elist_2Elist(A_27c),V5t_2E0)))))) & (all V2n_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) & (all V1n_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ETAKE__compute) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4891 (all A_27f all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27f),c_2Elist_2ECONS_2E2(s(A_27f,X0_2E0),s(tyop_2Elist_2Elist(A_27f),X1_2E0))) = s(tyop_2Elist_2Elist(A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Elist_2Elist(A_27f)),app_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Elist_2Elist(A_27f))),c_2Elist_2ECONS_2E0),s(A_27f,X0_2E0))),s(tyop_2Elist_2Elist(A_27f),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4892 (all A_27a ((all V0R_2E0 all V1l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & (all V2R_2E0 all V3h1_2E0 all V4t1_2E0 all V5l2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V5l2_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),f2295_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0)))))))) # label(thm_2Elist_2ELLEX__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4893 (all A_27a all V0h_2E0 all V1t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2260_0_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) # label(thm_2Elist_2EFRONT__DEF) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4894 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2473_0_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),f2473_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ef2473_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4895 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4896 (all A_27a all V0ls_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__REVERSE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4897 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(A_27c,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),X0_2E0),s(A_27c,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27c))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),X0_2E0))),s(A_27c,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4898 (all A_27a all V0h_2E0 all V1l1_2E0 all V2l2_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2ELAST__APPEND__CONS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4899 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4900 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4901 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4902 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Elist_2EINDEX__FIND_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EINDEX__FIND_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4903 (all A_27a all V0x_2E0 (s(tyop_2Elist_2Elist(A_27a),V0x_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) -> s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))) # label(thm_2Elist_2EHD__REVERSE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4904 (all A_27a all V1k_2E0 all V0ys_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))) = s(tyop_2Enum_2Enum,V1k_2E0) <-> p(s(tyop_2Emin_2Ebool,f2592_0_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))) # label(def0_2Ethm_2Elist_2ELUPDATE__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4905 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4906 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4907 (all A_27a all V0x_2E0 all V1l_2E0 ((exists V2l1_2E0 exists V3l2_2E0 s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EMEM__SPLIT) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4908 (all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))),s(tyop_2Elist_2Elist(A_27d),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0),s(tyop_2Elist_2Elist(A_27d),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4909 (all A_27a all V0f_2E0 all V1n_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__GENLIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4910 (all A_27a all V0n_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) # label(thm_2Elist_2EDROP__splitAtPki) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4911 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4912 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) -> (all V3ls_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3ls_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V3ls_2E0))))))))))) # label(thm_2Elist_2ELENGTH__FILTER__LEQ__MONO) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4913 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2l1_2E0 all V3l2_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0)))))))))) & p(s(tyop_2Emin_2Ebool,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V4x_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V4x_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_2E0)))))) # label(thm_2Elist_2EEVERY2__MEM__MONO) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4914 (all A_27a all A_27b all V1f_2E0 all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))))) = s(A_27b,f2310_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f_2E0),s(A_27a,V2x_2E0)))) # label(def0_2Ethm_2Elist_2EMAP__ZIP__SAME) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4915 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4916 (all A_27h all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27h),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Elist_2Elist(A_27h)),app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Elist_2Elist(A_27h))),c_2Elist_2ECONS_2E0),s(A_27h,X0_2E0))),s(tyop_2Elist_2Elist(A_27h),X1_2E0))) = s(tyop_2Elist_2Elist(A_27h),c_2Elist_2ECONS_2E2(s(A_27h,X0_2E0),s(tyop_2Elist_2Elist(A_27h),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27h) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4917 (all A_27a all A_27b all V0L_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0L_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0L_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0L_2E0)))) # label(thm_2Elist_2EUNZIP__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4918 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2709_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2709_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2709_0_2E2) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4919 (all A_27a all V0l_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2Elast__drop) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4920 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4921 (all A_27a all V0n_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))) # label(thm_2Elist_2ELENGTH__TAKE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4922 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0)) # label(thm_2Elist_2EAPPEND__NIL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4923 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),f2466_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f2466_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0)))) # label(arityeq2_2Ef2466_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4924 (all A_27a all A_27b all V0x_2E0 all V2f_2E0 s(A_27a,f2613_0_2E2(s(A_27b,V0x_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(A_27b,V0x_2E0)))) # label(def0_2Ethm_2Elist_2ESINGL__APPLY__PERMUTE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4925 (all A_27a all V0n_2E0 all V1m_2E0 all V2l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) # label(thm_2Elist_2ETAKE__SUM) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4926 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEVERYi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEVERYi_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4927 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,f2311_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),f2311_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2311_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4928 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4929 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4930 (all A_27a all A_27b all A_27c all V0l2_2E0 all V1l1_2E0 all V2f_2E0 all V3R_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0))),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) # label(thm_2Elist_2ELIST__REL__MAP1) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4931 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EEL_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4932 (all A_27a all A_27b all V0f_2E0 all V1e_2E0 all V2x_2E0 all V3l_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27b,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))),s(A_27a,V2x_2E0))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27b,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))))) # label(thm_2Elist_2EFOLDL__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4933 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2EUNCURRY_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4934 (all A_27a ((all V0i_2E0 all V1P_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,V0i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V2i_2E0 all V3P_2E0 all V4h_2E0 all V5t_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(A_27a,V4h_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(A_27a,V4h_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2i_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Elist_2EINDEX__FIND_2E3(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0)))))))) # label(thm_2Elist_2EINDEX__FIND__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4935 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2529_0_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2529_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2529_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4936 (all A_27a all V0P_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),c_2Epair_2ESND_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EINDEX__FIND_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EFIND_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) # label(thm_2Elist_2EFIND__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4937 (all A_27a all A_27b all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1f_2E0 all V2a_2E0 s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0))),s(A_27b,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(A_27b,c_2Epred__set_2EITSET_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27b,V2a_2E0)))))) # label(thm_2Elist_2EITSET__eq__FOLDL__SET__TO__LIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4938 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0R_2E0)))) & (all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,f2255_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(def2_2Ethm_2Elist_2ESET__TO__LIST__primitive__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4939 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4940 (all A_27a all V0xs_2E0 all V1n_2E0 all V2x_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) # label(thm_2Elist_2ELUPDATE__NIL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4941 (all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2ESOME_2E0),s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4942 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4943 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2EoEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EoEL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4944 (all A_27a all V0c_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f2529_0_2E2(s(tyop_2Emin_2Ebool,V0c_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,V0c_2E0)) # label(def0_2Ethm_2Elist_2EEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4945 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4946 (all A_27a all V4t1_2E0 all V7t2_2E0 (p(s(tyop_2Emin_2Ebool,f2294_1_2E2(s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))))) # label(def0_2Ethm_2Elist_2ESHORTLEX__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4947 (all A_27a all V2P_2E0 all V4i_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,V4i_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2597_0_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,V4i_2E0)))) # label(def0_2Ethm_2Elist_2EsplitAtPki__APPEND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4948 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> (s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),V1l2_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) # label(thm_2Elist_2EZIP__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4949 (all A_27a all V0x_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Elist_2EINDEX__OF_2E1(s(A_27a,V0x_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),c_2Epair_2EFST_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EINDEX__FIND_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0x_2E0)))))))) # label(thm_2Elist_2EINDEX__OF__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4950 (all A_27a all V0l_2E0 all V1x_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(A_27a,V1x_2E0)) # label(thm_2Elist_2EEL__LENGTH__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4951 (all A_27a all V0t_2E0 all V1h_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2425_0_2E1(s(tyop_2Elist_2Elist(A_27a),V0t_2E0))),s(A_27a,V1h_2E0),s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0t_2E0))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0)))))) # label(thm_2Elist_2ELAST__CONS__cond) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4952 (all A_27a ((all V1n_2E0 all V2x_2E0 all V3xs_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2258_0_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0)))))) & (all V0n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EDROP__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4953 (all A_27a all V0l_2E0 all V1Q_2E0 all V2P_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2EMONO__EVERY) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4954 (all A_27a all V0l_2E0 all V1n1_2E0 all V2n2_2E0 ((exists V3l1_2E0 exists V4l2_2E0 (s(tyop_2Enum_2Enum,V1n1_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l2_2E0))) = s(tyop_2Enum_2Enum,V2n2_2E0) & s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V4l2_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Enum_2Enum,V2n2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2ELENGTH__EQ__SUM) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4955 (all V0h_2E0 all V1t_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1t_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,V0h_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1t_2E0)))))) # label(thm_2Elist_2ESUM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4956 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4957 (all A_27a all A_27b all V0x_2E0 all V1fs_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),f2613_0_2E1(s(A_27b,V0x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V1fs_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),V1fs_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ESINGL__APPLY__PERMUTE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4958 (all A_27a ((all V0R_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) & (all V2R_2E0 all V3h1_2E0 all V4t1_2E0 all V5l2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V5l2_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),f2294_0_2E3(s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3h1_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0)))))) # label(thm_2Elist_2ESHORTLEX__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4959 (all A_27a all V0l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) <-> (all V1n1_2E0 all V2n2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n2_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> (s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n2_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) <-> s(tyop_2Enum_2Enum,V2n2_2E0) = s(tyop_2Enum_2Enum,V1n1_2E0)))))) # label(thm_2Elist_2EEL__ALL__DISTINCT__EL__EQ) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4960 (all A_27a all A_27b all A_27c all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> (all V2f_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))))) # label(thm_2Elist_2EMAP2__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4961 (all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ELIST__GUARD_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Elist_2Elist(tyop_2Eone_2Eone)),c_2Elist_2ELIST__GUARD_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__GUARD_2E1) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4962 (all A_27a ((all V1x_2E0 all V2h_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))) <-> s(A_27a,V1x_2E0) = s(A_27a,V2h_2E0) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))) & (all V0x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) # label(thm_2Elist_2EMEM) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4963 (all A_27a all X0_2E0 all X1_2E0 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)),f2294_2_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2294_2_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2294_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4964 (all A_27a all V0n_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) # label(thm_2Elist_2EEL__REVERSE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.94 4965 (all A_27a all A_27b all V0P_2E0 all V1l1_2E0 all V2l2_2E0 all V3v1_2E0 all V4v2_2E0 all V5n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V3v1_2E0))),s(A_27b,V4v2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V3v1_2E0),s(tyop_2Enum_2Enum,V5n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELUPDATE_2E3(s(A_27b,V4v2_2E0),s(tyop_2Enum_2Enum,V5n_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))))) # label(thm_2Elist_2EEVERY2__LUPDATE__same) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4966 (all A_27a all V0P_2E0 ((exists V1l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) | (exists V2h_2E0 exists V3t_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))))))) # label(thm_2Elist_2EEXISTS__LIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4967 (all V0x_2E0 all V1l_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ESNOC_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l_2E0))),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Elist_2ESUM__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4968 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),f2613_0_2E0),s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),f2613_0_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ef2613_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4969 (all A_27a ((all V1f_2E0 all V2a0_2E0 all V3a1_2E0 s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(A_27a,V2a0_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_2E0)))))))) & (all V0f_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2Elist__size__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4970 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4971 (all A_27a all A_27b all V2Q_2E0 all V8a_2E0 all V9b_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V8a_2E0))),s(A_27b,V9b_2E0))) = s(tyop_2Emin_2Ebool,f2468_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V8a_2E0),s(A_27b,V9b_2E0)))) # label(def1_2Ethm_2Elist_2ELIST__REL__CONJ) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4972 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4973 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) # label(thm_2Elist_2EEVERY2__EVERY) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4974 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4975 (all A_27a all X0_2E0 s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epred__set_2ECHOICE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4976 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4977 (all V1n_2E0 (p(s(tyop_2Emin_2Ebool,f2259_0_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(def0_2Ethm_2Elist_2ETAKE__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4978 (all A_27a all V0h_2E0 all V1t_2E0 s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(A_27a,V0h_2E0)) # label(thm_2Elist_2EHD) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4979 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))))),f2454_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))),s(tyop_2Elist_2Elist(A_27b),X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),f2454_0_2E4(s(A_27a,X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0),s(tyop_2Elist_2Elist(A_27b),X3_2E0)))) # label(arityeq4_2Ef2454_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4980 (all A_27a all V0M_2E0 all V1N_2E0 all V2f_2E0 all V3f_27_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1N_2E0)))))) -> s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_27_2E0),s(A_27a,V4x_2E0))))) & s(tyop_2Elist_2Elist(A_27a),V0M_2E0) = s(tyop_2Elist_2Elist(A_27a),V1N_2E0) -> s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1N_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0M_2E0))))) # label(thm_2Elist_2Elist__size__cong) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4981 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),f2260_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,f2260_0_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ef2260_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4982 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4983 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Elist_2ESET__TO__LIST__INV) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4984 (all A_27a (s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) & (all V0h_2E0 all V1t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4985 (all A_27a all V0x_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EFRONT__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4986 (all A_27a ((all V5f_2E0 all V6n_2E0 all V7l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V7l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V5f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V7l_2E0)))))) & (all V2f_2E0 all V3n_2E0 all V4l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0)))) & (all V0f_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) # label(thm_2Elist_2EGENLIST__AUX__compute) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4987 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4988 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4989 (all A_27a all A_27b all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4990 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),f2604_0_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),f2604_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ef2604_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4991 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELLEX_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4992 (all A_27a all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))))) # label(thm_2Elist_2EdropWhile__APPEND__EVERY) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4993 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4994 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4995 (all A_27a all V3h1_2E0 all V6h2_2E0 (s(A_27a,V3h1_2E0) = s(A_27a,V6h2_2E0) <-> p(s(tyop_2Emin_2Ebool,f2294_2_2E2(s(A_27a,V3h1_2E0),s(A_27a,V6h2_2E0)))))) # label(def1_2Ethm_2Elist_2ESHORTLEX__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4996 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2533_0_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2533_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2533_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4997 (all A_27a all V0c_2E0 all V1l_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) | p(s(tyop_2Emin_2Ebool,V0c_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2533_0_2E1(s(tyop_2Emin_2Ebool,V0c_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EEVERY__SIMP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4998 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2533_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2533_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef2533_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 4999 (all A_27a all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))))) -> (all V3l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))))))) # label(thm_2Elist_2EEVERY__MONOTONIC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5000 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Ecombin_2EK_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5001 (all A_27a all V0f_2E0 all V1n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Elist_2ETL__GENLIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5002 (all A_27a all A_27b all V0f_2E0 all V1n_2E0 all V2l_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EMAP__TAKE) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5003 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1l2_2E0)))))) # label(thm_2Elist_2EFLAT__APPEND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5004 (all A_27a all V0x_2E0 all V1l_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2ELENGTH__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5005 (all A_27a all A_27b all A_27c all V0f_2E0 all V1xs_2E0 all V2ys_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__LIFT2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0),s(tyop_2Elist_2Elist(A_27b),V1xs_2E0),s(tyop_2Elist_2Elist(A_27c),V2ys_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V0f_2E0),s(tyop_2Elist_2Elist(A_27b),V1xs_2E0))),s(tyop_2Elist_2Elist(A_27c),V2ys_2E0)))) # label(thm_2Elist_2ELIST__LIFT2__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5006 (all A_27a all A_27b all V0f_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) & s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) -> s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) # label(thm_2Elist_2EINJ__MAP__EQ) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5007 (all A_27a all A_27b all V0f_2E0 all V1ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) # label(thm_2Elist_2EALL__DISTINCT__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5008 (all A_27a all V0l_2E0 all V1e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) <-> (exists V2pfx_2E0 exists V3sfx_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3sfx_2E0)))))) & s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2pfx_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3sfx_2E0))))))) # label(thm_2Elist_2EMEM__SPLIT__APPEND__last) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5009 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5010 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27c)))),c_2Elist_2EFOLDL2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27c,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))),s(tyop_2Elist_2Elist(A_27b),X3_2E0))) = s(A_27c,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27c,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0),s(tyop_2Elist_2Elist(A_27b),X3_2E0)))) # label(arityeq4_2Ec_2Elist_2EFOLDL2_2E4_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5011 (all A_27c all X0_2E0 all X1_2E0 s(A_27c,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27c)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5012 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V1l_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) -> (all V2a_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))))) -> (all V3l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))) # label(thm_2Elist_2Elist__INDUCT0) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5013 (all A_27a all V0l_2E0 all V1e_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EREVERSE__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5014 (all V1h_2E0 all V2t_2E0 all V3acc_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2t_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Enum_2Enum,V3acc_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,V1h_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2t_2E0))),s(tyop_2Enum_2Enum,V3acc_2E0)))) # label(thm_2Elist_2ESUM__ACC__DEF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5015 (all V0acc_2E0 s(tyop_2Enum_2Enum,V0acc_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ENIL_2E0),s(tyop_2Enum_2Enum,V0acc_2E0)))) # label(thm_2Elist_2ESUM__ACC__DEF_AndRHS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5016 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2ELUPDATE_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5017 (all A_27a all V0R_2E0 ((exists V1a_2E0 exists V2b_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)),V0R_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0))))) -> -p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Elist_2ELLEX__not__WF) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5018 (all A_27a all V4h_2E0 all V5t_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),f2299_1_2E2(s(A_27a,V4h_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_2E0)))) # label(def0_2Ethm_2Elist_2EOPT__MMAP__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5019 (all X0_2E0 s(tyop_2Emin_2Ebool,f2301_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2301_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef2301_0_2E1) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5020 (all A_27a all X0_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2ELAST_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5021 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5022 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5023 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2ELAST__MAP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5024 (all A_27a ((all V1P_2E0 all V2h_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0))),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))),s(A_27a,V2h_2E0)))))) & (all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2Elist_2EEVERYi__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5025 (all A_27a all V0c_2E0 all V1l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),V1l_2E0) & p(s(tyop_2Emin_2Ebool,V0c_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2529_0_2E1(s(tyop_2Emin_2Ebool,V0c_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5026 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5027 (all A_27a all A_27b all V0ls_2E0 all V1f_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3y_2E0))) -> s(A_27a,V3y_2E0) = s(A_27a,V2x_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__MAP__INJ) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5028 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0)))))) -> (exists V3z_2E0 (s(A_27a,V0x_2E0) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3z_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3z_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2l_2E0)))))))))) # label(thm_2Elist_2Emem__exists__set) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5029 (all A_27a all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EFILTER__ALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5030 (all A_27a all V0P_2E0 all V1l_2E0 all V2h_2E0 all V3lr_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3lr_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) <-> (exists V4l1_2E0 exists V5l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0)))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V3lr_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V4l1_2E0))))))) # label(thm_2Elist_2EFILTER__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5031 (all A_27a -p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) # label(thm_2Elist_2EINFINITE__LIST__UNIV) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5032 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5033 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5034 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMIN_2E2) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5035 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2636_0_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2636_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2636_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5036 (all A_27a all V0ls_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0)))))))) # label(thm_2Elist_2ELIST__TO__SET__FLAT) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5037 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),f2493_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),f2493_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ef2493_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5038 (all A_27a all V0n_2E0 all V1l_2E0 (s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) & s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) # label(thm_2Elist_2EEL__simp) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5039 (all A_27a all A_27b all V0m1_2E0 all V1m2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__IGNORE__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0m1_2E0),s(tyop_2Elist_2Elist(A_27a),V1m2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0m1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Elist_2Elist(A_27a),V1m2_2E0)))))) # label(thm_2Elist_2ELIST__IGNORE__BIND__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5040 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5041 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2597_0_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2597_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2597_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5042 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ESNOC_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2ESNOC_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5043 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0),s(A_27a,V2x_2E0))),s(A_27b,V3y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0),s(A_27b,V3y_2E0))),s(A_27a,V2x_2E0)))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0),s(tyop_2Elist_2Elist(A_27b),V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R2_2E0),s(tyop_2Elist_2Elist(A_27b),V5y_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0)))))))) # label(thm_2Elist_2EEVERY2__sym) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5044 (all A_27a all V0l1_2E0 all V1l1_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0))) -> (all V2l2_2E0 all V3l2_27_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0))) -> (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) & s(tyop_2Elist_2Elist(A_27a),V3l2_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2EAPPEND__LENGTH__EQ) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5045 (all A_27a all A_27b all V3k_2E0 all V4h_2E0 all V6p_2E0 all V7s_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V6p_2E0))))),s(tyop_2Elist_2Elist(A_27b),V7s_2E0))) = s(A_27a,f2288_0_2E4(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V3k_2E0),s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V6p_2E0),s(tyop_2Elist_2Elist(A_27b),V7s_2E0)))) # label(def0_2Ethm_2Elist_2EsplitAtPki__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5046 (all A_27a all V0P1_2E0 all V1P2_2E0 all V2l_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2483_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) # label(thm_2Elist_2EEVERY__FILTER) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5047 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5048 (all A_27a ((all V0h_2E0 all V1t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27a),V0h_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V1t_2E0)))))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2EFLAT) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5049 (all A_27a ((all V1h_2E0 all V2t_2E0 all V3acc_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(tyop_2Elist_2Elist(A_27a),V3acc_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),V2t_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V3acc_2E0)))))) & (all V0acc_2E0 s(tyop_2Elist_2Elist(A_27a),V0acc_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V0acc_2E0)))))) # label(thm_2Elist_2EREV__DEF) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5050 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5051 (all A_27a all V0x_2E0 all V1y_2E0 all V2a_2E0 all V3b_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1y_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),V3b_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V3b_2E0) = s(tyop_2Elist_2Elist(A_27a),V1y_2E0) & s(A_27a,V0x_2E0) = s(A_27a,V2a_2E0))) # label(thm_2Elist_2ESNOC__11) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5052 (all A_27a all V1P_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2371_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) # label(def0_2Ethm_2Elist_2ELIST__TO__SET__FILTER) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5053 (all A_27a all V0f_2E0 all V1ls_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))))) # label(thm_2Elist_2ESUM__IMAGE__LIST__TO__SET__upper__bound) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5054 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5055 (all A_27b all X0_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5056 (all A_27a ((all V0e_2E0 all V1n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V5e_2E0 all V6n_2E0 all V7x_2E0 all V8l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_2E0)))))) & (all V2e_2E0 all V3x_2E0 all V4l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0)))))) # label(thm_2Elist_2ELUPDATE__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5057 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5058 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5059 (all V0n2_2E0 all V1n1_2E0 all V2a_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,V1n1_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Enum_2Enum,V2a_2E0))))),s(tyop_2Enum_2Enum,V0n2_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E1(s(tyop_2Enum_2Enum,V2a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Enum_2Enum,V0n2_2E0)))))) # label(thm_2Elist_2EGENLIST__PLUS__APPEND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5060 (all A_27a all V0P_2E0 all V1l_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2ENOT__EVERY) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5061 (all A_27a all V0P_2E0 all V1Q_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) & (all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EEVERY__MEM__MONO) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5062 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5063 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f2670_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))),s(A_27c,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Emin_2Ebool,f2670_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0),s(A_27c,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef2670_0_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5064 (all A_27a all V0n_2E0 all V1f_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Elist_2ENULL__GENLIST) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5065 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))))) # label(thm_2Elist_2EUNZIP__ZIP) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5066 (all A_27a all V0n_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Elist_2EHD__GENLIST__COR) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5067 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3E_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5068 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Elist_2ESET__TO__LIST__IN__MEM) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5069 (all A_27a all A_27b all V2P_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,f2676_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0)))))) # label(def0_2Ethm_2Elist_2Eevery__zip__fst) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5070 (all A_27a all V0L_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0L_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),V0L_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EREVERSE__REV) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5071 (all A_27a all V0l_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2ENULL__LENGTH) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5072 (all A_27a all V0n_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> (all V2x_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EEL__SNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5073 (all A_27a all A_27b all V0xs_2E0 all V1t_2E0 all V2h_2E0 all V3R_2E0 ((exists V4h_27_2E0 exists V5t_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V0xs_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4h_27_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V4h_27_2E0))),s(A_27b,V2h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V5t_27_2E0),s(tyop_2Elist_2Elist(A_27b),V1t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h_2E0),s(tyop_2Elist_2Elist(A_27b),V1t_2E0)))))))) # label(thm_2Elist_2ELIST__REL__CONS2) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5074 (all A_27a ((all V0x_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V1x_2E0 all V2x_27_2E0 all V3l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0)))))))) # label(thm_2Elist_2ESNOC) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5075 (all A_27a all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2527_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) # label(thm_2Elist_2EEVERY__NOT__EXISTS) # label(axiom) # label(non_clause). [assumption]. 107.95/107.95 5076 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f2312_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),f2312_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2312_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5077 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2491_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2491_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2491_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5078 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0l_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1f_2E0)))) # label(thm_2Elist_2ELIST__BIND__def) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5079 (all A_27a ((all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) & (all V1l1_2E0 all V2l2_2E0 all V3h_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))))) # label(thm_2Elist_2EAPPEND) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5080 (all A_27a all V0f_2E0 all V1l_2E0 all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0)))) -> s(A_27a,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V0f_2E0),s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) # label(thm_2Elist_2EFOLDL__EQ__FOLDR) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5081 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2637_0_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2637_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2637_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5082 (all A_27a all A_27b all A_27c all V0f_2E0 all V1ls_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),f2312_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1ls_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1ls_2E0)))))))))) # label(thm_2Elist_2EFOLDL__UNION__BIGUNION__paired) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5083 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27a_29_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5084 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c))),f2405_0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(A_27c,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),f2405_0_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ef2405_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5085 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)))),c_2Elist_2EOPT__MMAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EOPT__MMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5086 (all A_27a ((all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) & (all V1P_2E0 all V2h_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))))))) # label(thm_2Elist_2EEXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5087 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ETL_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5088 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),f2311_0_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),f2311_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),X0_2E0)))) # label(arityeq1_2Ef2311_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5089 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),f2299_1_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),f2299_1_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2299_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 107.95/107.96 5090 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2565_0_2E3(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool))),f2565_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),X2_2E0)))) # label(arityeq3_2Ef2565_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5091 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5092 (all A_27a all V0f_2E0 all V1n_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V2x_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0))))))) # label(thm_2Elist_2EEL__GENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5093 (all A_27a all V0x_2E0 all V1n_2E0 all V2f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) <-> (exists V3m_2E0 (s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V3m_2E0))) = s(A_27a,V0x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Elist_2EMEM__GENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5094 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2Elist_2EsplitAtPki_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EsplitAtPki_2E3_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5095 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elist_2ESUM__ACC_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ESUM__ACC_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5096 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5097 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ECONS_2E0),s(A_27c,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5098 (all A_27a all V0xs_2E0 all V1x_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))))) # label(thm_2Elist_2EDROP__cons) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5099 (all V0ls_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0ls_2E0))) <-> (all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0ls_2E0)))))) -> s(tyop_2Enum_2Enum,V1x_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Elist_2ESUM__eq__0) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5100 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2ELIST__TO__SET__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5101 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2483_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2483_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2483_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5102 (all A_27a all A_27b all V0l_2E0 all V1l_27_2E0 all V2b_2E0 all V3b_27_2E0 all V4f_2E0 all V5f_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0) & s(A_27b,V3b_27_2E0) = s(A_27b,V2b_2E0) & (all V6x_2E0 all V7a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0)))))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V4f_2E0),s(A_27b,V7a_2E0))),s(A_27a,V6x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V5f_27_2E0),s(A_27b,V7a_2E0))),s(A_27a,V6x_2E0))))) -> s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V5f_27_2E0),s(A_27b,V3b_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_27_2E0))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V4f_2E0),s(A_27b,V2b_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2EFOLDL__CONG) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5103 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5104 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),f2288_0_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)))),f2288_0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef2288_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5105 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2589_0_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),f2589_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ef2589_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5106 (all A_27a all V2SET__TO__LIST_2E0 all V3a_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Ecombin_2EI_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2255_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))),s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),V2SET__TO__LIST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0))))))))),s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2EARB_2E0))))) = s(tyop_2Elist_2Elist(A_27a),f2255_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),V2SET__TO__LIST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0)))) # label(def1_2Ethm_2Elist_2ESET__TO__LIST__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5107 (all A_27a all A_27b all A_27c all V0P_2E0 ((all V8f_2E0 all V9v4_2E0 all V10v5_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V8f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V9v4_2E0),s(tyop_2Elist_2Elist(A_27b),V10v5_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))))) & (all V6f_2E0 all V7y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V6f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27c),V7y_2E0))))) & (all V1f_2E0 all V2h1_2E0 all V3t1_2E0 all V4h2_2E0 all V5t2_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0))),s(tyop_2Elist_2Elist(A_27b),V3t1_2E0))),s(tyop_2Elist_2Elist(A_27c),V5t2_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V1f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h1_2E0),s(tyop_2Elist_2Elist(A_27b),V3t1_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h2_2E0),s(tyop_2Elist_2Elist(A_27c),V5t2_2E0)))))))) -> (all V11v_2E0 all V12v1_2E0 all V13v2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V11v_2E0))),s(tyop_2Elist_2Elist(A_27b),V12v1_2E0))),s(tyop_2Elist_2Elist(A_27c),V13v2_2E0))))))) # label(thm_2Elist_2EMAP2__ind) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5108 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),f2255_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a))),f2255_1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2255_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5109 (all A_27a all A_27b all V0f_2E0 all V1b_2E0 all V2l_2E0 s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V2l_2E0),s(A_27b,V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V0f_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))),s(A_27b,V1b_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V0f_2E0),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))) # label(thm_2Elist_2Elist__case__compute) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5110 (all A_27a all V0l1_2E0 all V1x_2E0 all V2l2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2EAPPEND__SNOC) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5111 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5112 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2534_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2534_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2534_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5113 (all A_27a all V0l_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) <-> (exists V1e_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))))) # label(thm_2Elist_2ENOT__NULL__MEM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5114 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5115 (all A_27a all A_27b all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EREVERSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),V0f_2E0)) # label(thm_2Elist_2EREVERSE__o__REVERSE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5116 (all A_27a all V0P_2E0 all V2x_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2527_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Elist_2EEVERY__NOT__EXISTS) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5117 (all A_27a all V0l_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2Enub__set) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5118 (all A_27a all V0t2_2E0 all V1t1_2E0 all V2h2_2E0 all V3h1_2E0 all V4R_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & ((s(A_27a,V2h2_2E0) = s(A_27a,V3h1_2E0) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_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)),V4R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V2h2_2E0))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))) | p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ESHORTLEX__THM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5119 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5120 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ENULL_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5121 (all A_27a all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27c),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27c),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5122 (all A_27a all A_27b all V0xs_2E0 all V1n_2E0 all V2f_2E0 all V3h_2E0 s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3h_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),V0xs_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3h_2E0))),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27a)),V0xs_2E0)))))) # label(thm_2Elist_2ELUPDATE__SOME__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5123 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5124 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),f2466_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))),s(A_27a,X2_2E0))),s(A_27c,X3_2E0))) = s(tyop_2Emin_2Ebool,f2466_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0),s(A_27a,X2_2E0),s(A_27c,X3_2E0)))) # label(arityeq4_2Ef2466_1_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5125 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5126 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,f2598_1_2E3(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),f2598_1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef2598_1_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5127 (all A_27a all A_27b all A_27c all V0f_2E0 all V1xs_2E0 all V2ys_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0),s(tyop_2Elist_2Elist(A_27b),V2ys_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2ys_2E0)))))) # label(thm_2Elist_2ELENGTH__MAP2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5128 (all A_27a all A_27b all V0t_2E0 all V1h_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V1h_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))))) # label(thm_2Elist_2ELIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5129 (all A_27a ((all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) & (all V5l_2E0 all V6n1_2E0 all V7n2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V6n1_2E0),s(tyop_2Enum_2Enum,V7n2_2E0))) <-> (exists V8l1_2E0 exists V9l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V9l2_2E0))) = s(tyop_2Enum_2Enum,V7n2_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V8l1_2E0),s(tyop_2Elist_2Elist(A_27a),V9l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V5l_2E0) & s(tyop_2Enum_2Enum,V6n1_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V8l1_2E0))))))) & (all V1l_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))) <-> (exists V3h_2E0 exists V4l_27_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))) & s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))))))))) # label(thm_2Elist_2ELENGTH__EQ__NUM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5130 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Elist_2EsplitAtPki_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EsplitAtPki_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5131 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5132 (all A_27a all V0t_2E0 (p(s(tyop_2Emin_2Ebool,f2425_0_2E1(s(tyop_2Elist_2Elist(A_27a),V0t_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),V0t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(def0_2Ethm_2Elist_2ELAST__CONS__cond) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5133 (all A_27a all V0P_2E0 all V1n_2E0 ((all V3l_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0) -> (all V4x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))))) <-> (all V2l_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))) # label(thm_2Elist_2ELENGTH__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5134 (all A_27a all V0f_2E0 all V2a_2E0 all V3e_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2a_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3e_2E0))))) = s(tyop_2Enum_2Enum,f2317_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V2a_2E0),s(A_27a,V3e_2E0)))) # label(def0_2Ethm_2Elist_2ESUM__MAP__FOLDL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5135 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0)) # label(thm_2Elist_2EREVERSE__REVERSE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5136 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),f2328_0_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)))),f2328_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0)))) # label(arityeq2_2Ef2328_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5137 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27c_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5138 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5139 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5140 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2255_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,f2255_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2255_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5141 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Elist_2EWF__SHORTLEX) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5142 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 all V2f_2E0 all V3f_27_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_27_2E0),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4x_2E0))))) & s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) -> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) # label(thm_2Elist_2EMAP__CONG) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5143 (all A_27a all A_27b all V0f_2E0 all V1ls_2E0 all V2a_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),f2493_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Elist_2Elist(A_27b),V2a_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Elist_2Elist(A_27b),V2a_2E0)))) # label(thm_2Elist_2EFOLDR__CONS) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5144 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5145 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2527_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2527_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2527_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5146 (all A_27a exists V0rep_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),f2267_0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),V0rep_2E0))))) # label(thm_2Elist_2Elist__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5147 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5148 (all A_27a all V0c_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f2533_0_2E2(s(tyop_2Emin_2Ebool,V0c_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,V0c_2E0)) # label(def0_2Ethm_2Elist_2EEVERY__SIMP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5149 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),c_2Elist_2ECONS_2E0),s(tyop_2Eone_2Eone,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ECONS_2E2(s(tyop_2Eone_2Eone,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5150 (all A_27a all A_27b all V0P_2E0 all V1f_2E0 all V2l_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2530_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) # label(thm_2Elist_2EEXISTS__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5151 (all A_27a all A_27b all V0t_2E0 all V1l_2E0 all V2h_2E0 all V3f_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) <-> (exists V4x0_2E0 exists V5t0_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x0_2E0),s(tyop_2Elist_2Elist(A_27a),V5t0_2E0))) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V4x0_2E0))) = s(A_27b,V2h_2E0) & s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V5t0_2E0))) = s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) # label(thm_2Elist_2EMAP__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5152 (all A_27a all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> (all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2e_2E0)))))))) # label(thm_2Elist_2EEVERY__MEM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5153 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Elist_2EINDEX__OF_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Elist_2EINDEX__OF_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EINDEX__OF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5154 (all A_27a all V0ys_2E0 all V1x_2E0 all V2i_2E0 all V3k_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V1x_2E0),s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2589_0_2E3(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))),s(A_27a,V1x_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))) # label(thm_2Elist_2EEL__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5155 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),f2328_0_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)))),f2328_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef2328_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5156 (all A_27a all V0l_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2ETAKE__LENGTH__TOO__LONG) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5157 (all A_27a (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & (all V0h_2E0 all V1t_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))))) # label(thm_2Elist_2EREVERSE__DEF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5158 (all A_27a all V1t_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1t_2E0) <-> p(s(tyop_2Emin_2Ebool,f2260_0_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) # label(def0_2Ethm_2Elist_2EFRONT__DEF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5159 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5160 (all A_27a all V0f_2E0 all V1ls_2E0 s(tyop_2Enum_2Enum,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),f2317_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) # label(thm_2Elist_2ESUM__MAP__FOLDL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5161 (all A_27a ((all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) & (all V1x_2E0 all V2y_2E0 all V3z_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3z_2E0))))))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3z_2E0)))))))) # label(thm_2Elist_2ELAST__CONS) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5162 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ELLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELLEX_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5163 (all A_27a all A_27b all A_27c all V0l_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V0l_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1g_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0)))))) # label(thm_2Elist_2ELIST__BIND__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5164 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> (all V1l_2E0 all V2s_2E0 ((all V3d_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V3d_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0)))) -> s(tyop_2Enum_2Enum,V1l_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3d_2E0))))) & (exists V4a_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0))))) -> (exists V5b_2E0 ((all V6c_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6c_2E0),s(tyop_2Elist_2Elist(A_27a),V5b_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V6c_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),V5b_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V2s_2E0)))))))))) # label(thm_2Elist_2EWF__SHORTLEX__same__lengths) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5165 (all A_27a all V0xs_2E0 all V1x_2E0 all V2n_2E0 all V3m_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V3m_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) -> s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) # label(thm_2Elist_2EoEL__TAKE__E) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5166 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.96 5167 (all A_27a all V0x_2E0 all V1xs_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0)))))))) # label(thm_2Elist_2ELENGTH__FRONT__CONS) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5168 (all A_27a all V0e_2E0 all V1L_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V0e_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EUNIQUE__FILTER) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5169 (all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f2670_1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2670_1_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0)))) # label(arityeq2_2Ef2670_1_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5170 (all A_27a all V0P_2E0 all V1L_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))))))))) # label(thm_2Elist_2EMEM__FILTER) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5171 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EOPT__MMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EOPT__MMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5172 (all A_27a all V0l_2E0 all V1P_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EFILTER__REVERSE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5173 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5174 (all A_27a all V0n_2E0 all V1f_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Elist_2EGENLIST__NUMERALS) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5175 (all A_27a all V1x_2E0 s(A_27a,f2548_0_2E1(s(A_27a,V1x_2E0))) = s(A_27a,V1x_2E0)) # label(def0_2Ethm_2Elist_2EMAP__ID) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5176 (all A_27a all V0y_2E0 all V1x_2E0 all V2R2_2E0 all V3R1_2E0 ((all V4x_2E0 all V5y_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)),V3R1_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0))))))) # label(thm_2Elist_2ESHORTLEX__MONO) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5177 (all A_27a all V0xs_2E0 all V1n_2E0 all V2m_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0)))) # label(thm_2Elist_2EoEL__DROP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5178 (all A_27a all A_27b all V0xs_2E0 all V1t_2E0 all V2h_2E0 all V3R_2E0 ((exists V4h_27_2E0 exists V5t_27_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_27_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_27_2E0))) = s(tyop_2Elist_2Elist(A_27b),V0xs_2E0) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_27_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V2h_2E0))),s(A_27b,V4h_27_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Elist_2Elist(A_27b),V0xs_2E0)))))) # label(thm_2Elist_2ELIST__REL__CONS1) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5179 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),c_2Elist_2Elist__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2Elist__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2Elist__size_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5180 (all A_27a all A_27b all A_27c all V3R_2E0 all V2f_2E0 all V6a_2E0 all V7b_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V6a_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(A_27c,V7b_2E0))))) = s(tyop_2Emin_2Ebool,f2466_1_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(A_27a,V6a_2E0),s(A_27c,V7b_2E0)))) # label(def0_2Ethm_2Elist_2ELIST__REL__MAP2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5181 (all A_27a all A_27b all V0R_2E0 all V1a0_2E0 all V2a1_2E0 ((exists V3h1_2E0 exists V4h2_2E0 exists V5t1_2E0 exists V6t2_2E0 (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h2_2E0),s(tyop_2Elist_2Elist(A_27b),V6t2_2E0))) = s(tyop_2Elist_2Elist(A_27b),V2a1_2E0) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V5t1_2E0),s(tyop_2Elist_2Elist(A_27b),V6t2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3h1_2E0))),s(A_27b,V4h2_2E0)))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V5t1_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1a0_2E0))) | s(tyop_2Elist_2Elist(A_27a),V1a0_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & s(tyop_2Elist_2Elist(A_27b),V2a1_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1a0_2E0),s(tyop_2Elist_2Elist(A_27b),V2a1_2E0)))))) # label(thm_2Elist_2ELIST__REL__cases) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5182 (all A_27a all V0l_2E0 all V1R_2E0 -p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2ESHORTLEX__NIL2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5183 (all A_27a all V0l1_2E0 all V1l2_2E0 all V2l3_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l3_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l3_2E0)))) # label(thm_2Elist_2EAPPEND__ASSOC) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5184 (all A_27a all V0P_2E0 all V1ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))))) # label(thm_2Elist_2EHD__dropWhile) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5185 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)))),c_2Elist_2ECONS_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5186 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0)))))) # label(thm_2Elist_2EMAP__o) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5187 (all A_27a all A_27b all X0_2E0 s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5188 (all A_27a all V1l2_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,f2635_0_2E2(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0),s(A_27a,V2x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))) # label(def0_2Ethm_2Elist_2Enub__append) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5189 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0)))) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5190 (all A_27a all V0h1_2E0 all V1h2_2E0 (s(A_27a,V1h2_2E0) = s(A_27a,V0h1_2E0) -> (all V2l1_2E0 all V3l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V3l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))))))) # label(thm_2Elist_2EEQ__LIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5191 (all A_27a p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),f2473_0_2E0))))) # label(thm_2Elist_2EWF__LIST__PRED) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5192 (all A_27a all A_27b all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d))),f2448_1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),f2448_1_2E1(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0)))) # label(arityeq1_2Ef2448_1_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5193 (all V1n_2E0 (p(s(tyop_2Emin_2Ebool,f2479_0_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V1n_2E0))) # label(def0_2Ethm_2Elist_2EEL__compute) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5194 (all A_27a all V0xs_2E0 all V1n_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0)))) # label(thm_2Elist_2EoEL__THM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5195 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDIFF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5196 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5197 (all A_27a all V0f_2E0 ((exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5198 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5199 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2530_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2530_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef2530_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5200 (all A_27a all V0f_2E0 all V1P_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) <-> (exists V3i_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V3i_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Elist_2EEXISTS__GENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5201 (all A_27a all A_27b all V0R_2E0 all V1LIST__REL_27_2E0 ((all V2h1_2E0 all V3h2_2E0 all V4t1_2E0 all V5t2_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2h1_2E0))),s(A_27b,V3h2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h2_2E0),s(tyop_2Elist_2Elist(A_27b),V5t2_2E0)))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) -> (all V6a0_2E0 all V7a1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),V1LIST__REL_27_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0))),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))))))) # label(thm_2Elist_2ELIST__REL__strongind) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5202 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f2598_1_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),f2598_1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ef2598_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5203 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))))) # label(thm_2Elist_2ESHORTLEX__total) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5204 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2635_0_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2Enub__append) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5205 (all V1n_2E0 (s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,f2301_0_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(def0_2Ethm_2Elist_2EoEL__def) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5206 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5207 (all A_27a all V0l_2E0 all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) # label(thm_2Elist_2EMEM__REVERSE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5208 (all A_27b all X0_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ETL_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5209 (all A_27a all V0R_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))))) # label(thm_2Elist_2ESHORTLEX__LENGTH__LE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5210 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,V2n_2E0) -> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),f2328_0_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))))))) # label(thm_2Elist_2EZIP__GENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5211 (all A_27a ((all V0l1_2E0 all V1l2_2E0 all V2l3_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l3_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V2l3_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) & (all V3l1_2E0 all V4l2_2E0 all V5l3_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5l3_2E0),s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),V5l3_2E0) = s(tyop_2Elist_2Elist(A_27a),V4l2_2E0))))) # label(thm_2Elist_2EAPPEND__11) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5212 (all A_27a all A_27b all V2P_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0))))) = s(tyop_2Emin_2Ebool,f2675_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3x_2E0)))) # label(def0_2Ethm_2Elist_2Eevery__zip__snd) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5213 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Elist_2ESHORTLEX__transitive) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5214 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5215 (all A_27a all A_27b all V0f_2E0 all V1l1_2E0 all V2l2_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2EMAP__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5216 (all A_27a all V0R_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) # label(thm_2Elist_2ELENGTH__LT__SHORTLEX) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5217 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28A_27c_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5218 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5219 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etotal_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etotal_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etotal_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5220 (all A_27a all V0l_2E0 all V1P_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & (all V3h_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3h_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) & (all V2h_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))))) # label(thm_2Elist_2EFILTER__COND__REWRITE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5221 (all A_27a all A_27b all V0P_2E0 all V1f_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Emin_2Ebool,f2534_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Elist_2EEVERY__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5222 (all A_27a all A_27b all V3R_2E0 all V4a_2E0 all V5b_2E0 s(tyop_2Emin_2Ebool,f2466_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V4a_2E0),s(A_27b,V5b_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0)))) # label(def1_2Ethm_2Elist_2ELIST__REL__MAP2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5223 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f2403_0_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0),s(A_27a,X2_2E0),s(A_27c,X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),f2403_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))),s(A_27a,X2_2E0))),s(A_27c,X3_2E0)))) # label(arityeq4_2Ef2403_0_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5224 (all A_27a all V0x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),V0x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2EisPREFIX__NILR) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5225 (all A_27a all V0x_2E0 all V1ls_2E0 all V2n_2E0 (s(A_27a,V0x_2E0) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))))) # label(thm_2Elist_2EMEM__DROP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5226 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5227 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f2313_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2313_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2313_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5228 (all A_27a all V0ls_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) -> s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))) # label(thm_2Elist_2ELAST__REVERSE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5229 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ESET__TO__LIST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ESET__TO__LIST_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5230 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5231 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))))),f2312_1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),f2312_1_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X1_2E0)))) # label(arityeq2_2Ef2312_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5232 (all A_27a all V0P_2E0 all V1ls_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))) # label(thm_2Elist_2EMEM__dropWhile__IMP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5233 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EFIND_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Elist_2EFIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EFIND_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5234 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2527_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2527_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2527_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5235 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Elist_2ELRC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ec_2Elist_2ELRC_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5236 (all A_27a all V0P1_2E0 all V1P2_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))) # label(thm_2Elist_2EEVERY__FILTER__IMP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5237 (all A_27a all V0m2_2E0 all V1m1_2E0 all V2l2_2E0 all V3l1_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) <-> (exists V5l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5l_2E0),s(tyop_2Elist_2Elist(A_27a),V0m2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) & s(tyop_2Elist_2Elist(A_27a),V1m1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) | (exists V4l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V3l1_2E0) & s(tyop_2Elist_2Elist(A_27a),V0m2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))))) # label(thm_2Elist_2EAPPEND__EQ__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5238 (all A_27a all A_27b all V0ls_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),f2310_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) # label(thm_2Elist_2EMAP__ZIP__SAME) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5239 (all A_27a all V0f_2E0 all V2b_2E0 all V3t_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3t_2E0),s(tyop_2Enum_2Enum,V2b_2E0))))) = s(A_27a,f2332_0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V3t_2E0)))) # label(def0_2Ethm_2Elist_2EGENLIST__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5240 (all X0_2E0 s(tyop_2Emin_2Ebool,f2479_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2479_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef2479_0_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5241 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5242 (all A_27a all A_27b all V0xs2_2E0 all V1P_2E0 all V2xs1_2E0 all V3zs_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27b),V3zs_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0)))))) <-> (exists V4ys1_2E0 exists V5ys2_2E0 (s(tyop_2Elist_2Elist(A_27b),V3zs_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27b),V4ys1_2E0),s(tyop_2Elist_2Elist(A_27a),V2xs1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys2_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs2_2E0)))))))) # label(thm_2Elist_2ELIST__REL__SPLIT2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5243 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFRONT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EFRONT_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5244 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) -> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2EMAP__TL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5245 (all A_27a all V0x_2E0 all V1l_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__SNOC) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5246 (all A_27a all V0l_2E0 all V1n_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2479_0_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2EEL__compute) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5247 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5248 (all A_27a all V0ls_2E0 p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))) # label(thm_2Elist_2ECARD__LIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5249 (all A_27a all V0xs_2E0 all V1x_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))))) # label(thm_2Elist_2ETAKE__cons) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5250 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2526_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2526_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2526_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5251 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5252 (all A_27a all V0P_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) <-> (all V1l_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2ELENGTH__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5253 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5254 (all A_27a all A_27b all V0f_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Elist_2Elist(A_27b),V4y_2E0))) = s(tyop_2Elist_2Elist(A_27b),f2493_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27b),V4y_2E0)))) # label(def0_2Ethm_2Elist_2EFOLDR__CONS) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5255 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),f2299_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),f2299_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2299_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5256 (all A_27a all V0ls_2E0 all V1n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__DROP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5257 (all A_27a all A_27b all V0f_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) -> (s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l2_2E0) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))) # label(thm_2Elist_2EINJ__MAP__EQ__IFF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5258 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),f2317_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),f2317_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ef2317_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5259 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5260 (all V0l1_2E0 all V1l2_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0l1_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0l1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l2_2E0)))))) # label(thm_2Elist_2ESUM__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5261 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))))))) # label(thm_2Elist_2EALL__DISTINCT__ZIP__SWAP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.97 5262 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5263 (all A_27a all V0list_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Ebool)),V0list_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0))))))) # label(thm_2Elist_2Edatatype__list) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5264 (all A_27a all A_27b all V0l2_2E0 all V1l1_2E0 all V2l_2E0 all V3f_2E0 ((exists V4l10_2E0 exists V5l20_2E0 (s(tyop_2Elist_2Elist(A_27b),V0l2_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V5l20_2E0))) & s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V4l10_2E0))) = s(tyop_2Elist_2Elist(A_27b),V1l1_2E0) & s(tyop_2Elist_2Elist(A_27a),V2l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l10_2E0),s(tyop_2Elist_2Elist(A_27a),V5l20_2E0))))) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) # label(thm_2Elist_2EMAP__EQ__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5265 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5266 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5267 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5268 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5269 (all A_27a all A_27b all V0f_2E0 all V3s_2E0 all V4x_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27a,V4x_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2313_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0),s(A_27a,V4x_2E0)))) # label(def0_2Ethm_2Elist_2EFOLDL__UNION__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5270 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),f2643_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),f2643_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ef2643_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5271 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2258_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f2258_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef2258_0_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5272 (all A_27a all A_27b all A_27c all V0f_2E0 all V1ts_2E0 all V2tt_2E0 all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EMIN_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ts_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2tt_2E0)))))))) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ts_2E0))))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27b),V2tt_2E0))))) = s(A_27c,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ts_2E0),s(tyop_2Elist_2Elist(A_27b),V2tt_2E0))))))) # label(thm_2Elist_2EEL__MAP2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5273 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5274 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2468_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2468_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2468_1_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5275 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 ((s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) & (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2EMAP__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5276 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),c_2Elist_2ELUPDATE_2E3(s(tyop_2Eoption_2Eoption(A_27b),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b))))),c_2Elist_2ELUPDATE_2E0),s(tyop_2Eoption_2Eoption(A_27b),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELUPDATE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5277 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5278 (all A_27a all A_27b all A_27c all V3s_2E0 all V0f_2E0 all V4x_2E0 all V5y_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f2312_1_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0),s(A_27a,V4x_2E0),s(A_27b,V5y_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))) # label(def0_2Ethm_2Elist_2EFOLDL__UNION__BIGUNION__paired) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5279 (all A_27a all V0s_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) <-> p(s(tyop_2Emin_2Ebool,f2370_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(def0_2Ethm_2Elist_2ESET__TO__LIST__THM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5280 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27d_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5281 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27b),f2493_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),f2493_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ef2493_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5282 (all A_27c all A_27d all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5283 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5284 (all A_27a all V0x_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESET__TO__LIST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2ESET__TO__LIST__SING) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5285 (all A_27a all V0l_2E0 all V1x_2E0 all V2y_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2y_2E0),s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) -> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))) # label(thm_2Elist_2EMEM__LUPDATE__E) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5286 (all A_27a ((all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) & (all V4l1_2E0 all V5l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V5l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27a),V4l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27a),V5l2_2E0))))) & (all V6l1_2E0 all V7l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V6l1_2E0) <-> s(tyop_2Elist_2Elist(A_27a),V7l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V6l1_2E0),s(tyop_2Elist_2Elist(A_27a),V7l2_2E0))))) & (all V2l1_2E0 all V3l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V3l2_2E0) <-> s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EAPPEND__EQ__SELF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5287 (all A_27d all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27d),c_2Elist_2ECONS_2E2(s(A_27d,X0_2E0),s(tyop_2Elist_2Elist(A_27d),X1_2E0))) = s(tyop_2Elist_2Elist(A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27d))),c_2Elist_2ECONS_2E0),s(A_27d,X0_2E0))),s(tyop_2Elist_2Elist(A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5288 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5289 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5290 (all A_27a ((all V2e_2E0 all V3x_2E0 all V4l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2e_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_2E0)))))) & (all V5e_2E0 all V6n_2E0 all V7x_2E0 all V8l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V8l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V5e_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7x_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_2E0)))))) & (all V9e_2E0 all V10n_2E0 all V11x_2E0 all V12l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V11x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V9e_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V12l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V9e_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V11x_2E0),s(tyop_2Elist_2Elist(A_27a),V12l_2E0)))))) & (all V0e_2E0 all V1n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2ELUPDATE__compute) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5291 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5292 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5293 (all A_27a all V0a1_2E0 all V1a0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1a0_2E0),s(tyop_2Elist_2Elist(A_27a),V0a1_2E0)))) # label(thm_2Elist_2ENOT__NIL__CONS) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5294 (all A_27a all V1h_2E0 all V2v1_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1h_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),f2300_0_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2v1_2E0)))) # label(def0_2Ethm_2Elist_2EoHD__def) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5295 (all A_27a all A_27b all A_27c all V0g2_2E0 all V1g1_2E0 all V2f2_2E0 all V3f1_2E0 all V4xs_2E0 all V5ys_2E0 (s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f2_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0g2_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f1_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))))) <-> s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V3f1_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f2_2E0),s(tyop_2Elist_2Elist(A_27a),V4xs_2E0))) & s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0g2_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g1_2E0),s(tyop_2Elist_2Elist(A_27b),V5ys_2E0))))) # label(thm_2Elist_2EMAP__APPEND__MAP__EQ) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5296 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27b_29_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5297 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2ECOMM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5298 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2t_2E0 (s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),f2454_0_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))))) & s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EUNZIP__THM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5299 (all A_27b all V0l_2E0 all V2P_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,f2598_0_2E3(s(tyop_2Elist_2Elist(A_27b),V0l_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,V3i_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V0l_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,V3i_2E0))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0)))))))) # label(def0_2Ethm_2Elist_2EsplitAtPki__EQN) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5300 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5301 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 all V2n_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Elist_2EMAP__GENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5302 (all A_27a all V0P_2E0 all V1ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EdropWhile_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2EdropWhile__eq__nil) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5303 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5304 (all A_27a all V4t1_2E0 all V2R_2E0 all V3h1_2E0 all V6h2_2E0 all V7t2_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4t1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2294_1_2E2(s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(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)),V2R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2294_2_2E2(s(A_27a,V3h1_2E0),s(A_27a,V6h2_2E0))),s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))))) = s(tyop_2Emin_2Ebool,f2294_0_2E5(s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3h1_2E0),s(A_27a,V6h2_2E0),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0)))) # label(def2_2Ethm_2Elist_2ESHORTLEX__def) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5305 (all A_27a all V0a1_2E0 all V1a0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1a0_2E0),s(tyop_2Elist_2Elist(A_27a),V0a1_2E0)))) # label(thm_2Elist_2Elist__distinct) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5306 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),f2300_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),f2300_0_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ef2300_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5307 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f2598_0_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2598_0_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef2598_0_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5308 (all A_27a all V0P_2E0 all V1L_2E0 all V2M_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2M_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1L_2E0),s(tyop_2Elist_2Elist(A_27a),V2M_2E0)))))) # label(thm_2Elist_2EFILTER__APPEND__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5309 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EINDEX__FIND_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Elist_2EINDEX__FIND_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EINDEX__FIND_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5310 (all A_27a all V0f_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Elist_2ELENGTH__GENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5311 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eprim__rec_2EPRE_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5312 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5313 (all A_27a all V7n_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),f2267_2_2E1(s(tyop_2Enum_2Enum,V7n_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0)) # label(def0_2Ethm_2Elist_2Elist__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5314 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5315 (all A_27a all V0c_2E0 all V1n_2E0 all V2s_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2s_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V0c_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2s_2E0))))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__RIGHT_2E3(s(A_27a,V0c_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2s_2E0)))) # label(thm_2Elist_2EPAD__RIGHT) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5316 (all A_27a all A_27b all V0a_2E0 all V1b_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0a_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1b_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0a_2E0)))))) -> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0a_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27b),V1b_2E0))))))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0a_2E0),s(tyop_2Elist_2Elist(A_27b),V1b_2E0))))))))) # label(thm_2Elist_2EZIP__DROP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5317 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 s(tyop_2Emin_2Ebool,f2295_0_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0),s(A_27a,X3_2E0),s(tyop_2Elist_2Elist(A_27a),X4_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),f2295_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))),s(A_27a,X3_2E0))),s(tyop_2Elist_2Elist(A_27a),X4_2E0)))) # label(arityeq5_2Ef2295_0_2E5_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5318 (all A_27a all V0x_2E0 all V1n_2E0 all V2ys_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2ys_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2ys_2E0)))))) # label(thm_2Elist_2ELENGTH__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5319 (all A_27a all A_27b all V1x_2E0 all V0y_2E0 all V3L1_2E0 all V4L2_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V3L1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0y_2E0),s(tyop_2Elist_2Elist(A_27b),V4L2_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),f2454_0_2E4(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0),s(tyop_2Elist_2Elist(A_27a),V3L1_2E0),s(tyop_2Elist_2Elist(A_27b),V4L2_2E0)))) # label(def0_2Ethm_2Elist_2EUNZIP__THM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5320 (all A_27a all V0n_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0)) # label(thm_2Elist_2ETAKE__DROP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5321 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f2332_0_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),f2332_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2332_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5322 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5323 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5324 (all A_27a all V0l1_2E0 all V1l2_2E0 all V2n_2E0 s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2EEL__APPEND__EQN) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5325 (all A_27a ((all V0x_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2Enub__def) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5326 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V0l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),V0l_2E0)))))) # label(thm_2Elist_2EMAP__FLAT) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5327 (all A_27a all X0_2E0 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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5328 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5329 (all A_27a ((all V0f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (all V1f_2E0 all V2n_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Elist_2EGENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5330 (all A_27a all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) # label(thm_2Elist_2ESWAP__REVERSE__SYM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5331 (all A_27a all V0R_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_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)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_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)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))))) -> (all V4x_2E0 all V5y_2E0 all V6z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V5y_2E0),s(tyop_2Elist_2Elist(A_27a),V6z_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V6z_2E0)))))))) # label(thm_2Elist_2EEVERY2__trans) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5332 (all A_27a all A_27b all V0l_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0)))))) # label(thm_2Elist_2EZIP__UNZIP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5333 (all A_27b all X0_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),c_2Elist_2ELAST_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5334 (all A_27a all V0a0_2E0 all V1a1_2E0 all V2a0_27_2E0 all V3a1_27_2E0 (s(A_27a,V0a0_2E0) = s(A_27a,V2a0_27_2E0) & s(tyop_2Elist_2Elist(A_27a),V1a1_2E0) = s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0a0_2E0),s(tyop_2Elist_2Elist(A_27a),V1a1_2E0))))) # label(thm_2Elist_2ECONS__11) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5335 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2ELENGTH__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5336 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2534_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2534_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef2534_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5337 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5338 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2EOPTION__MAP_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5339 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27a)))),c_2Elist_2EFOLDL2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))),s(tyop_2Elist_2Elist(A_27c),X3_2E0))) = s(A_27a,c_2Elist_2EFOLDL2_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0),s(tyop_2Elist_2Elist(A_27c),X3_2E0)))) # label(arityeq4_2Ec_2Elist_2EFOLDL2_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5340 (all A_27a all A_27b all A_27c ((all V5y_2E0 all V6f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V6f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27c),V5y_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (all V7v5_2E0 all V8v4_2E0 all V9f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V9f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V8v4_2E0),s(tyop_2Elist_2Elist(A_27b),V7v5_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0)))) & (all V0t2_2E0 all V1t1_2E0 all V2h2_2E0 all V3h1_2E0 all V4f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V4f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h1_2E0),s(tyop_2Elist_2Elist(A_27b),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V2h2_2E0),s(tyop_2Elist_2Elist(A_27c),V0t2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V4f_2E0),s(A_27b,V3h1_2E0))),s(A_27c,V2h2_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V4f_2E0),s(tyop_2Elist_2Elist(A_27b),V1t1_2E0),s(tyop_2Elist_2Elist(A_27c),V0t2_2E0)))))))) # label(thm_2Elist_2EMAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5341 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5342 (all A_27a all V0l_2E0 all V1m_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,V1m_2E0) -> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2ETAKE__LENGTH__ID__rwt) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5343 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5344 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5345 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 all V3x_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),f2328_0_2E3(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0),s(tyop_2Enum_2Enum,V3x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1f_2E0),s(tyop_2Enum_2Enum,V3x_2E0)))))) # label(def0_2Ethm_2Elist_2EZIP__GENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5346 (all A_27a all V0x_2E0 p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))))) # label(thm_2Elist_2EALL__DISTINCT__SING) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5347 (all A_27a ((all V3e_2E0 all V4n_2E0 all V5l_2E0 all V6p_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6p_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l_2E0)))))) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V6p_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V3e_2E0),s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2588_0_2E2(s(tyop_2Enum_2Enum,V6p_2E0),s(tyop_2Enum_2Enum,V4n_2E0))),s(A_27a,V3e_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V6p_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))))) & (all V0e_2E0 all V1n_2E0 all V2l_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0e_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))) # label(thm_2Elist_2ELUPDATE__SEM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5348 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0)))) # label(thm_2Elist_2ESINGL__APPLY__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5349 (all A_27a all A_27b all A_27c ((all V1n_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)) & (all V3n_2E0 all V4h_2E0 all V5t_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27c),V5t_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4h_2E0),s(tyop_2Elist_2Elist(A_27c),V5t_2E0)))))) & (all V6n_2E0 all V7h_2E0 all V8t_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V7h_2E0),s(tyop_2Elist_2Elist(A_27c),V8t_2E0))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Elist_2Elist(A_27c),V8t_2E0)))) & (all V2n_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) & (all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EDROP__compute) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5350 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),f2254_0_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),f2254_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ef2254_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5351 (all A_27a all V0f_2E0 all V1P_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) <-> (all V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V3i_2E0)))))))))) # label(thm_2Elist_2EEVERY__GENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5352 (all A_27a all A_27b all V0f_2E0 all V1ls_2E0 all V2n_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(A_27b,f2657_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(def0_2Ethm_2Elist_2EGENLIST__EL__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.98 5353 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2670_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f2670_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0)))) # label(arityeq2_2Ef2670_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5354 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5355 (all A_27a all V0P_2E0 ((all V1l_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) -> (all V2a_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) -> (all V3l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))) # label(thm_2Elist_2Elist__induction) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5356 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2598_0_2E3(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),f2598_0_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef2598_0_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5357 (all A_27a all A_27d all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27a_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5358 (all A_27a all V0ls_2E0 all V1f_2E0 all V2n_2E0 (s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) & (all V3i_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3i_2E0))))) -> s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))))) # label(thm_2Elist_2EGENLIST__EL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5359 (all A_27a all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) != s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) -> (all V2h1_2E0 all V3h2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) # label(thm_2Elist_2ELIST__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5360 (all A_27a all A_27b all A_27c all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) -> (all V2f_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0)))))) # label(thm_2Elist_2EMAP2__ZIP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5361 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5362 (all A_27a all V0xs_2E0 all V1i_2E0 all V2n_2E0 all V3x_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2709_0_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V3x_2E0),s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0)))))) # label(thm_2Elist_2EoEL__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5363 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5364 (all A_27a all A_27b all V1k_2E0 all V0l_2E0 all V4i_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,V4i_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))))) = s(A_27a,f2598_1_2E3(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),V1k_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0),s(tyop_2Enum_2Enum,V4i_2E0)))) # label(def1_2Ethm_2Elist_2EsplitAtPki__EQN) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5365 (all A_27a all V0l_2E0 all V1R_2E0 -p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2ELLEX__NIL2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5366 (all A_27a all A_27b all V0R_2E0 ((all V1h1_2E0 all V2h2_2E0 all V3t1_2E0 all V4t2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V3t1_2E0),s(tyop_2Elist_2Elist(A_27b),V4t2_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1h1_2E0))),s(A_27b,V2h2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h1_2E0),s(tyop_2Elist_2Elist(A_27a),V3t1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h2_2E0),s(tyop_2Elist_2Elist(A_27b),V4t2_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ELIST__REL__rules) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5367 (all A_27a all V0l_2E0 (s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) # label(thm_2Elist_2ELENGTH__NIL__SYM) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5368 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),f2604_0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2EI_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0l_2E0))))) # label(thm_2Elist_2ELIST__BIND__ID) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5369 (all A_27a all V0y_2E0 all V1x_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) | s(A_27a,V1x_2E0) = s(A_27a,V0y_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))))) # label(thm_2Elist_2EMEM__SNOC) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5370 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5371 (all A_27a all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2491_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) # label(thm_2Elist_2EFILTER__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5372 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__APPLY_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__APPLY_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5373 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__IGNORE__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__IGNORE__BIND_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__IGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5374 (all A_27a all A_27b (s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) & (all V0x_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))) # label(thm_2Elist_2EREVERSE__SNOC__DEF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5375 (all A_27a all V0x_2E0 all V1n_2E0 all V2l1_2E0 all V3l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0)))))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))))))) # label(thm_2Elist_2Elupdate__append) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5376 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ESHORTLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ESHORTLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ESHORTLEX_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5377 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Elist_2ESUM_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ESUM_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5378 (all A_27a all V0l_2E0 all V1n1_2E0 all V2n2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n2_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) -> (s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n2_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1n1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) <-> s(tyop_2Enum_2Enum,V2n2_2E0) = s(tyop_2Enum_2Enum,V1n1_2E0)))) # label(thm_2Elist_2EALL__DISTINCT__EL__IMP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5379 (all A_27a all V1t_2E0 (s(tyop_2Elist_2Elist(A_27a),V1t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> p(s(tyop_2Emin_2Ebool,f2261_0_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))) # label(def0_2Ethm_2Elist_2ELAST__DEF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5380 (all A_27a all A_27b all V0ls_2E0 all V1f_2E0 all V2e_2E0 s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),V1f_2E0),s(A_27b,V2e_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),f2311_0_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b)),V1f_2E0))),s(A_27b,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) # label(thm_2Elist_2EFOLDL__ZIP__SAME) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5381 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b))),f2448_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),f2448_0_2E1(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0)))) # label(arityeq1_2Ef2448_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5382 (all A_27a all V2i_2E0 all V3k_2E0 all V0ys_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))) & s(tyop_2Enum_2Enum,V3k_2E0) = s(tyop_2Enum_2Enum,V2i_2E0) <-> p(s(tyop_2Emin_2Ebool,f2589_0_2E3(s(tyop_2Enum_2Enum,V2i_2E0),s(tyop_2Enum_2Enum,V3k_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))) # label(def0_2Ethm_2Elist_2EEL__LUPDATE) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5383 (all A_27a all A_27b all A_27c all V0l1_2E0 all V1l1_27_2E0 all V2l2_2E0 all V3l2_27_2E0 all V4f_2E0 all V5f_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) & s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0) = s(tyop_2Elist_2Elist(A_27b),V2l2_2E0) & (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V7y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0)))))) -> s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V4f_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))))) -> s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V5f_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V4f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))) # label(thm_2Elist_2EMAP2__CONG) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5384 (all A_27a all A_27b all V0f_2E0 all V1ls_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),f2657_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) # label(thm_2Elist_2EGENLIST__EL__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5385 (all A_27a all V0xs_2E0 all V1x_2E0 all V2y_2E0 all V3ys_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V1x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2y_2E0),s(tyop_2Elist_2Elist(A_27a),V3ys_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V3ys_2E0)))))) # label(thm_2Elist_2ELUPDATE__LENGTH) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5386 (all A_27a all V0P_2E0 all V1l_2E0 all V2l1_2E0 all V3l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))) <-> (exists V4l3_2E0 exists V5l4_2E0 (s(tyop_2Elist_2Elist(A_27a),V3l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V5l4_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V4l3_2E0))) = s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l3_2E0),s(tyop_2Elist_2Elist(A_27a),V5l4_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) # label(thm_2Elist_2EFILTER__EQ__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5387 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5388 (all A_27a all A_27b all V1f_2E0 all V3t0_2E0 all V4h_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),f2299_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V3t0_2E0),s(A_27a,V4h_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V3t0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),f2299_1_2E1(s(A_27a,V4h_2E0)))))) # label(def1_2Ethm_2Elist_2EOPT__MMAP__def) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5389 (all A_27a all V0l2_2E0 all V1l1_2E0 all V2e_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l2_2E0) & s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) | s(tyop_2Elist_2Elist(A_27a),V0l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EAPPEND__EQ__SING) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5390 (all A_27a all V0l_2E0 all V1e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) <-> (exists V2pfx_2E0 exists V3sfx_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2pfx_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3sfx_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2pfx_2E0)))))))))) # label(thm_2Elist_2EMEM__SPLIT__APPEND__first) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5391 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2483_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2483_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2483_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5392 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5393 (all A_27a all A_27b all V0R_2E0 all V1l1_2E0 all V2l2_2E0 ((all V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))) # label(thm_2Elist_2ELIST__REL__EL__EQN) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5394 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5395 (all A_27a all V0a0_2E0 all V1a1_2E0 all V2a0_27_2E0 all V3a1_27_2E0 (s(tyop_2Elist_2Elist(A_27a),V1a1_2E0) = s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0) & s(A_27a,V0a0_2E0) = s(A_27a,V2a0_27_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a0_27_2E0),s(tyop_2Elist_2Elist(A_27a),V3a1_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0a0_2E0),s(tyop_2Elist_2Elist(A_27a),V1a1_2E0))))) # label(thm_2Elist_2Elist__11) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5396 (all V0L_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0L_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0L_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Elist_2ESUM__SUM__ACC) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5397 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Elist_2EoHD_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EoHD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5398 (all A_27a all V1P2_2E0 all V0P1_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,f2483_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(A_27a,V3x_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P2_2E0),s(A_27a,V3x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P1_2E0),s(A_27a,V3x_2E0))))))) # label(def0_2Ethm_2Elist_2EEVERY__FILTER) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5399 (all A_27a all A_27b all V0f_2E0 all V1ls_2E0 all V2n_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) = s(A_27b,f2656_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(def0_2Ethm_2Elist_2EIMAGE__EL__count__LENGTH) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5400 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 all V2P_2E0 all V3k_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERYi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2597_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))),s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))))) -> s(A_27b,c_2Elist_2EsplitAtPki_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3k_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V3k_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) # label(thm_2Elist_2EsplitAtPki__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5401 (all A_27a all A_27b all A_27c all V2f1_2E0 all V4p_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4p_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V4p_2E0))))) = s(tyop_2Epair_2Eprod(A_27c,A_27b),f2448_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V4p_2E0)))) # label(def1_2Ethm_2Elist_2EZIP__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5402 (all A_27a all V0ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))) # label(thm_2Elist_2EALL__DISTINCT__CARD__LIST__TO__SET) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5403 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f2255_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f2255_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2255_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5404 (all A_27a all A_27b all V0l2_2E0 all V1l1_2E0 all V2f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V1l1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0l2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0)))) # label(thm_2Elist_2ELIST__BIND__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5405 (all A_27a all V0a1_2E0 all V1a0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1a0_2E0),s(tyop_2Elist_2Elist(A_27a),V0a1_2E0))) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) # label(thm_2Elist_2ENOT__CONS__NIL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5406 (all A_27a all X0_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),f2267_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),f2267_1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef2267_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5407 (all A_27a ((all V0x_2E0 all V1xs_2E0 (s(tyop_2Elist_2Elist(A_27a),V1xs_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1xs_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) & (all V4x_2E0 all V5xs_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V5xs_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V5xs_2E0)))))))) & (all V2x_2E0 all V3xs_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V3xs_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))))))))) # label(thm_2Elist_2EFRONT__CONS__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5408 (all A_27e all A_27f all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27e),X1_2E0),s(tyop_2Elist_2Elist(A_27f),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27f),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27e),X1_2E0))),s(tyop_2Elist_2Elist(A_27f),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27e_20mono_2EA_27f) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5409 (all A_27a ((all V1P_2E0 all V2h_2E0 all V3t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2h_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))) & (all V0P_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)))) # label(thm_2Elist_2EEVERY__DEF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5410 (all A_27a all V0e_2E0 all V1L_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EUNIQUE_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),V1L_2E0)))) <-> (exists V2L1_2E0 exists V3L2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2L1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3L2_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1L_2E0) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3L2_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2L1_2E0)))))))))) # label(thm_2Elist_2EUNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5411 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EGENLIST__AUX_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EGENLIST__AUX_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5412 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0))) = s(A_27a,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5413 (all A_27a all V0n_2E0 all V1f_2E0 ((all V2m1_2E0 all V3m2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2m1_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) & s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V2m1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V3m2_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3m2_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Enum_2Enum,V3m2_2E0) = s(tyop_2Enum_2Enum,V2m1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Elist_2EALL__DISTINCT__GENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5414 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5415 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),f2657_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27b,f2657_0_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef2657_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5416 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5417 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))))),c_2Elist_2ECONS_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27c_2CA_27a_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27b_2CA_27c_29_2Ctyop_2Emin_2Efun_28A_27b_2CA_27a_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5418 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27c))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5419 (all A_27a all V0l1_2E0 all V1l2_2E0 all V2P_2E0 all V3P_27_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V4x_2E0))))) & s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) -> s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) # label(thm_2Elist_2EEXISTS__CONG) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5420 (all A_27a all V1x_2E0 s(tyop_2Elist_2Elist(A_27a),f2604_0_2E1(s(tyop_2Elist_2Elist(A_27a),V1x_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1x_2E0)) # label(def0_2Ethm_2Elist_2ELIST__BIND__ID) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5421 (all A_27a all A_27b all V0f0_2E0 all V1f1_2E0 exists V2fn_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(A_27b,V0f0_2E0) & (all V3a0_2E0 all V4a1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),V1f1_2E0),s(A_27a,V3a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V4a1_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),V4a1_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),V2fn_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3a0_2E0),s(tyop_2Elist_2Elist(A_27a),V4a1_2E0)))))))) # label(thm_2Elist_2Elist__Axiom) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5422 (all A_27a all V0l1_2E0 all V1l2_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) # label(thm_2Elist_2ELENGTH__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5423 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ELIST__BIND_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELIST__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5424 (all A_27a all A_27b all V0bs_2E0 all V1b_2E0 all V2as_2E0 all V3a_2E0 all V4R_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) & s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1b_2E0),s(tyop_2Elist_2Elist(A_27b),V0bs_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3a_2E0),s(tyop_2Elist_2Elist(A_27a),V2as_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1b_2E0),s(tyop_2Elist_2Elist(A_27b),V0bs_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V3a_2E0))),s(A_27b,V1b_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V2as_2E0),s(tyop_2Elist_2Elist(A_27b),V0bs_2E0))))) & s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3a_2E0),s(tyop_2Elist_2Elist(A_27a),V2as_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(thm_2Elist_2ELIST__REL__def) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5425 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2EDROP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5426 (all A_27a all V0l_2E0 ((all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V1x_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EALL__DISTINCT__FILTER) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5427 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5428 (all A_27a all V0l_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),f2300_0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2EoHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2EoHD__def) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5429 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5430 (all A_27a all V0L1_2E0 all V1L2_2E0 (p(s(tyop_2Emin_2Ebool,f2473_0_2E2(s(tyop_2Elist_2Elist(A_27a),V0L1_2E0),s(tyop_2Elist_2Elist(A_27a),V1L2_2E0)))) <-> (exists V2h_2E0 s(tyop_2Elist_2Elist(A_27a),V1L2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V0L1_2E0)))))) # label(def0_2Ethm_2Elist_2EWF__LIST__PRED) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5431 (all A_27a all A_27b ((all V0f_2E0 all V1e_2E0 s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27b,V1e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(A_27b,V1e_2E0)) & (all V2f_2E0 all V3e_2E0 all V4x_2E0 all V5l_2E0 s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V2f_2E0),s(A_27b,V3e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_2E0))))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V2f_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V2f_2E0),s(A_27b,V3e_2E0))),s(A_27a,V4x_2E0))),s(tyop_2Elist_2Elist(A_27a),V5l_2E0)))))) # label(thm_2Elist_2EFOLDL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5432 (all A_27a (p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & (all V0h_2E0 all V1t_2E0 -p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))))))) # label(thm_2Elist_2ENULL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5433 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2468_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,f2468_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef2468_1_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5434 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5435 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5436 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5437 (all A_27a all A_27b all X0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27a)),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5438 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Erelation_2ERC_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Erelation_2ERC_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERC_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5439 (all A_27a all V0l_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2ELENGTH__NIL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5440 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5441 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27b_29_29) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5442 (all A_27a all A_27b all A_27c all V0xs_2E0 all V1gs_2E0 all V2fs_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),V2fs_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),V1gs_2E0))),s(tyop_2Elist_2Elist(A_27b),V0xs_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27c,A_27a)),V2fs_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27c)),V1gs_2E0),s(tyop_2Elist_2Elist(A_27b),V0xs_2E0)))))) # label(thm_2Elist_2ELIST__APPLY__o) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5443 (all A_27a all V0ls_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) != s(tyop_2Elist_2Elist(A_27a),V0ls_2E0) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) # label(thm_2Elist_2ELAST__EL) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5444 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2526_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2526_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2526_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5445 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2ENULL__EQ) # label(axiom) # label(non_clause). [assumption]. 108.00/107.99 5446 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2536_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2536_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2536_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5447 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5448 (all V0L_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0L_2E0))),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM__ACC_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),V0L_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Elist_2ESUM__ACC__SUM__LEM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5449 (all A_27a all V0e_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))))) # label(thm_2Elist_2EMEM__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5450 (all A_27a (s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) & (all V0h_2E0 all V1t_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0)))))))) # label(thm_2Elist_2ENULL__DEF) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5451 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5452 (all A_27a all A_27b all A_27c all V0f1_2E0 all V1f2_2E0 all V2l1_2E0 all V3l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f2403_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27c),V3l2_2E0)))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),V3l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0),s(tyop_2Elist_2Elist(A_27c),V3l2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))))) # label(thm_2Elist_2EMAP__EQ__EVERY2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5453 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),f2332_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,f2332_0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef2332_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5454 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) # label(thm_2Elist_2EREVERSE__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5455 (all A_27a all V0L_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),V0L_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0L_2E0))),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Elist_2ELEN__LENGTH__LEM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5456 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5457 (all A_27a all A_27b all V0l_2E0 all V1f_2E0 all V2x_2E0 ((exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) & s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V3y_2E0))) = s(A_27b,V2x_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))))) # label(thm_2Elist_2EMEM__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5458 (all A_27a all A_27b all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))) # label(thm_2Elist_2EEVERY2__LENGTH) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5459 (all A_27a all A_27b ((all V0x_2E0 s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) = s(A_27a,V0x_2E0)) & (all V1h1_2E0 all V2h2_2E0 all V3t_2E0 s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h1_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h2_2E0),s(tyop_2Elist_2Elist(A_27b),V3t_2E0))))))) = s(A_27b,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h2_2E0),s(tyop_2Elist_2Elist(A_27b),V3t_2E0)))))))) # label(thm_2Elist_2ELAST__compute) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5460 (all A_27a all A_27b all A_27c all A_27d all A_27e all A_27f all A_27g all A_27h ((all V8P_2E0 all V9xs_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Ebool)),V8P_2E0),s(tyop_2Elist_2Elist(A_27e),V9xs_2E0),s(tyop_2Elist_2Elist(A_27f),c_2Elist_2ENIL_2E0)))) <-> s(tyop_2Elist_2Elist(A_27e),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27e),V9xs_2E0))) & (all V10P_2E0 all V11xxs_2E0 all V12y_2E0 all V13ys_2E0 ((exists V14x_2E0 exists V15xs_2E0 (s(tyop_2Elist_2Elist(A_27g),c_2Elist_2ECONS_2E2(s(A_27g,V14x_2E0),s(tyop_2Elist_2Elist(A_27g),V15xs_2E0))) = s(tyop_2Elist_2Elist(A_27g),V11xxs_2E0) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V10P_2E0),s(tyop_2Elist_2Elist(A_27g),V15xs_2E0),s(tyop_2Elist_2Elist(A_27h),V13ys_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V10P_2E0),s(A_27g,V14x_2E0))),s(A_27h,V12y_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),V10P_2E0),s(tyop_2Elist_2Elist(A_27g),V11xxs_2E0),s(tyop_2Elist_2Elist(A_27h),c_2Elist_2ECONS_2E2(s(A_27h,V12y_2E0),s(tyop_2Elist_2Elist(A_27h),V13ys_2E0)))))))) & (all V2P_2E0 all V3yys_2E0 all V4x_2E0 all V5xs_2E0 ((exists V6y_2E0 exists V7ys_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27c,V4x_2E0))),s(A_27d,V6y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Elist_2Elist(A_27c),V5xs_2E0),s(tyop_2Elist_2Elist(A_27d),V7ys_2E0)))) & s(tyop_2Elist_2Elist(A_27d),V3yys_2E0) = s(tyop_2Elist_2Elist(A_27d),c_2Elist_2ECONS_2E2(s(A_27d,V6y_2E0),s(tyop_2Elist_2Elist(A_27d),V7ys_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V2P_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V4x_2E0),s(tyop_2Elist_2Elist(A_27c),V5xs_2E0))),s(tyop_2Elist_2Elist(A_27d),V3yys_2E0)))))) & (all V0P_2E0 all V1ys_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),V1ys_2E0)))) <-> s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27b),V1ys_2E0))))) # label(thm_2Elist_2EEVERY2__THM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5461 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),f2643_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Enum_2Enum,f2643_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2643_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5462 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREST_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5463 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5464 (all A_27a all V0ys_2E0 all V1y_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V2x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1y_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))) <-> (exists V3xs_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1y_2E0),s(tyop_2Elist_2Elist(A_27a),V3xs_2E0))) = s(tyop_2Elist_2Elist(A_27a),V2x_2E0) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V3xs_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))) | s(tyop_2Elist_2Elist(A_27a),V2x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2EisPREFIX__CONSR) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5465 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5466 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) != s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) -> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))))) # label(thm_2Elist_2EAPPEND__FRONT__LAST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5467 (all A_27a all A_27b all V0t_2E0 all V1h_2E0 all V2f_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0),s(A_27b,V1h_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),V0t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),V2f_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) # label(thm_2Elist_2ELIST__BIND__THM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5468 (all A_27a all V0l_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) # label(thm_2Elist_2ECONS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5469 (all A_27a ((all V1l_2E0 all V2n_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) & (all V0l_2E0 s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) # label(thm_2Elist_2EEL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5470 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))))),f2454_0_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),f2454_0_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef2454_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5471 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5472 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),f2314_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(A_27a,f2314_0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef2314_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5473 (all A_27a all V0ls_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0ls_2E0)))))) # label(thm_2Elist_2EFLAT__EQ__NIL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5474 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0))) & s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0))) -> s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l2_2E0) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l1_2E0))) # label(thm_2Elist_2ELIST__EQ__MAP__PAIR) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5475 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(A_27a))),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5476 (all A_27a all A_27b all V0t_2E0 all V1h_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V1h_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V0t_2E0))))))) # label(thm_2Elist_2ELIST__TO__SET__THM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5477 (all A_27a all V0P_2E0 ((all V1l_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) -> (all V2a_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) -> (all V3l_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))))) # label(thm_2Elist_2Elist__INDUCT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5478 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Elist_2ESHORTLEX_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ESHORTLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ESHORTLEX_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5479 (all A_27a all A_27b all V1f_2E0 all V2x_2E0 ((exists V3y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V3y_2E0))) = s(A_27a,V2x_2E0)) <-> p(s(tyop_2Emin_2Ebool,f2639_0_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Elist_2EEXISTS__LIST__EQ__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5480 (all A_27a all V0P_2E0 all V1Q_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2536_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EEVERY__CONJ) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5481 (all V0b_2E0 s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ECONS_2E2(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Elist_2ELIST__GUARD_2E1(s(tyop_2Emin_2Ebool,V0b_2E0)))) # label(thm_2Elist_2ELIST__GUARD__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5482 (all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ewhile_2EOLEAST_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ewhile_2EOLEAST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ewhile_2EOLEAST_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5483 (all A_27a all X0_2E0 s(tyop_2Eind__type_2Erecspace(A_27a),f2267_2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),f2267_2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef2267_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5484 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5485 (all A_27a all A_27b all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) -> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V1l2_2E0))))))))) # label(thm_2Elist_2ELENGTH__ZIP) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5486 (all A_27b all A_27c all A_27d all V4Q_2E0 all V2g_2E0 all V8x_2E0 all V9y_2E0 s(tyop_2Emin_2Ebool,f2670_1_2E4(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(A_27c,V8x_2E0),s(A_27b,V9y_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0),s(A_27c,V8x_2E0))),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(A_27b,V9y_2E0)))))) # label(def0_2Ethm_2Elist_2EEVERY2__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5487 (all A_27a all A_27b ((all V0x_2E0 all V1l_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0))))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0x_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1l_2E0)))))))))) & s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EUNZIP_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))) # label(thm_2Elist_2EUNZIP) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5488 (all A_27a all V0xs_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0xs_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Elist_2Elist(A_27a),V0xs_2E0)))))) # label(thm_2Elist_2ELENGTH__TAKE__EQ) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5489 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),f2610_0_2E0)))) # label(thm_2Elist_2ESINGL__LIST__APPLY__R) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5490 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2370_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,f2370_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2370_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5491 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f2310_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),f2310_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X0_2E0)))) # label(arityeq1_2Ef2310_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5492 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5493 (all A_27a all A_27b all V3P_2E0 all V6a_2E0 all V7b_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V6a_2E0))),s(A_27b,V7b_2E0))) = s(tyop_2Emin_2Ebool,f2468_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V6a_2E0),s(A_27b,V7b_2E0)))) # label(def2_2Ethm_2Elist_2ELIST__REL__CONJ) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5494 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELEN_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elist_2ELEN_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ELEN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5495 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2R_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1x_2E0)) & (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),V0y_2E0)))) <-> s(tyop_2Elist_2Elist(A_27b),V0y_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))) # label(thm_2Elist_2ELIST__REL__NIL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5496 (all A_27a all V0n_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f2314_0_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Elist_2EREVERSE__GENLIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5497 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2637_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2637_0_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ef2637_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5498 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),f2657_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),f2657_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ef2657_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5499 (all A_27a all A_27b all X0_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Elist_2EZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5500 (all A_27c all X0_2E0 s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EFLAT_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5501 (all A_27a all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27d),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27d)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27d),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5502 (all A_27a all A_27b all V0l1_2E0 all V1l1_27_2E0 all V2l2_2E0 all V3l2_27_2E0 all V4P_2E0 all V5P_27_2E0 ((all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V7y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V6x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0)))))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4P_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_27_2E0),s(A_27a,V6x_2E0))),s(A_27b,V7y_2E0))))) & s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0) = s(tyop_2Elist_2Elist(A_27b),V2l2_2E0) & s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0) -> s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_27_2E0),s(tyop_2Elist_2Elist(A_27b),V3l2_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))) # label(thm_2Elist_2EEVERY2__cong) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5503 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f2313_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2313_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2313_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5504 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5505 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2ETAKE__0) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5506 (all A_27a all V0P_2E0 all V1l_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) <-> (exists V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2e_2E0)))))))) # label(thm_2Elist_2EEXISTS__MEM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5507 (all A_27a all V0n_2E0 all V1ls_2E0 all V2l_2E0 (s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2l_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))) & s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2l_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0))))))) # label(thm_2Elist_2EEL__simp__restricted) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5508 (all A_27a all A_27b all V0l2_2E0 all V1l1_2E0 all V2R2_2E0 all V3R1_2E0 ((all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) # label(thm_2Elist_2ELIST__REL__mono) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5509 (all A_27a all A_27b all A_27c all V0f_2E0 all V3s_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f2312_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),f2312_1_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V0f_2E0)))))) # label(def1_2Ethm_2Elist_2EFOLDL__UNION__BIGUNION__paired) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5510 (all A_27a all V0l1_2E0 all V1l2_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) & (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) -> s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) -> s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) # label(thm_2Elist_2ELIST__EQ) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5511 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))),f2295_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),f2295_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ef2295_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5512 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27a,f2613_0_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),A_27a)),f2613_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ef2613_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5513 (all A_27a all A_27b all V0x_2E0 all V1f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(A_27b,V0x_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__APPLY_2E2(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ECONS_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,A_27a)),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V0x_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ESINGL__SINGL__APPLY) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5514 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5515 (all A_27a all V0t2_2E0 all V1t1_2E0 all V2h2_2E0 all V3h1_2E0 all V4R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0)))))) & (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_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)),V4R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V2h2_2E0)))) | s(A_27a,V3h1_2E0) = s(A_27a,V2h2_2E0) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0),s(tyop_2Elist_2Elist(A_27a),V0t2_2E0))))) & -p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V1t1_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2ELLEX__THM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5516 (all A_27a all V0l_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) # label(thm_2Elist_2EALL__DISTINCT__REVERSE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5517 (all A_27a all A_27b all A_27c all V0f1_2E0 all V1f2_2E0 all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,f2403_0_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0),s(A_27a,V4x_2E0),s(A_27c,V5y_2E0)))) <-> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f2_2E0),s(A_27c,V5y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_2E0),s(A_27a,V4x_2E0))))) # label(def0_2Ethm_2Elist_2EMAP__EQ__EVERY2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5518 (all A_27a all V0P_2E0 ((all V1s_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) -> (all V2v_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2v_2E0))))))) # label(thm_2Elist_2ESET__TO__LIST__IND) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5519 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5520 (all A_27a all A_27b all V0s_2E0 all V1ls_2E0 all V2f_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V1ls_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0),s(A_27b,V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),V1ls_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Elist_2EBIGUNION__IMAGE__set__SUBSET) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5521 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ECONS_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5522 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5523 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5524 (all A_27a ((all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) & (all V2l1_2E0 all V3l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) & s(tyop_2Elist_2Elist(A_27a),V3l2_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l2_2E0))))))) # label(thm_2Elist_2EAPPEND__eq__NIL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5525 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),f2565_0_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),tyop_2Emin_2Ebool))),f2565_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),X1_2E0)))) # label(arityeq2_2Ef2565_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5526 (all A_27a all V0P_2E0 all V1Q_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2536_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))))) # label(def0_2Ethm_2Elist_2EEVERY__CONJ) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5527 (all A_27a all V0R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELLEX_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Elist_2ELLEX__transitive) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5528 (all A_27a all V0R_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) <-> (exists V3n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_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)),V0R_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))))))))) # label(thm_2Elist_2ELLEX__EL__THM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5529 (all A_27a all A_27b all A_27c all A_27d all V0l2_2E0 all V1l1_2E0 all V2g_2E0 all V3f_2E0 all V4Q_2E0 all V5P_2E0 (s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2670_1_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0))),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)),V4Q_2E0),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27d),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V2g_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))) & s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2670_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0))),s(tyop_2Elist_2Elist(A_27c),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))) # label(thm_2Elist_2EEVERY2__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/108.00 5530 (all A_27a all V0l_2E0 all V1n_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))) <-> (exists V2h_2E0 exists V3l_27_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3l_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0) & s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l_27_2E0))))))) # label(thm_2Elist_2ELENGTH__CONS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5531 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),f2425_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,f2425_0_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ef2425_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5532 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) | (exists V1h_2E0 exists V2t_2E0 s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0)))))) # label(thm_2Elist_2Elist__nchotomy) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5533 (all A_27a all A_27b all A_27c all V2f_2E0 all V4a_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0),s(A_27c,V4a_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),f2405_0_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0),s(A_27c,V4a_2E0)))) # label(def0_2Ethm_2Elist_2EFOLDL2__FOLDL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5534 (all A_27a all A_27b all V0v_27_2E0 all V1f_27_2E0 all V2M_2E0 all V3M_27_2E0 all V4v_2E0 all V5f_2E0 (s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0) = s(tyop_2Elist_2Elist(A_27a),V2M_2E0) & (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0) -> s(A_27b,V0v_27_2E0) = s(A_27b,V4v_2E0)) & (all V6a0_2E0 all V7a1_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6a0_2E0),s(tyop_2Elist_2Elist(A_27a),V7a1_2E0))) = s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V1f_27_2E0),s(A_27a,V6a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V7a1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V5f_2E0),s(A_27a,V6a0_2E0))),s(tyop_2Elist_2Elist(A_27a),V7a1_2E0))))) -> s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V3M_27_2E0),s(A_27b,V0v_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V1f_27_2E0))) = s(A_27b,c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V2M_2E0),s(A_27b,V4v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),V5f_2E0))))) # label(thm_2Elist_2Elist__case__cong) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5535 (all A_27a all A_27b all V0f_2E0 all V1x_2E0 all V2l_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ESNOC_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EMAP__SNOC) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5536 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5537 (all A_27a all A_27b all V0l2_2E0 all V1l1_2E0 all V2Q_2E0 all V3P_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2468_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2468_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2468_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))))) # label(thm_2Elist_2ELIST__REL__CONJ) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5538 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2639_0_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2639_0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2639_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5539 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Ebool,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Ebool,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5540 (all A_27a all V0l1_2E0 all V1l2_2E0 all V2P_2E0 all V3P_27_2E0 ((all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))) -> s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4x_2E0))))) & s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) -> s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3P_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))) # label(thm_2Elist_2EEVERY__CONG) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5541 (all A_27a all V0l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V0l_2E0)) # label(thm_2Elist_2ETAKE__LENGTH__ID) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5542 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5543 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2Enub_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2Enub_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2Enub_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5544 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2l_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))) # label(thm_2Elist_2EMAP__MAP__o) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5545 (all V1n_2E0 (p(s(tyop_2Emin_2Ebool,f2258_0_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))) <-> s(tyop_2Enum_2Enum,V1n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) # label(def0_2Ethm_2Elist_2EDROP__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5546 (all A_27a all V0P_2E0 all V1x_2E0 all V2l_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))))))) # label(thm_2Elist_2EEXISTS__SNOC) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5547 (all A_27a all V0f_2E0 all V1g_2E0 all V2ls_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),f2643_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0))),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0)))))) # label(thm_2Elist_2ESUM__MAP__PLUS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5548 (all A_27a all V0f_2E0 all V1g_2E0 all V3x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Enum_2Enum,f2643_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0),s(A_27a,V3x_2E0)))) # label(def0_2Ethm_2Elist_2ESUM__MAP__PLUS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5549 (all A_27a all V0P_2E0 all V1l_2E0 all V2n1_2E0 all V3n2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n1_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3n2_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) & s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V2n1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V3n2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) -> s(tyop_2Enum_2Enum,V2n1_2E0) = s(tyop_2Enum_2Enum,V3n2_2E0))) # label(thm_2Elist_2EALL__DISTINCT__FILTER__EL__IMP) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5550 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5551 (all A_27a all V0P_2E0 all V1ls_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))) -> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1ls_2E0)))))))) # label(thm_2Elist_2ENULL__FILTER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5552 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5553 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5554 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),f2299_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),f2299_1_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ef2299_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5555 (all A_27g all A_27h all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27g),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27h),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27g),X1_2E0))),s(tyop_2Elist_2Elist(A_27h),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27g),X1_2E0),s(tyop_2Elist_2Elist(A_27h),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27g_20mono_2EA_27h) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5556 (all A_27a all A_27b all A_27c all V5P_2E0 all V3f_2E0 all V6x_2E0 all V7y_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0),s(A_27c,V6x_2E0))))),s(A_27b,V7y_2E0))) = s(tyop_2Emin_2Ebool,f2670_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5P_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V3f_2E0),s(A_27c,V6x_2E0),s(A_27b,V7y_2E0)))) # label(def1_2Ethm_2Elist_2EEVERY2__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5557 (all A_27a all X0_2E0 s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EHD_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5558 (all A_27a all V0R_2E0 all V1l1_2E0 all V2l2_2E0 all V3l3_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0),s(tyop_2Elist_2Elist(A_27a),V3l3_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0)))) & (all V4n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_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)),V0R_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V3l3_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)),V0R_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V2l2_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)),V0R_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),V3l3_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V3l3_2E0)))))) # label(thm_2Elist_2ELIST__REL__trans) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5559 (all A_27a all V0ls_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0)))))) # label(thm_2Elist_2ECARD__LIST__TO__SET__ALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5560 (all A_27a all V0f_2E0 all V1x_2E0 all V2ls_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2ls_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ESUM_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2ls_2E0)))))))))) # label(thm_2Elist_2ESUM__MAP__MEM__bound) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5561 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5562 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,f2310_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X0_2E0),s(A_27a,X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f2310_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27b),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2310_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5563 (all A_27a all A_27b all X0_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5564 (all A_27d all A_27e all A_27f all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Elist_2Elist(A_27f)))),c_2Elist_2EMAP2_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X0_2E0))),s(tyop_2Elist_2Elist(A_27d),X1_2E0))),s(tyop_2Elist_2Elist(A_27e),X2_2E0))) = s(tyop_2Elist_2Elist(A_27f),c_2Elist_2EMAP2_2E3(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X0_2E0),s(tyop_2Elist_2Elist(A_27d),X1_2E0),s(tyop_2Elist_2Elist(A_27e),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27f_20mono_2EA_27d_20mono_2EA_27e) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5565 (all A_27a all X0_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),f2610_0_2E0),s(A_27a,X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),f2610_0_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2610_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5566 (all A_27a all V0l1_2E0 all V2x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,f2637_0_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Elist_2Elength__nub__append) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5567 (all A_27a all V0y_2E0 all V1x_2E0 all V2R2_2E0 all V3R1_2E0 ((all V4x_2E0 all V5y_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)),V3R1_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_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)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0y_2E0))))))) # label(thm_2Elist_2ELLEX__MONO) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5568 (all A_27a all V2R_2E0 all V3h1_2E0 all V4t1_2E0 all V6h2_2E0 all V7t2_2E0 s(tyop_2Emin_2Ebool,f2295_0_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(A_27a,V6h2_2E0),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(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)),V2R_2E0),s(A_27a,V3h1_2E0))),s(A_27a,V6h2_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2295_1_2E2(s(A_27a,V3h1_2E0),s(A_27a,V6h2_2E0))),s(tyop_2Emin_2Ebool,c_2Elist_2ELLEX_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),V4t1_2E0),s(tyop_2Elist_2Elist(A_27a),V7t2_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))))) # label(def1_2Ethm_2Elist_2ELLEX__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5569 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5570 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5571 (all A_27a all V0y_2E0 all V1x_2E0 all V2t_2E0 all V3h_2E0 all V4e_2E0 all V5R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V2t_2E0))),s(A_27a,V1x_2E0),s(A_27a,V0y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V2t_2E0)))))) -> (exists V6z_2E0 exists V7p_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)),V5R_2E0),s(A_27a,V6z_2E0))),s(A_27a,V4e_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Elist_2ELRC_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V5R_2E0),s(tyop_2Elist_2Elist(A_27a),V7p_2E0),s(A_27a,V1x_2E0),s(A_27a,V6z_2E0)))))))) # label(thm_2Elist_2ELRC__MEM__right) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5572 (all A_27b all X0_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5573 (all A_27a all A_27b all V0n_2E0 all V1ls_2E0 all V2l_2E0 (s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Elist_2Elist(A_27b),V1ls_2E0))) = s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2l_2E0),s(tyop_2Elist_2Elist(A_27b),V1ls_2E0))))) & s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EHD_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) # label(thm_2Elist_2EEL__restricted) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5574 (all A_27a all V0ys_2E0 all V1k_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V3y_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2592_0_2E2(s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V2x_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ESNOC_2E2(s(A_27a,V3y_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELUPDATE_2E3(s(A_27a,V2x_2E0),s(tyop_2Enum_2Enum,V1k_2E0),s(tyop_2Elist_2Elist(A_27a),V0ys_2E0)))))))) # label(thm_2Elist_2ELUPDATE__SNOC) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5575 (all A_27a all V0L1_2E0 all V1L2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREV_2E2(s(tyop_2Elist_2Elist(A_27a),V0L1_2E0),s(tyop_2Elist_2Elist(A_27a),V1L2_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0L1_2E0))),s(tyop_2Elist_2Elist(A_27a),V1L2_2E0)))) # label(thm_2Elist_2EREV__REVERSE__LEM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5576 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5577 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5578 (all A_27a all A_27b all V0P_2E0 all V1l1_2E0 all V2l2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))) # label(thm_2Elist_2ELIST__REL__LENGTH) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5579 (all A_27a all V0f_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),f2332_0_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,V2b_2E0))),s(tyop_2Enum_2Enum,V1a_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))))) # label(thm_2Elist_2EGENLIST__APPEND) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5580 (all A_27a all V0l_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),f2548_0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) & s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) # label(thm_2Elist_2EMAP__ID) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5581 (all A_27a all V0l2_2E0 all V1l1_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))),s(tyop_2Enum_2Enum,V2n_2E0)))) -> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))))) # label(thm_2Elist_2ETAKE__APPEND2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5582 (all A_27a all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5583 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f2676_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),f2676_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2676_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5584 (all A_27a all A_27b all V0l2_2E0 all V1l1_2E0 all V2R2_2E0 all V3R1_2E0 ((all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) # label(thm_2Elist_2EEVERY2__mono) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5585 (all A_27a all A_27b all V0ps_2E0 all V1p_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1p_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),V0ps_2E0)))))))))) # label(thm_2Elist_2EMEM__ZIP__MEM__MAP) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5586 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EPAD__LEFT_2E3(s(A_27a,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EPAD__LEFT_2E0),s(A_27a,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2EPAD__LEFT_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5587 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5588 (all A_27a ((all V0f_2E0 all V1l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0)) & (all V2f_2E0 all V3n_2E0 all V4l_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST__AUX_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Elist_2Elist(A_27a),V4l_2E0)))))))) # label(thm_2Elist_2EGENLIST__AUX) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5589 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5590 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EFCONS_2E2(s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)))),c_2Eind__type_2EFCONS_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) # label(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5591 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Elist_2EsplitAtPki_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EsplitAtPki_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EsplitAtPki_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5592 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Eone_2Eone)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X2_2E0))) = s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Eone_2Eone),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5593 (all A_27a all A_27b all A_27c all V0f_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2EREVERSE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),V0f_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27c)),V0f_2E0))) & s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0))) # label(thm_2Elist_2ELENGTH__o__REVERSE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5594 (all A_27a all A_27b ((all V1f_2E0 all V2h0_2E0 all V3t0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h0_2E0),s(tyop_2Elist_2Elist(A_27b),V3t0_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1f_2E0),s(A_27b,V2h0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),f2299_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V3t0_2E0)))))) & (all V0f_2E0 s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))) # label(thm_2Elist_2EOPT__MMAP__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5595 (all A_27a all V3h1_2E0 all V6h2_2E0 (s(A_27a,V3h1_2E0) = s(A_27a,V6h2_2E0) <-> p(s(tyop_2Emin_2Ebool,f2295_1_2E2(s(A_27a,V3h1_2E0),s(A_27a,V6h2_2E0)))))) # label(def0_2Ethm_2Elist_2ELLEX__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5596 (all A_27a all V0t_2E0 all V1l2_2E0 all V2l1_2E0 all V3h_2E0 ((exists V4lt_2E0 (s(tyop_2Elist_2Elist(A_27a),V0t_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4lt_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) & s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V4lt_2E0))))) | s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V2l1_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V0t_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) # label(thm_2Elist_2EAPPEND__EQ__CONS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5597 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2588_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,f2588_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2588_0_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5598 (all A_27a all V0a_2E0 all V1b_2E0 all V2c_2E0 all V3d_2E0 all V4x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0a_2E0)))))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1b_2E0)))))) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2c_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3d_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0a_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27a),V1b_2E0))) -> s(tyop_2Elist_2Elist(A_27a),V0a_2E0) = s(tyop_2Elist_2Elist(A_27a),V2c_2E0) & s(tyop_2Elist_2Elist(A_27a),V3d_2E0) = s(tyop_2Elist_2Elist(A_27a),V1b_2E0))) # label(thm_2Elist_2EMEM__APPEND__lemma) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5599 (all A_27a all A_27b all A_27c all V0l2_2E0 all V1l1_2E0 all V2f_2E0 all V3R_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f2466_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27c),V0l2_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2466_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V0l2_2E0)))))) # label(thm_2Elist_2ELIST__REL__MAP2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5600 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5601 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),f2299_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),f2299_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ef2299_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5602 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27d))),f2448_1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27d),f2448_1_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef2448_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5603 (all A_27a all V0xs_2E0 s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0xs_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E1(s(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V0xs_2E0)))))) # label(thm_2Elist_2EALL__DISTINCT__FLAT__REVERSE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5604 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))),f2403_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f2403_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0)))) # label(arityeq2_2Ef2403_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5605 (all A_27a all A_27b all V0f1_2E0 all V1f2_2E0 all V2x1_2E0 all V3x2_2E0 ((all V4a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V3x2_2E0)))))) -> s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f1_2E0),s(A_27a,V4a_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f2_2E0),s(A_27a,V4a_2E0))))) & s(tyop_2Elist_2Elist(A_27a),V3x2_2E0) = s(tyop_2Elist_2Elist(A_27a),V2x1_2E0) -> s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0f1_2E0),s(tyop_2Elist_2Elist(A_27a),V2x1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Elist_2EOPT__MMAP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1f2_2E0),s(tyop_2Elist_2Elist(A_27a),V3x2_2E0))))) # label(thm_2Elist_2EOPT__MMAP__cong) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5606 (all A_27a all A_27b all A_27c all V0l_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ELIST__BIND_2E2(s(tyop_2Elist_2Elist(A_27c),V0l_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Elist_2Elist(A_27b)),V1g_2E0)))))) # label(thm_2Elist_2EMAP__LIST__BIND) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5607 (all A_27a all A_27b all V3P_2E0 all V2Q_2E0 all V4a_2E0 all V5b_2E0 (p(s(tyop_2Emin_2Ebool,f2468_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V4a_2E0),s(A_27b,V5b_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2Q_2E0),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3P_2E0),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0)))))) # label(def0_2Ethm_2Elist_2ELIST__REL__CONJ) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5608 (all A_27a all V0l1_2E0 all V1l2_2E0 (s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) <-> s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) # label(thm_2Elist_2EREVERSE__11) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5609 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5610 (all V0i_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0i_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V0i_2E0)))))) # label(thm_2Enumeral__bit_2EiDUB__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5611 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Enumeral__bit_2EiBITWISE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ec_2Enumeral__bit_2EiBITWISE_2E4) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5612 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral__bit_2EiMOD__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumeral__bit_2EiMOD__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5613 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ESBIT_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2ESBIT_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5614 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiLOG2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral__bit_2EiLOG2_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5615 (all V0x_2E0 s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5616 (all V4n_2E0 all V5x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V5x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))),s(tyop_2Enum_2Enum,V5x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5617 (all V2n_2E0 all V3x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,V3x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5618 (all V1y_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5619 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5620 (all V0n_2E0 (s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) & s(tyop_2Enum_2Enum,V0n_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) & s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) & s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) # label(thm_2Enumeral__bit_2ENUMERAL__iDIV2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5621 (all V3x_2E0 all V4opr_2E0 all V5a_2E0 all V6b_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f2727_0_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4opr_2E0),s(tyop_2Enum_2Enum,V5a_2E0),s(tyop_2Enum_2Enum,V6b_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4opr_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V5a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V6b_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4opr_2E0),s(tyop_2Enum_2Enum,V5a_2E0),s(tyop_2Enum_2Enum,V6b_2E0)))) # label(thm_2Enumeral__bit_2EiBITWISE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5622 (all V8x_2E0 all V9opr_2E0 all V10a_2E0 all V11b_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f2727_1_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V9opr_2E0),s(tyop_2Enum_2Enum,V10a_2E0),s(tyop_2Enum_2Enum,V11b_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V9opr_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V10a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V11b_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V8x_2E0))))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V9opr_2E0),s(tyop_2Enum_2Enum,V10a_2E0),s(tyop_2Enum_2Enum,V11b_2E0)))) # label(thm_2Enumeral__bit_2EiBITWISE_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5623 (all V0opr_2E0 all V1a_2E0 all V2b_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0opr_2E0),s(tyop_2Enum_2Enum,V1a_2E0),s(tyop_2Enum_2Enum,V2b_2E0)))) # label(thm_2Enumeral__bit_2EiBITWISE_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5624 (all V0base_20_3C_202_20or_20n_20_3D_200_2E0 all V1m_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2742_0_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ecombin_2EFAIL_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2ELOG_2E0),s(tyop_2Emin_2Ebool,V0base_20_3C_202_20or_20n_20_3D_200_2E0))),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,V1m_2E0))))))))))) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))) # label(thm_2Enumeral__bit_2ELOG__compute) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5625 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5626 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral_2EiDUB_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5627 (all V0x_2E0 s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5628 (all V2n_2E0 all V3x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,V3x_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,V3x_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5629 (all V4n_2E0 all V5x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,V5x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))),s(tyop_2Enum_2Enum,V5x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5630 (all V1y_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,V1y_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5631 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ELOG2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ebit_2ELOG2_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5632 (all A_27a ((all V0x_2E0 all V1f_2E0 all V2a_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) & (all V6x_2E0 all V7f_2E0 all V8b_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,V6x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V7f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V8b_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V6x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V7f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V8b_2E0)))))) & (all V9x_2E0 all V10f_2E0 all V11a_2E0 all V12b_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,V9x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V10f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V11a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V12b_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V9x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V10f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V11a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V12b_2E0)))))) & (all V3x_2E0 all V4f_2E0 all V5a_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiBITWISE_2E4(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V5a_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V5a_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__BITWISE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5633 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiSUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral__bit_2EiSUC_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5634 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2Enumeral__bit_2EFDUB__iDIV2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5635 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5636 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,V0x_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2Enumeral__bit_2EFDUB__iDUB) # label(axiom) # label(non_clause). [assumption]. 108.00/108.01 5637 (all V2n_2E0 all V3y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V3y_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V3y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5638 (all V4n_2E0 all V5y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V5y_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V5y_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5639 (all V6n_2E0 all V7x_2E0 all V8y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V7x_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V7x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V8y_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V8y_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V7x_2E0))),s(tyop_2Enum_2Enum,V8y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5640 (all V9n_2E0 all V10x_2E0 all V11y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V9n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V10x_2E0))),s(tyop_2Enum_2Enum,V11y_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V9n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V10x_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V10x_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V11y_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V11y_2E0)))))))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5641 (all V0x_2E0 all V1y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0))) = s(tyop_2Enum_2Enum,V1y_2E0)) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REV_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5642 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5643 (all V0n_2E0 (s(tyop_2Enum_2Enum,V0n_2E0) != s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) -> s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V0n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))))))) # label(thm_2Enumeral__bit_2ELOWEST__SET__BIT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5644 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5645 (all V1n_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2x_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2x_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__DIV__2EXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5646 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral__bit_2ENUMERAL__DIV__2EXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5647 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral__bit_2EFDUB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Enumeral__bit_2EFDUB_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5648 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ecombin_2EFAIL_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ecombin_2EFAIL_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5649 (all V0f_2E0 ((all V3x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V3x_2E0)))))) & (all V2x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V2x_2E0)))))))) & (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiSUC_2E1(s(tyop_2Enum_2Enum,V1x_2E0)))))))) & s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))) # label(thm_2Enumeral__bit_2EFDUB__FDUB) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5650 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2742_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2742_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2742_0_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5651 (all V0m_2E0 all V1f_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral__bit_2EBIT__MODIFY__EVAL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5652 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5653 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ebit_2EMOD__2EXP__MAX_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EMOD__2EXP__MAX_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5654 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f2727_1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f2727_1_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef2727_1_2E3) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5655 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5656 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f2727_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,f2727_0_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef2727_0_2E4) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5657 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Elogroot_2ELOG_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Elogroot_2ELOG_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elogroot_2ELOG_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5658 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5659 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),c_2Ebit_2EBITWISE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBITWISE_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ec_2Ebit_2EBITWISE_2E4) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5660 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2A_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2A_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5661 (all V5n_2E0 all V6f_2E0 all V7x_2E0 all V8b_2E0 all V9e_2E0 all V10y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,V5n_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V7x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V8b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V9e_2E0))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,V8b_2E0))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V7x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V9e_2E0),s(tyop_2Enum_2Enum,V10y_2E0))),s(tyop_2Enum_2Enum,V10y_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V5n_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,V7x_2E0),s(tyop_2Enum_2Enum,V8b_2E0),s(tyop_2Enum_2Enum,V9e_2E0),s(tyop_2Enum_2Enum,V10y_2E0)))) # label(thm_2Enumeral__bit_2EBIT__MODF__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5662 (all V0f_2E0 all V1x_2E0 all V2b_2E0 all V3e_2E0 all V4y_2E0 s(tyop_2Enum_2Enum,V4y_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V3e_2E0),s(tyop_2Enum_2Enum,V4y_2E0)))) # label(thm_2Enumeral__bit_2EBIT__MODF__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5663 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5664 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) # label(thm_2Enumeral__bit_2EiLOG2__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5665 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumeral__bit_2EBIT__REV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumeral__bit_2EBIT__REV_2E3) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5666 (all A_27a ((all V1x_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))) & (all V3x_2E0 all V4n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V4n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V4n_2E0)))))) & (all V9x_2E0 all V10n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V9x_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V9x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10n_2E0)))))) & (all V7x_2E0 all V8n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V8n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V8n_2E0)))))) & (all V5x_2E0 all V6n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V5x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5x_2E0))))),s(tyop_2Enum_2Enum,V6n_2E0)))))) & (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumeral__bit_2Enumeral__imod__2exp) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5667 (all V4opr_2E0 all V5a_2E0 all V6b_2E0 all V7w_2E0 s(tyop_2Enum_2Enum,f2727_0_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V4opr_2E0),s(tyop_2Enum_2Enum,V5a_2E0),s(tyop_2Enum_2Enum,V6b_2E0),s(tyop_2Enum_2Enum,V7w_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(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)),V4opr_2E0),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V5a_2E0))))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V6b_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V7w_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V7w_2E0)))))) # label(def1_2Ethm_2Enumeral__bit_2EiBITWISE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5668 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Enumeral__bit_2ESFUNPOW_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Enumeral__bit_2ESFUNPOW_2E3) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5669 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EDIV_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EDIV_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5670 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 all X5_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))),c_2Enumeral__bit_2EBIT__MODF_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))),s(tyop_2Enum_2Enum,X4_2E0))),s(tyop_2Enum_2Enum,X5_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0),s(tyop_2Enum_2Enum,X4_2E0),s(tyop_2Enum_2Enum,X5_2E0)))) # label(arityeq6_2Ec_2Enumeral__bit_2EBIT__MODF_2E6) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5671 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5672 (all V2m_2E0 all V3f_2E0 all V4n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V4n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V3f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V4n_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODIFY_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5673 (all V0m_2E0 all V1f_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODIFY_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5674 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5675 (all V0m_2E0 all V1n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2Enumeral__bit_2EBIT__REVERSE__EVAL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5676 (all V2n_2E0 all V3a_2E0 all V4b_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V3a_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V4b_2E0)))))) & s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V3a_2E0))) = s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V4b_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V3a_2E0),s(tyop_2Enum_2Enum,V4b_2E0)))))) # label(thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5677 (all V5n_2E0 all V6a_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,V5n_2E0),s(tyop_2Enum_2Enum,V6a_2E0),s(tyop_2Enum_2Enum,V6a_2E0)))) # label(thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5678 (all V0a_2E0 all V1b_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0a_2E0),s(tyop_2Enum_2Enum,V1b_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(thm_2Enumeral__bit_2EMOD__2EXP__EQ_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5679 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__EQ_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Ebit_2EMOD__2EXP__EQ_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2EMOD__2EXP__EQ_2E3) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5680 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5681 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5682 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2EMOD_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2EMOD_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5683 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))))) # label(thm_2Enumeral__bit_2Enumeral__log2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5684 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))) # label(thm_2Enumeral__bit_2Enumeral__log2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5685 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Enumeral__bit_2EFDUB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Enumeral__bit_2EFDUB_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5686 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5687 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EDIV2_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5688 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5689 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))) # label(thm_2Enumeral__bit_2Enumeral__mod2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5690 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EMOD_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) # label(thm_2Enumeral__bit_2Enumeral__mod2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5691 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5692 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EMOD__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EMOD__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5693 (all V1m_2E0 all V2n_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) | s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> p(s(tyop_2Emin_2Ebool,f2742_0_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(def0_2Ethm_2Enumeral__bit_2ELOG__compute) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5694 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5695 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5696 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5697 (all X0_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EODD_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EODD_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5698 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5699 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EiDIV2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiDIV2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enumeral__bit_2EiDIV2_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5700 (all V1n_2E0 all V2m_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REVERSE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5701 (all V0m_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__REVERSE_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5702 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f2727_0_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f2727_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ef2727_0_2E3) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5703 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5704 (all V0f_2E0 all V1x_2E0 all V2b_2E0 all V3e_2E0 all V4y_2E0 s(tyop_2Enum_2Enum,V4y_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2b_2E0),s(tyop_2Enum_2Enum,V3e_2E0),s(tyop_2Enum_2Enum,V4y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5705 (all V5n_2E0 all V6f_2E0 all V7b_2E0 all V8e_2E0 all V9y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V7b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V8e_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,V7b_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V8e_2E0))),s(tyop_2Enum_2Enum,V9y_2E0))),s(tyop_2Enum_2Enum,V9y_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V5n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V6f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V7b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V8e_2E0))),s(tyop_2Enum_2Enum,V9y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5706 (all V15n_2E0 all V16f_2E0 all V17x_2E0 all V18b_2E0 all V19e_2E0 all V20y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V15n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V16f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V17x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V18b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V19e_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V16f_2E0),s(tyop_2Enum_2Enum,V18b_2E0))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V17x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V19e_2E0))),s(tyop_2Enum_2Enum,V20y_2E0))),s(tyop_2Enum_2Enum,V20y_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V15n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V16f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V17x_2E0))),s(tyop_2Enum_2Enum,V18b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V19e_2E0))),s(tyop_2Enum_2Enum,V20y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5707 (all V21n_2E0 all V22f_2E0 all V23x_2E0 all V24b_2E0 all V25e_2E0 all V26y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V21n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V22f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V23x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V24b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V25e_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V22f_2E0),s(tyop_2Enum_2Enum,V24b_2E0))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V23x_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V25e_2E0))),s(tyop_2Enum_2Enum,V26y_2E0))),s(tyop_2Enum_2Enum,V26y_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V21n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V22f_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V23x_2E0))),s(tyop_2Enum_2Enum,V24b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V25e_2E0))),s(tyop_2Enum_2Enum,V26y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5708 (all V10n_2E0 all V11f_2E0 all V12b_2E0 all V13e_2E0 all V14y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V11f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V12b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V13e_2E0))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V11f_2E0),s(tyop_2Enum_2Enum,V12b_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V13e_2E0))),s(tyop_2Enum_2Enum,V14y_2E0))),s(tyop_2Enum_2Enum,V14y_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__MODF_2E6(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V10n_2E0))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V11f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V12b_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V13e_2E0))),s(tyop_2Enum_2Enum,V14y_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__BIT__MODF_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5709 (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,f2717_0_2E1(s(tyop_2Enum_2Enum,V4x_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,V4x_2E0))) # label(def0_2Ethm_2Enumeral__bit_2ESFUNPOW__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5710 (all V0n_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV2_2E0),s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1x_2E0)))) # label(thm_2Enumeral__bit_2EDIV__2EXP) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5711 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5712 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),f2717_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,f2717_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef2717_0_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5713 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5714 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebit_2EBIT__MODIFY_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__MODIFY_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebit_2EBIT__MODIFY_2E3) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5715 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5716 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5717 (all V9opr_2E0 all V10a_2E0 all V11b_2E0 all V12w_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(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)),V9opr_2E0),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V10a_2E0))))),s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V11b_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V12w_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E1(s(tyop_2Enum_2Enum,V12w_2E0))))) = s(tyop_2Enum_2Enum,f2727_1_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V9opr_2E0),s(tyop_2Enum_2Enum,V10a_2E0),s(tyop_2Enum_2Enum,V11b_2E0),s(tyop_2Enum_2Enum,V12w_2E0)))) # label(def0_2Ethm_2Enumeral__bit_2EiBITWISE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5718 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5719 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ETIMES__2EXP_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral__bit_2ENUMERAL__TIMES__2EXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5720 (all V1n_2E0 all V2x_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ETIMES__2EXP_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2x_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral_2EiDUB_2E0),s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V2x_2E0)))))) # label(thm_2Enumeral__bit_2ENUMERAL__TIMES__2EXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5721 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EBIT__REVERSE_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EBIT__REVERSE_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EBIT__REVERSE_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5722 (all V1x_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V1x_2E0),s(tyop_2Enum_2Enum,V2n_2E0)))))) # label(thm_2Enumeral__bit_2EMOD__2EXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5723 (all V0x_2E0 s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) = s(tyop_2Enum_2Enum,c_2Ebit_2EMOD__2EXP_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) # label(thm_2Enumeral__bit_2EMOD__2EXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5724 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5725 (all V0f_2E0 ((all V3n_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V4x_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V3n_2E0))))),s(tyop_2Enum_2Enum,V4x_2E0)))) & (all V5n_2E0 all V6x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,V5n_2E0))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,V6x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V5n_2E0))))),s(tyop_2Enum_2Enum,V6x_2E0)))) & (all V2y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,V2y_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) & (all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enumeral__bit_2EFDUB_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,V1x_2E0)))) # label(thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__FDUB) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5726 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral__bit_2ELOWEST__SET__BIT__compute_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5727 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))))))) # label(thm_2Enumeral__bit_2ELOWEST__SET__BIT__compute_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5728 (all V0f_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) # label(thm_2Enumeral__bit_2EFDUB__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5729 (all V1f_2E0 all V2n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EFDUB_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0)))))))) # label(thm_2Enumeral__bit_2EFDUB__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5730 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2EDIV__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2EDIV__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2EDIV__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5731 (all V0x_2E0 all V1y_2E0 s(tyop_2Enum_2Enum,V1y_2E0) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1y_2E0)))) # label(thm_2Enumeral__bit_2EBIT__REV__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5732 (all V2n_2E0 all V3x_2E0 all V4y_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,V2n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V4y_2E0))),s(tyop_2Enum_2Enum,c_2Ebit_2ESBIT_2E2(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V3x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EBIT__REV_2E3(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V2n_2E0))),s(tyop_2Enum_2Enum,V3x_2E0),s(tyop_2Enum_2Enum,V4y_2E0)))) # label(thm_2Enumeral__bit_2EBIT__REV__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5733 (all V0f_2E0 all V1x_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V1x_2E0))) = s(tyop_2Enum_2Enum,V1x_2E0)) # label(thm_2Enumeral__bit_2ESFUNPOW__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5734 (all V2f_2E0 all V3n_2E0 all V4x_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2717_0_2E1(s(tyop_2Enum_2Enum,V4x_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,V3n_2E0),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,V4x_2E0))))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2ESFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V3n_2E0))),s(tyop_2Enum_2Enum,V4x_2E0)))) # label(thm_2Enumeral__bit_2ESFUNPOW__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5735 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5736 (all V0n_2E0 s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,V0n_2E0)))))) # label(thm_2Enumeral__bit_2Enumeral__ilog2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5737 (all V1n_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,V1n_2E0))))) = s(tyop_2Enum_2Enum,c_2Enumeral__bit_2EiLOG2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))))) # label(thm_2Enumeral__bit_2Enumeral__ilog2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5738 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebit_2ELOWEST__SET__BIT_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Ebit_2ELOWEST__SET__BIT_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Ebit_2ELOWEST__SET__BIT_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5739 (all V1n_2E0 all V2a_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(s(tyop_2Enum_2Enum,V2a_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E1(s(tyop_2Enum_2Enum,V2a_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0))),s(tyop_2Enum_2Enum,V2a_2E0)))))) # label(thm_2Enumeral__bit_2EMOD__2EXP__MAX_AndLHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5740 (all V0a_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebit_2EMOD__2EXP__MAX_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,V0a_2E0)))) # label(thm_2Enumeral__bit_2EMOD__2EXP__MAX_AndRHS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5741 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5742 (all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),f2727_1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Enum_2Enum,f2727_1_2E4(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef2727_1_2E4) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5743 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Ebit_2ETIMES__2EXP_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebit_2ETIMES__2EXP_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Ebit_2ETIMES__2EXP_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5744 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2796_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2796_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2796_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5745 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2773_0_2E0),s(A_27b,X0_2E0))) = s(tyop_2Emin_2Ebool,f2773_0_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ef2773_0_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5746 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5747 (all A_27b all V1s_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Ebool,f2757_1_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(A_27b,V4x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE__T) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5748 (all A_27a all V0P_2E0 all V2i_2E0 s(tyop_2Emin_2Ebool,f2776_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2i_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__EQUAL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5749 (all A_27b all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,f2752_0_2E1(s(A_27b,V3x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE__SING) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5750 (all A_27a all A_27b all A_27c all V0P_2E0 all V1s_2E0 all V2x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2758_0_2E0))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__F) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5751 (all A_27a all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,f2780_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) # label(def2_2Ethm_2Eres__quan_2ERES__FORALL__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5752 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5753 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2796_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2796_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2796_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5754 (all A_27a all V0p_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) # label(thm_2Eres__quan_2ERES__FORALL__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5755 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_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_3F_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5756 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f158_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef158_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5757 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2762_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2762_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2762_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5758 (all A_27a all V2R_2E0 all V5i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_2E0))) = s(tyop_2Emin_2Ebool,f2795_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_2E0)))) # label(def3_2Ethm_2Eres__quan_2ERES__FORALL__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5759 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2758_0_2E0),s(A_27b,X0_2E0))) = s(tyop_2Emin_2Ebool,f2758_0_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ef2758_0_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5760 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5761 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__FORALL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5762 (all A_27a all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,f2761_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5763 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,f2791_0_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2791_0_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ef2791_0_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5764 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2779_1_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2779_1_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2779_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5765 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f158_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f158_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef158_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5766 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2762_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2762_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2762_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5767 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2762_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2762_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2762_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5768 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2778_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2778_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2778_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5769 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2757_0_2E0),s(A_27b,X0_2E0))) = s(tyop_2Emin_2Ebool,f2757_0_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ef2757_0_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5770 (all A_27a all V1x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,f2750_0_2E1(s(A_27a,V1x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__SELECT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5771 (all A_27a all A_27b all V0p_2E0 all V1m_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0),s(A_27a,V2x_2E0))) = s(A_27b,c_2Ebool_2ERES__ABSTRACT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0),s(A_27a,V2x_2E0))))) # label(thm_2Eres__quan_2ERES__ABSTRACT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5772 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5773 (all A_27a all A_27b all V1Q_2E0 all V2R_2E0 all V3i_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2792_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3i_2E0))))) = s(tyop_2Emin_2Ebool,f2792_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3i_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__FORALL__REORDER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5774 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2792_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2792_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef2792_2_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5775 (all A_27b all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,f2757_0_2E1(s(A_27b,V3x_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE__T) # label(axiom) # label(non_clause). [assumption]. 108.00/108.02 5776 (all A_27a all A_27b all V2R_2E0 all V5j_2E0 all V6i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V6i_2E0))),s(A_27b,V5j_2E0))) = s(tyop_2Emin_2Ebool,f2775_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27b,V5j_2E0),s(A_27a,V6i_2E0)))) # label(def2_2Ethm_2Eres__quan_2ERES__EXISTS__REORDER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5777 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2764_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2764_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2764_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5778 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f159_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f159_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef159_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5779 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2760_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2760_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2760_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5780 (all A_27a all A_27b all V1R_2E0 all V5i_2E0 ((all V6x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V5i_2E0))),s(A_27b,V6x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,f2793_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V5i_2E0)))))) # label(def1_2Ethm_2Eres__quan_2ERES__FORALL__FORALL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5781 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5782 (all A_27a all V1m_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f2753_0_2E2(s(tyop_2Emin_2Ebool,V1m_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,V1m_2E0)) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE__NULL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5783 (all A_27a all A_27b all A_27c all V0P_2E0 all V1s_2E0 all V2x_2E0 (s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0) != s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2773_0_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__T) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5784 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2780_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2780_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2780_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5785 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2763_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,f2763_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2763_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5786 (all A_27a all V0x_2E0 all V1sos_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2781_0_2E1(s(A_27a,V0x_2E0)))))) # label(thm_2Eres__quan_2EIN__BIGINTER__RES__FORALL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5787 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2761_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2761_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2761_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5788 (all A_27a all A_27b all V0P_2E0 all V1s_2E0 all V2t_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2782_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2782_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Eres__quan_2ERES__FORALL__DIFF) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5789 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2796_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2796_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2796_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5790 (all A_27a all V0x_2E0 all V2s_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Emin_2Ebool,f2763_0_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) # label(def0_2Ethm_2Eres__quan_2EIN__BIGUNION__RES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5791 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2761_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2761_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2761_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5792 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2792_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2792_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef2792_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5793 (all A_27a all A_27b all A_27c all V0P_2E0 all V1s_2E0 all V2x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2x_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f2774_0_2E0))))) # label(thm_2Eres__quan_2ERES__EXISTS__F) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5794 (all A_27a all V2R_2E0 all V5i_2E0 s(tyop_2Emin_2Ebool,f2778_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__EXISTS__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5795 (all A_27a all V0p_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))))) # label(thm_2Eres__quan_2ERES__FORALL__EMPTY) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5796 (all A_27a all V0P_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__EXISTS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5797 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2796_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2796_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2796_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5798 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2775_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2775_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef2775_2_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5799 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5800 (all A_27b all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,f2790_0_2E1(s(A_27b,V3x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__F) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5801 (all A_27a all V0P_2E0 all V1Q_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2795_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2795_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2795_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2795_3_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))))) # label(thm_2Eres__quan_2ERES__FORALL__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5802 (all A_27a all V0P_2E0 all V3s_2E0 s(tyop_2Emin_2Ebool,f2762_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2762_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(def1_2Ethm_2Eres__quan_2ERES__EXISTS__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5803 (all A_27a all V0P_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,f2762_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5804 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2768_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2768_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2768_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5805 (all A_27a all A_27b all V2R_2E0 all V3i_2E0 all V4j_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3i_2E0))),s(A_27b,V4j_2E0))) = s(tyop_2Emin_2Ebool,f2775_3_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3i_2E0),s(A_27b,V4j_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__REORDER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5806 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2780_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2780_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2780_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5807 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2782_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2782_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2782_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5808 (all A_27a all V1f_2E0 all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,f158_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0),s(A_27a,V4y_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V4y_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0)))) -> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5809 (all A_27a all V0P_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Eres__quan_2ERES__FORALL__UNION) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5810 (all A_27a all V1f_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f158_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))) # label(def2_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5811 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2760_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2760_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2760_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5812 (all A_27b all V3x_2E0 s(tyop_2Emin_2Ebool,f2791_0_2E1(s(A_27b,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__T) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5813 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2770_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2770_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef2770_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5814 (all A_27c all V3s_2E0 s(tyop_2Emin_2Ebool,f2774_0_2E1(s(A_27c,V3s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__F) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5815 (all A_27a all V1Q_2E0 all V2R_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3i_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V3i_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2796_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V3i_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__CONJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5816 (all A_27a all V0p_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5817 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5818 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2775_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2775_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2775_2_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5819 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2787_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2787_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef2787_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5820 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2768_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2768_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2768_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5821 (all A_27a all V2R_2E0 all V4i_2E0 s(tyop_2Emin_2Ebool,f2795_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V4i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V4i_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__FORALL__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5822 (all A_27a all V1Q_2E0 all V4i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4i_2E0))) = s(tyop_2Emin_2Ebool,f2796_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4i_2E0)))) # label(def2_2Ethm_2Eres__quan_2ERES__FORALL__CONJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5823 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2764_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2764_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2764_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5824 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5825 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5826 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2782_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2782_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2782_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5827 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5828 (all A_27a all A_27b all V0p_2E0 all V1m1_2E0 all V2m2_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1m1_2E0),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2m2_2E0),s(A_27a,V3x_2E0))))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2m2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m1_2E0))))) # label(thm_2Eres__quan_2ERES__ABSTRACT__EQUAL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5829 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2762_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2762_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2762_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5830 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2794_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2794_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2794_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5831 (all A_27a all V0x_2E0 all V2s_2E0 s(tyop_2Emin_2Ebool,f2781_0_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) # label(def0_2Ethm_2Eres__quan_2EIN__BIGINTER__RES__FORALL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5832 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f159_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f159_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef159_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5833 (all A_27a all V0P_2E0 all V1j_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V1j_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2776_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1j_2E0)))) # label(thm_2Eres__quan_2ERES__EXISTS__EQUAL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5834 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2777_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2777_3_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2777_3_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5835 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2778_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2778_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2778_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5836 (all A_27a all V0P_2E0 all V1sos_2E0 ((exists V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2761_1_2E1(s(A_27a,V3x_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2761_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Eres__quan_2ERES__EXISTS__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5837 (all A_27a all V1m_2E0 all V0p_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2751_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(A_27a,V2x_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(A_27a,V2x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2751_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(A_27a,V2x_2E0)))))) # label(def1_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE__ALT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5838 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2795_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2795_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2795_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5839 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2792_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2792_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2792_3_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5840 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef158_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5841 (all A_27a all V0P_2E0 all V3x_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2786_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ENOT__RES__FORALL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5842 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2757_1_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2757_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef2757_1_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5843 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2780_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2780_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2780_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5844 (all A_27a all A_27b all V0P_2E0 all V2R_2E0 all V5j_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2792_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27b,V5j_2E0))))) = s(tyop_2Emin_2Ebool,f2792_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27b,V5j_2E0)))) # label(def3_2Ethm_2Eres__quan_2ERES__FORALL__REORDER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5845 (all A_27a all A_27b all V1Q_2E0 all V2R_2E0 all V3i_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2775_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3i_2E0))))) = s(tyop_2Emin_2Ebool,f2775_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3i_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__EXISTS__REORDER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5846 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2786_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2786_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2786_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5847 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5848 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f158_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef158_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5849 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2795_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2795_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2795_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5850 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS__UNIQUE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS__UNIQUE_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5851 (all A_27a all V2R_2E0 all V4i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V4i_2E0))) = s(tyop_2Emin_2Ebool,f2777_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V4i_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__DISJ__EXISTS__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5852 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2792_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2792_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef2792_1_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5853 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) | p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5854 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS__UNIQUE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS__UNIQUE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5855 (all A_27b all V3x_2E0 s(tyop_2Emin_2Ebool,f2758_0_2E1(s(A_27b,V3x_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE__F) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5856 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ebool_2ERES__ABSTRACT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__ABSTRACT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5857 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2790_0_2E0),s(A_27b,X0_2E0))) = s(tyop_2Emin_2Ebool,f2790_0_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ef2790_0_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5858 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f2750_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2750_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2750_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5859 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2793_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2793_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2793_1_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5860 (all A_27a all X0_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5861 (all A_27a all A_27b all V0P_2E0 all V2R_2E0 all V5j_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2775_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27b,V5j_2E0))))) = s(tyop_2Emin_2Ebool,f2775_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27b,V5j_2E0)))) # label(def3_2Ethm_2Eres__quan_2ERES__EXISTS__REORDER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5862 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2780_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2780_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2780_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5863 (all A_27a all V0P_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,f2782_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__FORALL__DIFF) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5864 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5865 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2777_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2777_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2777_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5866 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2761_1_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2761_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2761_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5867 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5868 (all A_27a all V1m_2E0 all V2x_2E0 all V3y_2E0 ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(A_27a,V3y_2E0)))) -> s(A_27a,V3y_2E0) = s(A_27a,V2x_2E0)) <-> p(s(tyop_2Emin_2Ebool,f2751_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE__ALT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5869 (all A_27a all V0p_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2787_0_2E1(s(tyop_2Emin_2Ebool,V1m_2E0)))))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) | p(s(tyop_2Emin_2Ebool,V1m_2E0)))) # label(thm_2Eres__quan_2ERES__FORALL__NULL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5870 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5871 (all A_27a all X0_2E0 all X1_2E0 s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a)),c_2Ebool_2ERES__SELECT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__SELECT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5872 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2751_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2751_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2751_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5873 (all A_27a all V0x_2E0 all V1sos_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2763_0_2E1(s(A_27a,V0x_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0)))))) # label(thm_2Eres__quan_2EIN__BIGUNION__RES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5874 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5875 (all A_27a all A_27b all V2R_2E0 all V5j_2E0 all V6i_2E0 s(tyop_2Emin_2Ebool,f2792_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27b,V5j_2E0),s(A_27a,V6i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V6i_2E0))),s(A_27b,V5j_2E0)))) # label(def2_2Ethm_2Eres__quan_2ERES__FORALL__REORDER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5876 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2763_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2763_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2763_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5877 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2795_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2795_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2795_3_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5878 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5879 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5880 (all A_27b all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,f2773_0_2E1(s(A_27b,V3x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__T) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5881 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2761_1_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2761_1_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2761_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5882 (all A_27a all V0P_2E0 all V1f_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f159_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ERES__SELECT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5883 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2768_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2768_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2768_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5884 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDIFF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5885 (all A_27a all A_27b all V0p_2E0 all V1m1_2E0 all V2m2_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) -> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2m2_2E0),s(A_27a,V3x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1m1_2E0),s(A_27a,V3x_2E0))))) <-> s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2m2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m1_2E0))))) # label(thm_2Eres__quan_2ERES__ABSTRACT__EQUAL__EQ) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5886 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5887 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2753_0_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2753_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2753_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5888 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5889 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2793_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2793_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef2793_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5890 (all A_27a all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,f2762_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) # label(def2_2Ethm_2Eres__quan_2ERES__EXISTS__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5891 (all A_27a all X0_2E0 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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5892 (all A_27a all V0P_2E0 all V1s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2786_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2786_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Eres__quan_2ENOT__RES__FORALL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5893 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2768_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2768_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2768_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5894 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2793_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2793_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2793_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5895 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2794_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2794_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2794_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5896 (all A_27a all V0P_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2768_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2768_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Eres__quan_2ENOT__RES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5897 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2777_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2777_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2777_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5898 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2777_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2777_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2777_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5899 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__FORALL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5900 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2770_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2770_0_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2770_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5901 (all A_27a all V0p_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__ALT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5902 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2782_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2782_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2782_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5903 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5904 (all A_27a all V1Q_2E0 all V4i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4i_2E0))) = s(tyop_2Emin_2Ebool,f2778_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V4i_2E0)))) # label(def2_2Ethm_2Eres__quan_2ERES__EXISTS__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5905 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2764_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2764_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2764_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5906 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2792_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2792_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef2792_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5907 (all A_27a all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f2779_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5908 (all A_27a all V0P_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))) # label(thm_2Eres__quan_2ERES__EXISTS__SUBSET) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5909 (all A_27a all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,f2768_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) # label(def1_2Ethm_2Eres__quan_2ENOT__RES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.03 5910 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2779_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2779_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2779_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5911 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2775_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,f2775_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef2775_1_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5912 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2778_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2778_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2778_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5913 (all A_27a all V0P_2E0 all V1f_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f159_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0))))) = s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))) # label(thm_2Eres__quan_2ERES__SELECT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5914 (all A_27a all V0P_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))))) # label(thm_2Eres__quan_2ERES__FORALL__SUBSET) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5915 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2775_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2775_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2775_3_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5916 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2781_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2781_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2781_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5917 (all A_27a all V0P_2E0 all V1Q_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2777_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2777_3_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2777_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2777_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))))) # label(thm_2Eres__quan_2ERES__DISJ__EXISTS__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5918 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ebool_2ERES__ABSTRACT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) = s(A_27b,c_2Ebool_2ERES__ABSTRACT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ERES__ABSTRACT_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5919 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2786_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2786_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2786_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5920 (all A_27a all V0P_2E0 all V1sos_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2780_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2780_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Eres__quan_2ERES__FORALL__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5921 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2753_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2753_0_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ef2753_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5922 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2776_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2776_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2776_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5923 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f158_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef158_2_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5924 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2R_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2792_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2792_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0)))))) # label(thm_2Eres__quan_2ERES__FORALL__REORDER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5925 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2764_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2764_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2764_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5926 (all A_27a all V0P_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNION) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5927 (all A_27a all V2R_2E0 all V6i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V6i_2E0))) = s(tyop_2Emin_2Ebool,f2795_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V6i_2E0)))) # label(def2_2Ethm_2Eres__quan_2ERES__FORALL__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5928 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2778_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2778_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2778_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5929 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2775_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,f2775_3_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef2775_3_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5930 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f158_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef158_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5931 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2795_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2795_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2795_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5932 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2779_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2779_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2779_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5933 (all A_27a all V0p_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))))) # label(thm_2Eres__quan_2ERES__EXISTS__EMPTY) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5934 (all A_27a all V0p_2E0 s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))) = s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) # label(thm_2Eres__quan_2ERES__SELECT__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5935 (all A_27a all V0p_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__EMPTY) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5936 (all A_27a all V0P_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,f2780_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5937 (all A_27a all V0P_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,f2768_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ENOT__RES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5938 (all A_27a all V0P_2E0 all V1s_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2760_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2760_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__ELIM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5939 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5940 (all A_27a all V0P_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Eres__quan_2ERES__FORALL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5941 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2775_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2775_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef2775_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5942 (all A_27a all V0P_2E0 all V1sos_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2762_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2762_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5943 (all A_27a all V0P_2E0 all V1f_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Emin_2Ebool,f158_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V3x_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5944 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__FORALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5945 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2781_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,f2781_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2781_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5946 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2795_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2795_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2795_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5947 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5948 (all A_27a all V0P_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Eres__quan_2ERES__EXISTS__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5949 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5950 (all A_27a all V3x_2E0 all V4s_2E0 s(tyop_2Emin_2Ebool,f2779_1_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__FORALL__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5951 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2775_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2775_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ef2775_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5952 (all A_27a all A_27b all V2R_2E0 all V3i_2E0 all V4j_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3i_2E0))),s(A_27b,V4j_2E0))) = s(tyop_2Emin_2Ebool,f2792_3_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0),s(A_27a,V3i_2E0),s(A_27b,V4j_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__REORDER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5953 (all A_27a all V0P_2E0 all V1Q_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2778_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2778_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2778_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))))) # label(thm_2Eres__quan_2ERES__EXISTS__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5954 (all A_27a all V2t_2E0 all V0P_2E0 all V5x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2764_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5x_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__DIFF) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5955 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5956 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5957 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2762_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2762_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2762_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5958 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5959 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2776_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2776_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2776_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5960 (all A_27a all V0P_2E0 all V1sos_2E0 ((all V3x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2779_1_2E1(s(A_27a,V3x_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1sos_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2779_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))))) # label(thm_2Eres__quan_2ERES__FORALL__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5961 (all A_27a all V1Q_2E0 all V2R_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3i_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V3i_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2778_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V3i_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5962 (all A_27a all A_27b all A_27c all V0P_2E0 all V1s_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2757_0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2757_1_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__T) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5963 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2795_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2795_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2795_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5964 (all A_27a all A_27b all V0P_2E0 all V1R_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2793_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0)))))) <-> (all V3x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2793_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27b,V3x_2E0))))))))) # label(thm_2Eres__quan_2ERES__FORALL__FORALL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5965 (all A_27a all A_27b all V0p_2E0 all V1m_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1m_2E0)))))) # label(thm_2Eres__quan_2ERES__ABSTRACT__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5966 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2757_1_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f2757_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2757_1_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5967 (all A_27a all V0p_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5968 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 all V2R_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2775_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2775_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__REORDER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5969 (all A_27a all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,f2786_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) # label(def1_2Ethm_2Eres__quan_2ENOT__RES__FORALL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5970 (all A_27a all V2R_2E0 all V6i_2E0 s(tyop_2Emin_2Ebool,f2777_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V6i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V6i_2E0)))) # label(def2_2Ethm_2Eres__quan_2ERES__DISJ__EXISTS__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5971 (all A_27a all V0P_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))) <-> (exists V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0),s(A_27a,V2x_2E0)))))))) # label(thm_2Eres__quan_2ERES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5972 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2779_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,f2779_1_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2779_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5973 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5974 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2777_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2777_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2777_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5975 (all A_27a all A_27b all A_27c all V0P_2E0 all V1s_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2752_0_2E0)))) <-> (exists V4y_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27b,V4y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__SING) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5976 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2762_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2762_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2762_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5977 (all A_27a all V0P_2E0 all V1Q_2E0 all V3j_2E0 (p(s(tyop_2Emin_2Ebool,f2795_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3j_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3j_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3j_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__DISJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5978 (all A_27a all A_27b all A_27c all V0P_2E0 all V1s_2E0 all V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2791_0_2E0))))) # label(thm_2Eres__quan_2ERES__FORALL__T) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5979 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2796_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2796_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2796_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5980 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2777_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2777_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2777_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5981 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2782_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2782_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2782_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5982 (all A_27a all A_27b all V0P_2E0 all V1s_2E0 all V2t_2E0 all V3x_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2764_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2764_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__DIFF) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5983 (all A_27a all V1s_2E0 all V0P_2E0 all V3x_2E0 (p(s(tyop_2Emin_2Ebool,f2760_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE__ELIM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5984 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGINTER_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGINTER_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGINTER_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5985 (all A_27a all A_27b all V0m_2E0 s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0m_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0m_2E0)) # label(thm_2Eres__quan_2ERES__ABSTRACT__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5986 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2795_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2795_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2795_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5987 (all A_27a all V0P_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5988 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2751_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2751_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2751_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5989 (all A_27a all A_27b all V1R_2E0 all V3x_2E0 all V4i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4i_2E0))),s(A_27b,V3x_2E0))) = s(tyop_2Emin_2Ebool,f2793_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27b,V3x_2E0),s(A_27a,V4i_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__FORALL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5990 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2778_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2778_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2778_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5991 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2793_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2793_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2793_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5992 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2786_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2786_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2786_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5993 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2786_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2786_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2786_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5994 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2760_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2760_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2760_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5995 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2796_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2796_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2796_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5996 (all A_27a all V0P_2E0 all V1Q_2E0 all V3i_2E0 (p(s(tyop_2Emin_2Ebool,f2777_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3i_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3i_2E0)))) | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3i_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ERES__DISJ__EXISTS__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5997 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2751_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2751_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2751_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5998 (all A_27a all V2R_2E0 all V5i_2E0 s(tyop_2Emin_2Ebool,f2777_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_2E0)))) # label(def3_2Ethm_2Eres__quan_2ERES__DISJ__EXISTS__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 5999 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6000 (all A_27a all V1m_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,V1m_2E0) = s(tyop_2Emin_2Ebool,f2770_0_2E2(s(tyop_2Emin_2Ebool,V1m_2E0),s(A_27a,V2x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__EXISTS__NULL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6001 (all A_27a all V0p_2E0 all V1m_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & p(s(tyop_2Emin_2Ebool,V1m_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2770_0_2E1(s(tyop_2Emin_2Ebool,V1m_2E0)))))))) # label(thm_2Eres__quan_2ERES__EXISTS__NULL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6002 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2792_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2792_2_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2792_2_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6003 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2777_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2777_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2777_3_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6004 (all A_27a all A_27b all A_27c all V0P_2E0 all V1s_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2790_0_2E0)))) <-> s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Eres__quan_2ERES__FORALL__F) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6005 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6006 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2778_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2778_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2778_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6007 (all A_27a all V0P_2E0 all V2i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2i_2E0))) = s(tyop_2Emin_2Ebool,f2794_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2i_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6008 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f2792_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,f2792_3_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef2792_3_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6009 (all A_27a all V0P_2E0 all V1s_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) # label(thm_2Eres__quan_2ERES__FORALL__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6010 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2751_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2751_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2751_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6011 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2780_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2780_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2780_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6012 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2780_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2780_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2780_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6013 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6014 (all A_27a all V0P_2E0 all V3s_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2780_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) = s(tyop_2Emin_2Ebool,f2780_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__FORALL__BIGUNION) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6015 (all A_27a all V0p_2E0 s(A_27a,c_2Ebool_2ERES__SELECT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0))) = s(A_27a,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2750_0_2E0)))) # label(thm_2Eres__quan_2ERES__SELECT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6016 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2787_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2787_0_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2787_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6017 (all A_27a all V0p_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,V1m_2E0)) & (exists V3x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2753_0_2E1(s(tyop_2Emin_2Ebool,V1m_2E0)))))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__NULL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6018 (all A_27c all X0_2E0 s(tyop_2Emin_2Ebool,f2774_0_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f2774_0_2E0),s(A_27c,X0_2E0)))) # label(arityeq1_2Ef2774_0_2E1_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6019 (all A_27a all V2R_2E0 all V5i_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_2E0))) = s(tyop_2Emin_2Ebool,f2796_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V5i_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__FORALL__CONJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6020 (all A_27a all V0P_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,f2764_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V4x_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__EXISTS__DIFF) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6021 (all A_27a all V0P_2E0 all V1Q_2E0 all V2R_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2796_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2796_2_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2796_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0)))))))) # label(thm_2Eres__quan_2ERES__FORALL__CONJ__DIST) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6022 (all A_27a all V1m_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,V1m_2E0) = s(tyop_2Emin_2Ebool,f2787_0_2E2(s(tyop_2Emin_2Ebool,V1m_2E0),s(A_27a,V2x_2E0)))) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__NULL) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6023 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2775_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2775_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2775_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6024 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2760_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2760_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2760_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6025 (all A_27a all V0P_2E0 all V2x_2E0 s(tyop_2Emin_2Ebool,f2760_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__EXISTS__UNIQUE__ELIM) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6026 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2792_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2792_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2792_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6027 (all A_27b all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f2752_0_2E0),s(A_27b,X0_2E0))) = s(tyop_2Emin_2Ebool,f2752_0_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ef2752_0_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6028 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2795_3_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2795_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2795_3_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6029 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6030 (all A_27a all V3x_2E0 all V4s_2E0 s(tyop_2Emin_2Ebool,f2761_1_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4s_2E0)))) # label(def1_2Ethm_2Eres__quan_2ERES__EXISTS__BIGINTER) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6031 (all A_27a all V0P_2E0 all V1f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f158_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6032 (all A_27a all V0p_2E0 all V1m_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2751_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0p_2E0)))))) # label(thm_2Eres__quan_2ERES__EXISTS__UNIQUE__ALT) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6033 (all A_27a all V0P_2E0 all V1j_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1j_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(A_27a,V1j_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2794_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2Eres__quan_2ERES__FORALL__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6034 (all A_27a all V2t_2E0 all V0P_2E0 all V5x_2E0 ((-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V5x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,f2782_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V5x_2E0)))))) # label(def0_2Ethm_2Eres__quan_2ERES__FORALL__DIFF) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6035 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2777_2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,f2777_2_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2777_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6036 (all A_27a all V0xss_2E0 all V1choice_2E0 ((all V2xs_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),V1choice_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,f2829_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),V1choice_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Eall__choices__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6037 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2960_3_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2960_3_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2960_3_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.04 6038 (all A_27a all V0r_2E0 all V1s_2E0 all V2x_2E0 (-p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),f2947_0_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))))))) # label(thm_2Eset__relation_2Eextend__linear__order) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6039 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),f2971_1_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))))),f2971_1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef2971_1_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6040 (all A_27a all V1x_2E0 all V2y_2E0 all V0r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & s(A_27a,V1x_2E0) != s(A_27a,V2y_2E0) <-> p(s(tyop_2Emin_2Ebool,f2806_1_2E3(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Estrict__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6041 (all A_27a all A_27b all V0r_27_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0)))))))) # label(thm_2Eset__relation_2Edomain__mono) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6042 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6043 (all A_27a all A_27b all V1x_2E0 all V0r_2E0 (p(s(tyop_2Emin_2Ebool,f2802_1_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))) <-> (exists V2y_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))))))) # label(def0_2Ethm_2Eset__relation_2Edomain__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6044 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6045 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2825_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2825_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2825_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6046 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 s(tyop_2Eoption_2Eoption(A_27a),f2970_0_2E5(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Enum_2Enum,X3_2E0),s(tyop_2Eoption_2Eoption(A_27a),X4_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))))),f2970_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X4_2E0)))) # label(arityeq5_2Ef2970_0_2E5_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6047 (all A_27a all V0r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) # label(thm_2Eset__relation_2Etransitive__tc) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6048 (all A_27a all V0xss_2E0 all V1xs_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2828_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1xs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eper__restrict_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1xs_2E0)))) # label(thm_2Eset__relation_2Eper__restrict__def) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6049 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EStrongLinearOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EStrongLinearOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6050 (all A_27a all V0f_2E0 all V12x_2E0 all V13y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V12x_2E0),s(A_27a,V13y_2E0))),s(tyop_2Emin_2Ebool,f2960_3_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(A_27a,V12x_2E0),s(A_27a,V13y_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2960_1_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(A_27a,V12x_2E0),s(A_27a,V13y_2E0)))) # label(def1_2Ethm_2Eset__relation_2Enat__order__iso__thm) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6051 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 ((exists V6z_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__ind) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6052 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),f2947_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),f2947_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2947_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6053 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2806_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),f2806_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2806_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6054 (all A_27a all A_27b all V0r_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Ereln__to__rel__inv) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6055 (all A_27a all V0r_2E0 all V1x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Eacyclic__irreflexive) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6056 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Epartial__order_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Epartial__order_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6057 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2826_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2826_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2826_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.00/108.05 6058 (all A_27a all V0s_2E0 all V1r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eirreflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Eset__relation_2Eirreflexive__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6059 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakLinearOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWeakLinearOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6060 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eupper__bounds_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2Eupper__bounds_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Eupper__bounds_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6061 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V0y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0)))))))) # label(thm_2Eset__relation_2Ein__dom__rg) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6062 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Enum_2ESUC_2E1) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6063 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),f2951_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Elinear__order) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6064 (all A_27a all V0xss_2E0 all V1choice_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),V1choice_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0))),s(tyop_2Emin_2Ebool,f2829_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),V1choice_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2829_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),V1choice_2E0)))) # label(def1_2Ethm_2Eset__relation_2Eall__choices__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6065 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Etransitive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Etransitive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6066 (all A_27a all V0s_2E0 all V1r_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))))))) # label(thm_2Eset__relation_2Efinite__linear__order__has__maximal) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6067 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2ERRUNIV_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2ERRUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2Eset__relation_2ERRUNIV_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6068 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6069 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 s(tyop_2Eoption_2Eoption(A_27a),f2971_0_2E5(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Enum_2Enum,X3_2E0),s(tyop_2Eoption_2Eoption(A_27a),X4_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))))),f2971_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X4_2E0)))) # label(arityeq5_2Ef2971_0_2E5_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6070 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6071 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),f2860_0_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),f2860_0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef2860_0_2E3_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6072 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V0_2E0) = s(A_27a,V1_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6073 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Erange_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6074 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6075 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6076 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2807_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),f2807_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2807_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6077 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Elinear__order_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Elinear__order_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6078 (all A_27a all V0s_2E0 all V1lo_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1lo_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Eset__relation_2Eminimal__elements__subset) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6079 (all A_27a all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Enum__order_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Elinear__order__num__order) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6080 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)) # label(thm_2Eset__relation_2ERREFL__EXP__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6081 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Eset__relation_2Erel__to__reln_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Erel__to__reln_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6082 (all A_27a all V0xs_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2807_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Euniv__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) # label(thm_2Eset__relation_2Euniv__reln__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6083 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6084 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6085 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6086 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6087 (all A_27a all A_27b all V0r_2E0 all V1x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Ebool,f2802_1_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2802_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(A_27a,V1x_2E0)))) # label(def1_2Ethm_2Eset__relation_2Edomain__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6088 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERRANGE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERRANGE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6089 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2829_1_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Ebool)),f2829_1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X1_2E0)))) # label(arityeq2_2Ef2829_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6090 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),f2960_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2960_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0)))) # label(arityeq1_2Ef2960_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6091 (all A_27a all V0xs_2E0 all V1x1_2E0 all V2x2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2807_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(A_27a,V1x1_2E0),s(A_27a,V2x2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x1_2E0),s(A_27a,V2x2_2E0))),s(tyop_2Emin_2Ebool,f2807_1_2E3(s(A_27a,V1x1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(A_27a,V2x2_2E0)))))) # label(def1_2Ethm_2Eset__relation_2Euniv__reln__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6092 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V4x_2E0 all V5y_2E0 ((exists V6z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__strongind) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6093 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Epartial__order__linear__order) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6094 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6095 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6096 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Erelation_2ERSUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6097 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2963_2_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2963_2_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2963_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6098 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eantisym_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Eantisym_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6099 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6100 (all A_27a all A_27b all V0r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))) # label(thm_2Eset__relation_2Edomain__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6101 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eirreflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Eirreflexive__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6102 (all A_27a all A_27b all X0_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6103 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2963_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,f2963_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef2963_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6104 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6105 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V4x_2E0 all V5y_2E0 ((exists V6z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__ind__left) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6106 (all A_27a all V0xs_2E0 all V1r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))))) # label(thm_2Eset__relation_2Eminimal__elements__rrestrict) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6107 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6108 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6109 (all A_27a ((all V0s_2E0 all V1r_27_2E0 all V2r_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Enth__min_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Eget__min_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0)))))) & (all V8s_2E0 all V9r_27_2E0 all V10r_2E0 all V11n_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Enth__min_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V9r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,V11n_2E0))))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),f2971_1_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V9r_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0),s(tyop_2Enum_2Enum,V11n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Eget__min_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V9r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0)))))))) & (all V3s_2E0 all V4r_27_2E0 all V5r_2E0 all V6n_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Enth__min_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),f2971_0_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0),s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Eget__min_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0)))))))))) # label(thm_2Eset__relation_2Enth__min__def__compute) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6110 (all A_27a all V4r_27_2E0 all V3s_2E0 all V5r_2E0 all V6n_2E0 all V7min_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2970_1_2E1(s(tyop_2Eoption_2Eoption(A_27a),V7min_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Enth__min_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V7min_2E0))))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0))),s(tyop_2Enum_2Enum,V6n_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),f2970_0_2E5(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0),s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Eoption_2Eoption(A_27a),V7min_2E0)))) # label(def1_2Ethm_2Eset__relation_2Enth__min__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6111 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Etc_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etc_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Etc_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6112 (all A_27a all V0r_2E0 all V1s_2E0 all V2s_27_2E0 all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0))) # label(thm_2Eset__relation_2Eminimal__linear__order__unique) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6113 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6114 (all A_27a all V0f_2E0 all V1s_2E0 ((all V6m_2E0 all V7x_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V7x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V6m_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V7x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) & (all V4x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (exists V5m_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V5m_2E0)))))) & (all V2n_2E0 all V3m_2E0 (s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V3m_2E0))) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) & s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V2n_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V3m_2E0))) -> s(tyop_2Enum_2Enum,V2n_2E0) = s(tyop_2Enum_2Enum,V3m_2E0))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2960_0_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2960_1_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0))))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Enat__order__iso__thm) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6115 (all A_27a all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6116 (all A_27a all V0x_2E0 all V1s_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Eset__relation_2Ein__rrestrict__alt) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6117 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))))),f2861_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),f2861_0_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef2861_0_2E4_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6118 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Eset__relation_2Ercomp_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Ercomp_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6119 (all A_27a all V0r_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) # label(thm_2Eset__relation_2Etc__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6120 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2830_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))),f2830_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef2830_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6121 (all A_27a all A_27b all V0r_2E0 all V1r_27_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))))) # label(thm_2Eset__relation_2Efinite__prefixes__subset__r) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6122 (all A_27a all V0xs_2E0 all V1r_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,f2822_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2822_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(A_27a,V2x_2E0)))) # label(def1_2Ethm_2Eset__relation_2Emaximal__elements__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6123 (all A_27a all A_27b all V0R_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f2819_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))))))) # label(thm_2Eset__relation_2Erel__to__reln__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6124 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6125 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eall__choices_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Eall__choices_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Eall__choices_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.05 6126 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6127 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f2819_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f2819_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2819_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6128 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) -> (exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))))) # label(thm_2Eset__relation_2Efinite__acyclic__has__maximal__path) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6129 (all A_27a all A_27b all A_27c all V2x_2E0 all V0r1_2E0 all V3y_2E0 all V1r2_2E0 (p(s(tyop_2Emin_2Ebool,f2805_1_2E4(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0),s(A_27b,V3y_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0)))) <-> (exists V4z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27c,V4z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,V4z_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0)))))))) # label(def0_2Ethm_2Eset__relation_2Ercomp__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6130 (all A_27a all V0f_2E0 all V8x_2E0 all V9y_2E0 ((exists V10m_2E0 exists V11n_2E0 (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V8x_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V10m_2E0))) & s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V11n_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V9y_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V10m_2E0),s(tyop_2Enum_2Enum,V11n_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,f2960_2_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(A_27a,V8x_2E0),s(A_27a,V9y_2E0)))))) # label(def2_2Ethm_2Eset__relation_2Enat__order__iso__thm) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6131 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6132 (all A_27a all V0r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Eacyclic__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6133 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Efchains_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efchains_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Efchains_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6134 (all A_27a all V0f_2E0 all V8x_2E0 all V9y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2960_0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(A_27a,V8x_2E0),s(A_27a,V9y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V8x_2E0),s(A_27a,V9y_2E0))),s(tyop_2Emin_2Ebool,f2960_2_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(A_27a,V8x_2E0),s(A_27a,V9y_2E0)))))) # label(def3_2Ethm_2Eset__relation_2Enat__order__iso__thm) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6135 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Eset__relation_2Erel__to__reln_2E0)) # label(thm_2Eset__relation_2Erel__to__reln__IS__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6136 (all A_27a s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)) # label(thm_2Eset__relation_2Etc__empty__eqn) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6137 (all A_27a ((all V3s_2E0 all V4r_27_2E0 all V5r_2E0 all V6n_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Enth__min_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),f2970_0_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0),s(tyop_2Enum_2Enum,V6n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Eget__min_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0)))))))) & (all V0s_2E0 all V1r_27_2E0 all V2r_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Eget__min_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Enth__min_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))))) # label(thm_2Eset__relation_2Enth__min__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6138 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))) # label(thm_2Eset__relation_2Eacyclic__WF) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6139 (all A_27a all A_27b all V0r_2E0 all V1y_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2803_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(A_27a,V1y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Ebool,f2803_1_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(def1_2Ethm_2Eset__relation_2Erange__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6140 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Edomain_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6141 (all A_27a all V2x_2E0 all V1s_2E0 all V3y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3y_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2947_0_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V3y_2E0)))) # label(def0_2Ethm_2Eset__relation_2Eextend__linear__order) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6142 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6143 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6144 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIGUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6145 (all A_27a all V4r_27_2E0 all V3s_2E0 all V5r_2E0 all V6n_2E0 all V7min_2E0 s(tyop_2Eoption_2Eoption(A_27a),f2971_0_2E5(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0),s(tyop_2Enum_2Enum,V6n_2E0),s(tyop_2Eoption_2Eoption(A_27a),V7min_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2971_3_2E1(s(tyop_2Eoption_2Eoption(A_27a),V7min_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Enth__min_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V7min_2E0))))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V5r_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V6n_2E0))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))))) # label(def1_2Ethm_2Eset__relation_2Enth__min__def__compute) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6146 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> (all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Ereflexive__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6147 (all A_27a all V0r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Eacyclic__SWAP) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6148 (all A_27a all V0s_2E0 all V1R_2E0 p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))))) # label(thm_2Eset__relation_2ERREFL__EXP__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6149 (all A_27a all A_27b all V0y_2E0 all V1x_2E0 all V2r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereln__to__rel_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0),s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_2E0)))) # label(thm_2Eset__relation_2Ereln__to__rel__app) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6150 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2Eminimal__elements_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Eminimal__elements_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6151 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2823_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2823_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2823_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6152 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6153 (all A_27a all V0xs_2E0 all V1r_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2823_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,f2823_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) # label(def1_2Ethm_2Eset__relation_2Eminimal__elements__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6154 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ETC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6155 (all A_27a all V0x_2E0 all V1s_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eall__choices_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))))) -> (exists V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3z_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3z_2E0)))))))) # label(thm_2Eset__relation_2Eall__choices__thm) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6156 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Estrict__linear__order_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Estrict__linear__order_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6157 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2951_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),f2951_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2951_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6158 (all A_27a all V0xs_2E0 all V1r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2823_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) # label(thm_2Eset__relation_2Eminimal__elements__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6159 (all A_27a all V0r_2E0 all V1s_2E0 all V2x_2E0 all V3s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) -> (exists V4x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_27_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Efinite__prefix__po__has__minimal__path) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6160 (all A_27a all A_27b all V0r_2E0 all V1x_2E0 all V2x_27_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereln__to__rel_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(A_27a,V1x_2E0),s(A_27b,V2x_27_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2x_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))) # label(thm_2Eset__relation_2Ereln__to__rel__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6161 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Erelation_2ESTRORD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ESTRORD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6162 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3y_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) # label(thm_2Eset__relation_2Emaximal__linear__order) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6163 (all A_27a all X0_2E0 s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6164 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINSERT_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6165 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6166 (all A_27a all A_27b all V0s_2E0 all V1t_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1t_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0s_2E0) <-> (all V2x_2E0 all V3y_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1t_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Eset__relation_2Erextension) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6167 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2823_1_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2823_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef2823_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6168 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2963_2_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2963_2_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2963_2_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6169 (all A_27a all V0xs_2E0 all V1xss_2E0 all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eper_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eper_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(A_27a,V2e_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2963_0_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))))))))) # label(thm_2Eset__relation_2Eper__delete) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6170 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eacyclic_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Eacyclic_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6171 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 ((exists V6z_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__strongind__right) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6172 (all A_27a all A_27b all A_27c all V0r1_2E0 all V1r2_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f2805_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0)))) # label(thm_2Eset__relation_2Ercomp__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6173 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6174 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6175 (all A_27a all V2x_2E0 all V3y_2E0 all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,f2804_1_2E4(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Errestrict__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6176 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERRUNIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2ERRUNIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2ERRUNIV_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6177 (all A_27a all V0xss_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eall__choices_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2829_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0)))))) # label(thm_2Eset__relation_2Eall__choices__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6178 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) -> (all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))))))) # label(thm_2Eset__relation_2Efinite__acyclic__has__maximal) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6179 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6180 (all A_27a all V0s_2E0 all V1x_2E0 all V2x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2ERRUNIV_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V1x_2E0),s(A_27a,V2x_27_2E0)))))) # label(thm_2Eset__relation_2ERRUNIV__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6181 (all A_27a all A_27b all A_27c all V0r1_2E0 all V1r2_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f2805_0_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0),s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))),s(tyop_2Emin_2Ebool,f2805_1_2E4(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V0r1_2E0),s(A_27b,V3y_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V1r2_2E0)))))) # label(def1_2Ethm_2Eset__relation_2Ercomp__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6182 (all A_27a all V0r_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) # label(thm_2Eset__relation_2Esubset__tc) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6183 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),f2831_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),f2831_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2831_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6184 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6185 (all A_27a all V1xs_2E0 all V0xss_2E0 all V2xs_27_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2828_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1xs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs_27_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1xs_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0xss_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Eper__restrict__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6186 (all A_27a all A_27b all V0r2_2E0 all V1r1_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r1_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r2_2E0) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r1_2E0))))) # label(thm_2Eset__relation_2Ereln__to__rel__11) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6187 (all A_27a all A_27b all A_27c all V0r2_2E0 all V1r1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V1r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V0r2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V0r2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V1r1_2E0)))))))) # label(thm_2Eset__relation_2Ercomp__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6188 (all A_27a all V0r1_2E0 all V1r2_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0)))))) -> (all V4x_2E0 all V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0)))))))))) # label(thm_2Eset__relation_2Etc__implication) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6189 (all A_27a all A_27b all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(thm_2Eset__relation_2Erel__to__reln__inv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6190 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6191 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))))) # label(thm_2Eset__relation_2Eminimal__TC) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6192 (all A_27a all A_27b all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6193 (all A_27a all V0r_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) # label(thm_2Eset__relation_2Estrict__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6194 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6195 (all A_27a all V12min_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V12min_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> p(s(tyop_2Emin_2Ebool,f2971_2_2E1(s(tyop_2Eoption_2Eoption(A_27a),V12min_2E0)))))) # label(def2_2Ethm_2Eset__relation_2Enth__min__def__compute) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6196 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),f2971_2_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,f2971_2_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ef2971_2_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6197 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Eset__relation_2Etc__closure) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6198 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6199 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6200 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Ereflexive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6201 (all A_27a all X0_2E0 s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epred__set_2ECHOICE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6202 (all A_27a all V0r_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Efchains_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2826_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Efchains__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6203 (all A_27a all V0r_2E0 ((all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) & (all V3x_2E0 all V4y_2E0 ((exists V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V5z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5z_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))))) # label(thm_2Eset__relation_2Etc__rules) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6204 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0)))))) & (all V3x_2E0 all V4y_2E0 ((exists V5z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5z_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_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)),V1tc_27_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))) -> (all V6x_2E0 all V7y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27a,V7y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))))) # label(thm_2Eset__relation_2Ertc__ind__right) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6205 (all A_27a all V0s_2E0 all V1r_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3y_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Echain_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) # label(thm_2Eset__relation_2Echain__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.06 6206 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6207 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Etc__domain__range) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6208 (all A_27a all V2e_2E0 all V4es_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f2963_2_2E2(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4es_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4es_2E0),s(A_27a,V2e_2E0)))) # label(def0_2Ethm_2Eset__relation_2Eper__delete) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6209 (all A_27a all A_27b all V0r_2E0 all V1R_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))) <-> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0))))) # label(thm_2Eset__relation_2Erel__to__reln__swap) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6210 (all A_27a all V0s_2E0 all V1r_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))))))) # label(thm_2Eset__relation_2Estrict__linear__order__restrict) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6211 (all A_27a all V1s_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2951_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Elinear__order) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6212 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2803_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2803_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2803_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6213 (all A_27a all V0r_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Elinear__order__dom__rng) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6214 (all A_27a all V3es_2E0 all V2e_2E0 all V1xss_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3es_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3es_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2963_2_2E1(s(A_27a,V2e_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,f2963_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3es_2E0),s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))))) # label(def1_2Ethm_2Eset__relation_2Eper__delete) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6215 (all A_27a all V0x_2E0 all V1y_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) # label(thm_2Eset__relation_2Etc__empty) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6216 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),f2828_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2828_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef2828_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6217 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6218 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) & (all V4x_2E0 all V5y_2E0 ((exists V6z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V6z_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__ind__right) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6219 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))))))) # label(thm_2Eset__relation_2Efinite__linear__order__has__minimal) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6220 (all A_27a all V7min_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V7min_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) <-> p(s(tyop_2Emin_2Ebool,f2970_1_2E1(s(tyop_2Eoption_2Eoption(A_27a),V7min_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Enth__min__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6221 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),f2828_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2828_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2828_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6222 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6223 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2960_1_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),f2960_1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0)))) # label(arityeq1_2Ef2960_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6224 (all A_27a all V0s_2E0 all V1r_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Eset__relation_2Errestrict__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6225 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6226 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6227 (all A_27a all V0r_2E0 all V1r_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0)))))))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0)))))))) # label(thm_2Eset__relation_2Eacyclic__union) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6228 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Etc_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Etc_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6229 (all A_27a all V0f_2E0 all V12x_2E0 all V13y_2E0 (p(s(tyop_2Emin_2Ebool,f2960_3_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(A_27a,V12x_2E0),s(A_27a,V13y_2E0)))) <-> (exists V14m_2E0 exists V15n_2E0 (s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V15n_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V13y_2E0))) & s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,V14m_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V12x_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V14m_2E0),s(tyop_2Enum_2Enum,V15n_2E0)))))))) # label(def0_2Ethm_2Eset__relation_2Enat__order__iso__thm) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6230 (all A_27a all V0s_2E0 all V1r_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Eset__relation_2Erange__rrestrict__SUBSET) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6231 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6232 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6233 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6234 (all A_27a all V0lo_2E0 all V1X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))) # label(thm_2Eset__relation_2Elinear__order__dom__rg) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6235 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2822_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,f2822_1_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef2822_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6236 (all A_27a all V0r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Ereflexive__reln__to__rel__conv__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6237 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2963_0_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),f2963_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef2963_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6238 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Erange_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6239 (all A_27a all V1k_2E0 all V0r_2E0 (p(s(tyop_2Emin_2Ebool,f2826_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1k_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Echain_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1k_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1k_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & (all V2C_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1k_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eupper__bounds_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2C_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2C_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1k_2E0))) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Echain_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2C_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eupper__bounds_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2C_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2C_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eupper__bounds_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2C_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2C_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1k_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))))) # label(def0_2Ethm_2Eset__relation_2Efchains__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6240 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6241 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2808_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2808_0_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2808_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6242 (all A_27a all V0r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) <-> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Eset__relation_2Eempty__strict__linear__order) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6243 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6244 (all A_27a all V0r_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Epartial__order__dom__rng) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6245 (all A_27a all A_27b all V0r1_2E0 all V1r2_2E0 all V2s1_2E0 all V3s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r2_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s2_2E0)))))))) # label(thm_2Eset__relation_2Efinite__prefixes__union) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6246 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2802_1_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2802_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2802_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6247 (all A_27a all A_27b all V0x_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0)))))) <-> (exists V2y_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0))))))) # label(thm_2Eset__relation_2Ein__domain) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6248 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),f2806_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2806_0_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2806_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6249 (all A_27a all V0t_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0t_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1s_2E0))))))) # label(thm_2Eset__relation_2Eantisym__subset) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6250 (all A_27a all A_27b all V0r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERRANGE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) # label(thm_2Eset__relation_2Erange__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6251 (all A_27a all V0r_2E0 all V1k_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2826_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1k_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1k_2E0),s(tyop_2Emin_2Ebool,f2826_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1k_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(def1_2Ethm_2Eset__relation_2Efchains__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6252 (all A_27a all A_27b all V0y_2E0 all V1r_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V2x_2E0),s(A_27a,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))) # label(thm_2Eset__relation_2Ein__range) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6253 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),f2861_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))))),f2861_0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2861_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6254 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2ERSUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERRUNIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Eset__relation_2Epartial__order__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6255 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6256 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6257 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EINTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6258 (all A_27a all A_27b all V0r_2E0 all V1s_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_27_2E0)))))) # label(thm_2Eset__relation_2Efinite__prefixes__subset__s) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6259 (all A_27a all A_27b all V0f_2E0 all V1r_2E0 all V5x_2E0 all V6y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V6y_2E0))))),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27a,V6y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),f2861_0_2E4(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(A_27a,V5x_2E0),s(A_27a,V6y_2E0)))) # label(def0_2Ethm_2Eset__relation_2Efinite__prefixes__inj__image) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6260 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6261 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2823_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2823_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2823_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6262 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))),f2804_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2804_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2804_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6263 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6264 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Estrict__partial__order) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6265 (all A_27a all V0r_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Estrict__linear__order__dom__rng) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6266 (all A_27a all A_27b all V1r_2E0 all V0s_2E0 all V2x_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,f2825_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2825_0_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0),s(A_27a,V2x_2E0)))) # label(def1_2Ethm_2Eset__relation_2Eupper__bounds__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6267 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2960_2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2960_2_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2960_2_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6268 (all A_27a all V2e_2E0 all V1xss_2E0 all V3es_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2963_0_2E3(s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3es_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3es_2E0),s(tyop_2Emin_2Ebool,f2963_1_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3es_2E0),s(A_27a,V2e_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))))) # label(def2_2Ethm_2Eset__relation_2Eper__delete) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6269 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Eset__relation_2ERREFL__EXP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2ERREFL__EXP_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6270 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),c_2Erelation_2EO_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EO_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6271 (all A_27a all V0r_2E0 all V1s_2E0 all V2x1_2E0 all V3x2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x1_2E0),s(A_27a,V3x2_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eupper__bounds_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eupper__bounds_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Eupper__bounds__lem) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6272 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Epartial__order__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6273 (all A_27a all V1s_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,f2821_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(A_27a,V3y_2E0) = s(A_27a,V2x_2E0))) # label(def0_2Ethm_2Eset__relation_2ERREFL__EXP__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6274 (all A_27a all V7min_2E0 (p(s(tyop_2Emin_2Ebool,f2971_3_2E1(s(tyop_2Eoption_2Eoption(A_27a),V7min_2E0)))) <-> s(tyop_2Eoption_2Eoption(A_27a),V7min_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) # label(def0_2Ethm_2Eset__relation_2Enth__min__def__compute) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6275 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2Eupper__bounds_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eupper__bounds_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Eupper__bounds_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6276 (all A_27a all V0r_2E0 all V1s_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2804_0_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Ebool,f2804_1_2E4(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(def1_2Ethm_2Eset__relation_2Errestrict__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6277 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) <-> (exists V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Etc__cases__left) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6278 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & (all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Echain_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eupper__bounds_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) -> (exists V3x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))))) # label(thm_2Eset__relation_2Ezorns__lemma) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6279 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2808_0_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2808_0_2E3(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2808_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6280 (all A_27a all V0r_2E0 all V1s_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))))) # label(thm_2Eset__relation_2Elinear__order__subset) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6281 (all A_27a all V0r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Etransitive__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6282 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),f2960_1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2960_1_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2960_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6283 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6284 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Echain_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Echain_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Echain_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6285 (all A_27a all V0x_2E0 all V1s_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0)))))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (exists V3y_2E0 ((p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3y_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0)))))) | s(A_27a,V0x_2E0) = s(A_27a,V3y_2E0)) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0))))))))))) # label(thm_2Eset__relation_2EWF__has__minimal__path) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6286 (all A_27a all V0P_2E0 ((all V4r_27_2E0 all V5s_2E0 all V6r_2E0 all V7n_2E0 ((all V8min_2E0 (s(tyop_2Eoption_2Eoption(A_27a),V8min_2E0) != s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) & s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Eget__min_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V6r_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),V8min_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5s_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V8min_2E0))))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V6r_2E0))))),s(tyop_2Enum_2Enum,V7n_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V4r_27_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V6r_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V7n_2E0)))))))) & (all V1r_27_2E0 all V2s_2E0 all V3r_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r_2E0))))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) -> (all V9v_2E0 all V10v1_2E0 all V11v2_2E0 all V12v3_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V9v_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V10v1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V11v2_2E0))))),s(tyop_2Enum_2Enum,V12v3_2E0))))))) # label(thm_2Eset__relation_2Enth__min__ind) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6287 (all A_27a all V0e_2E0 all V1s_2E0 all V2r1_2E0 all V3r2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r2_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r1_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r2_2E0)))))))) # label(thm_2Eset__relation_2Eminimal__union) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6288 (all A_27a all A_27b all V0r_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0)))))))) # label(thm_2Eset__relation_2Efinite__prefixes__range) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6289 (all A_27a all V0r_2E0 all V1s_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eper_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eper_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eper__restrict_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))))))) # label(thm_2Eset__relation_2Eper__restrict__per) # label(axiom) # label(non_clause). [assumption]. 108.11/108.07 6290 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2825_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2825_0_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2825_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6291 (all A_27a all V0f_2E0 all V1s_2E0 all V2t_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2t_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Enum__order_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Enum__order__finite__prefix) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6292 (all A_27a all A_27b all V0R2_2E0 all V1R1_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R2_2E0))) # label(thm_2Eset__relation_2Erel__to__reln__11) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6293 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V1_2E0)) & p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6294 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESING_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2ESING_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6295 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6296 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2829_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),f2829_0_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X1_2E0)))) # label(arityeq2_2Ef2829_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6297 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2ECURRY_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0)) # label(thm_2Eset__relation_2Ereln__to__rel__IS__CURRY) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6298 (all A_27a all V0s_2E0 all V1r_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))))))) # label(thm_2Eset__relation_2Efinite__strict__linear__order__has__maximal) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6299 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6300 (all A_27a all V0x_2E0 all V1r_2E0 all V2e_2E0 all V3e_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2e_2E0),s(A_27a,V3e_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2e_2E0),s(A_27a,V3e_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))) # label(thm_2Eset__relation_2Errestrict__tc) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6301 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eset__relation_2Eper__restrict_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Eset__relation_2Eper__restrict_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Eper__restrict_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6302 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereflexive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Ereflexive_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6303 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))),f2804_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))),s(A_27a,X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2804_0_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0),s(A_27a,X3_2E0)))) # label(arityeq4_2Ef2804_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6304 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) <-> (exists V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Etc__cases) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6305 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6306 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0)))) # label(thm_2Eset__relation_2Errestrict__rrestrict) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6307 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2826_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2826_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2826_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6308 (all A_27a all V0r_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) # label(thm_2Eset__relation_2Etc__idemp) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6309 (all A_27a all V0x_2E0 all V1y_2E0 all V2r_2E0 all V3s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0)))))) # label(thm_2Eset__relation_2Ein__rrestrict) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6310 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6311 (all A_27a all V2x_2E0 all V1s_2E0 all V3y_2E0 all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V3y_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2830_1_2E4(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Enum__order__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6312 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6313 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),f2860_0_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))),f2860_0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2860_0_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6314 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6315 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6316 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2822_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2822_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2822_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6317 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f2970_1_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),f2970_1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ef2970_1_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6318 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6319 (all A_27a all V0r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Estrict__linear__order__reln__to__rel__conv__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6320 (all A_27a all V0s_2E0 all V1r_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))))))) # label(thm_2Eset__relation_2Elinear__order__restrict) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6321 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),f2805_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))),s(A_27b,X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f2805_0_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef2805_0_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6322 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Enum__order_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Eset__relation_2Enum__order_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Enum__order_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6323 (all A_27a all A_27b all A_27c all V0y_2E0 all V1xy_2E0 all V2x_2E0 all V3s_2E0 all V4r2_2E0 all V5r2_2E0 all V6r1_2E0 all V7r1_2E0 all V8r_2E0 all V9r_2E0 all V10r_2E0 all V11R2_2E0 all V12R1_2E0 all V13R_2E0 all V14R_2E0 (s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereln__to__rel_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V9r_2E0),s(A_27a,V2x_2E0),s(A_27b,V0y_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V9r_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V13R_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V13R_2E0) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V9r_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V9r_2E0))))) & (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V7r1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5r2_2E0))) <-> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V7r1_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5r2_2E0)) & (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V11R2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V12R1_2E0))) <-> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V12R1_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V11R2_2E0)) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V14R_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V14R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERRUNIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Euniv__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))) & s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))))))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))) & s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))))) & s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) & s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EStrongLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))))) & s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))))) & s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))) & s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) & s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eirreflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V6r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V4r2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Erelation_2EO_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),V4r2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),V6r1_2E0))))))) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_2E0))))) & s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ESTRORD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))))))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERRANGE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V8r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V8r_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V9r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V9r_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V14R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V14R_2E0) & s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1xy_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V13R_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V13R_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1xy_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V1xy_2E0))))))) # label(thm_2Eset__relation_2Ereln__rel__conv__thms) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6324 (all A_27b all A_27c all V3s2_2E0 all V1r2_2E0 all V4x_2E0 s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),f2860_0_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0),s(A_27b,V4x_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,V4x_2E0),s(tyop_2Emin_2Ebool,f2860_1_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0),s(A_27b,V4x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0)))))) # label(def1_2Ethm_2Eset__relation_2Efinite__prefixes__comp) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6325 (all A_27a all V0r_2E0 ((all V1x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Eacyclic__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6326 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6327 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2821_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2821_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2821_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6328 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f2830_1_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)))),f2830_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X3_2E0)))) # label(arityeq4_2Ef2830_1_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6329 (all A_27a all V0s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) -> (all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))))))) # label(thm_2Eset__relation_2Efinite__acyclic__has__minimal) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6330 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool))),c_2Eset__relation_2Ercomp_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Ercomp_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6331 (all A_27a all V0r_2E0 all V1s_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))))) # label(thm_2Eset__relation_2Efinite__prefixes__subset) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6332 (all A_27a all V0r_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) # label(thm_2Eset__relation_2Eantisym__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6333 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6334 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6335 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Edomain_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6336 (all A_27a all V0s_2E0 all V1r_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) # label(thm_2Eset__relation_2Edomain__rrestrict__SUBSET) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6337 (all A_27a all V0r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) <-> (all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2y_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0))))) # label(thm_2Eset__relation_2Eantisym__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6338 (all A_27a all V0y_2E0 all V1x_2E0 all V2lo_2E0 all V3X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2lo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3X_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2lo_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3X_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3X_2E0))))))) # label(thm_2Eset__relation_2Elinear__order__in__set) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6339 (all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2860_1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,f2860_1_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef2860_1_2E3_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6340 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDELETE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6341 (all A_27a all V2x_2E0 all V0xs_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,f2823_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) & (all V3x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_27_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) -> s(A_27a,V2x_2E0) = s(A_27a,V3x_27_2E0))))) # label(def0_2Ethm_2Eset__relation_2Eminimal__elements__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6342 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Erelation_2ERUNION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2ERUNION_2E2_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6343 (all A_27a all V0r1_2E0 all V1r2_2E0 all V2s_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) # label(thm_2Eset__relation_2Errestrict__union) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6344 (all A_27a all V9r_27_2E0 all V8s_2E0 all V10r_2E0 all V11n_2E0 all V12min_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2971_2_2E1(s(tyop_2Eoption_2Eoption(A_27a),V12min_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Enth__min_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V9r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8s_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),V12min_2E0))))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,V11n_2E0))))))))) = s(tyop_2Eoption_2Eoption(A_27a),f2971_1_2E5(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V9r_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V8s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V10r_2E0),s(tyop_2Enum_2Enum,V11n_2E0),s(tyop_2Eoption_2Eoption(A_27a),V12min_2E0)))) # label(def3_2Ethm_2Eset__relation_2Enth__min__def__compute) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6345 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6346 (all A_27b all A_27c all V3s2_2E0 all V4x_2E0 all V1r2_2E0 ((exists V5y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27c,V5y_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,V4x_2E0),s(A_27c,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,f2860_1_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0),s(A_27b,V4x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Efinite__prefixes__comp) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6347 (all A_27a all A_27b all V2x_2E0 all V1r_2E0 all V0s_2E0 (p(s(tyop_2Emin_2Ebool,f2825_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0)))) <-> (all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3y_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V3y_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))) # label(def0_2Ethm_2Eset__relation_2Eupper__bounds__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6348 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6349 (all A_27a all A_27b all V0r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2803_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) # label(thm_2Eset__relation_2Erange__def) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6350 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2947_0_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),f2947_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2947_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6351 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2Emaximal__elements_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Emaximal__elements_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6352 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),f2960_0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2960_0_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2960_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.08 6353 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2830_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))))),f2830_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ef2830_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.09 6354 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Eset__relation_2Errestrict_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Errestrict_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.09 6355 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2951_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2951_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2951_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.09 6356 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Eantisymmetric_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2Eantisymmetric_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Eantisymmetric_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.09 6357 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2826_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2826_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2826_1_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.09 6358 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))))),f2971_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),f2971_0_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef2971_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.11/108.09 6359 (all A_27a all V0rs_2E0 ((all V3r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r_2E0)))))) & (all V1r_2E0 all V2r_27_2E0 (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0) != s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0)))))))))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0rs_2E0)))))))) # label(thm_2Eset__relation_2Eacyclic__bigunion) # label(axiom) # label(non_clause). [assumption]. 108.11/108.09 6360 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> (exists V2r_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Eset__relation_2Elinear__order__of__countable__po) # label(axiom) # label(non_clause). [assumption]. 108.11/108.09 6361 (all A_27a all V0xs_2E0 all V1r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) # label(thm_2Eset__relation_2Eminimal__elements__SWAP) # label(axiom) # label(non_clause). [assumption]. 108.11/108.09 6362 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f2805_1_2E4(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),f2805_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X3_2E0)))) # label(arityeq4_2Ef2805_1_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.11/108.09 6363 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & (all V2x_2E0 -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) & (all V3x_2E0 all V4y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & s(A_27a,V3x_2E0) != s(A_27a,V4y_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4y_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27a,V4y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Estrict__linear__order__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6364 (all A_27a all V0s_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Euniv__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERRUNIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Eset__relation_2Euniv__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6365 (all A_27a all V0f_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Enum__order_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2830_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0)))))))) # label(thm_2Eset__relation_2Enum__order__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6366 (all A_27a all V0r_27_2E0 all V1s_2E0 all V2r_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),f2831_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_27_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Eget__min_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_27_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0)))))) # label(thm_2Eset__relation_2Eget__min__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6367 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6368 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2802_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2802_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2802_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6369 (all A_27a all V0x_2E0 all V1r_2E0 all V2s_2E0 all V3s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3s_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))) # label(thm_2Eset__relation_2Efinite__prefix__linear__order__has__unique__minimal) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6370 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) # label(thm_2Eset__relation_2Eminimal__linear__order) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6371 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERDOM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Erelation_2ERDOM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2ERDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6372 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))))) # label(thm_2Eset__relation_2Emaximal__TC) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6373 (all A_27a all A_27b all V1y_2E0 all V0r_2E0 ((exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V2x_2E0),s(A_27a,V1y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) <-> p(s(tyop_2Emin_2Ebool,f2803_1_2E2(s(A_27a,V1y_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Erange__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6374 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Eget__min_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(A_27a))),c_2Eset__relation_2Eget__min_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Eget__min_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6375 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6376 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,A_27b))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27b),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6377 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Etransitive_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2Etransitive_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2Etransitive_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6378 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epred__set_2EUNION_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6379 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6380 (all A_27a all A_27b all V0r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2802_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Edomain__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6381 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2821_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = 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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2821_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2821_0_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6382 (all A_27a all V0R_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)) # label(thm_2Eset__relation_2EREL__RESTRICT__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6383 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2803_1_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2803_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2803_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6384 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Erange_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6385 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Ebool,f2806_1_2E3(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2806_0_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(A_27a,V1x_2E0),s(A_27a,V2y_2E0)))) # label(def1_2Ethm_2Eset__relation_2Estrict__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6386 (all A_27a all X0_2E0 s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6387 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6388 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6389 (all A_27a all V1x1_2E0 all V0xs_2E0 all V2x2_2E0 (p(s(tyop_2Emin_2Ebool,f2807_1_2E3(s(A_27a,V1x1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(A_27a,V2x2_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Euniv__reln__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6390 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6391 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6392 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6393 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6394 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Estrict__partial__order__acyclic) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6395 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,f2971_3_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),f2971_3_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) # label(arityeq1_2Ef2971_3_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6396 (all A_27a all V2x_2E0 all V0xs_2E0 all V1r_2E0 ((all V3x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3x_27_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) -> s(A_27a,V2x_2E0) = s(A_27a,V3x_27_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2822_1_2E3(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Emaximal__elements__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6397 (all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Ereln__to__rel_2E1_2Emono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6398 (all A_27a all V0r1_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))))) -> (all V3r2_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r2_2E0))))))))))) # label(thm_2Eset__relation_2Etc__union) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6399 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27b_2CA_27b_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6400 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6401 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6402 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6403 (all A_27a all V0r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakLinearOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Elinear__order__reln__to__rel__conv__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6404 (all A_27a all A_27b all V0f_2E0 all V1r_2E0 all V2s_2E0 ((all V3x_2E0 all V4y_2E0 (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V4y_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))) -> s(A_27a,V3x_2E0) = s(A_27a,V4y_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27b,A_27b),tyop_2Emin_2Ebool))),f2861_0_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))))))) # label(thm_2Eset__relation_2Efinite__prefixes__inj__image) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6405 (all A_27a all V0R_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f2821_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2ERREFL__EXP__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6406 (all A_27a all A_27b all V0R_2E0 all V1x_2E0 all V2y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f2819_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Erel__to__reln__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6407 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6408 (all A_27a all V0r_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Epartial__order__reln__to__rel__conv__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6409 (all A_27a all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6410 (all A_27a all V3mins_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3mins_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3mins_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),f2831_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3mins_2E0)))) # label(def0_2Ethm_2Eset__relation_2Eget__min__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6411 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2829_0_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2829_0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2829_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6412 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EIMAGE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6413 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),f2819_0_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),f2819_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef2819_0_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6414 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),f2822_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2822_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2822_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6415 (all A_27a all V0r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))) <-> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))) # label(thm_2Eset__relation_2Eempty__linear__order) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6416 (all A_27a all A_27b all V0r_2E0 all V1s_2E0 ((all V2e_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2808_0_2E2(s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Efinite__prefixes__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6417 (all A_27a all V0r_2E0 ((all V1x_2E0 all V2y_2E0 all V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2y_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Etransitive__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6418 (all A_27a all A_27b all A_27c all V0r1_2E0 all V1r2_2E0 all V2s1_2E0 all V3s2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),f2860_0_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),c_2Eset__relation_2Ercomp_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),V1r2_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3s2_2E0)))))) # label(thm_2Eset__relation_2Efinite__prefixes__comp) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6419 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Epred__set_2EREL__RESTRICT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EREL__RESTRICT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EREL__RESTRICT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6420 (all A_27a all V0xs_2E0 all V1xss_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eper_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))))) # label(thm_2Eset__relation_2Ecountable__per) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6421 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eantisym_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3y_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Elinear__order__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6422 (all A_27a all A_27b all V0r_2E0 all V1s_2E0 all V2r_27_2E0 all V3s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2r_27_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_27_2E0)))))))) # label(thm_2Eset__relation_2Efinite__prefixes__subset__rs) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6423 (all A_27a all A_27b all V0s_2E0 all V1r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eupper__bounds_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2825_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0)))))) # label(thm_2Eset__relation_2Eupper__bounds__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6424 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6425 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6426 (all A_27a all V1s_2E0 all V0f_2E0 all V2x_2E0 all V3y_2E0 s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),f2830_0_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Ebool,f2830_1_2E4(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0)))))) # label(def1_2Ethm_2Eset__relation_2Enum__order__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6427 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6428 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),f2804_1_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X3_2E0))) = s(tyop_2Emin_2Ebool,f2804_1_2E4(s(A_27a,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X3_2E0)))) # label(arityeq4_2Ef2804_1_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6429 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6430 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6431 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EDIFF_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6432 (all A_27a all V0r_2E0 all V1x_2E0 all V2y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) | (exists V3z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V3z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3z_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Etc__cases__right) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6433 (all A_27a all V0xs_2E0 all V1r_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2822_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) # label(thm_2Eset__relation_2Emaximal__elements__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6434 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27c,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6435 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))),f2805_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),f2805_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2805_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.09 6436 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2807_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),f2807_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2807_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6437 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),f2807_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Ebool,f2807_1_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2807_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6438 (all A_27a all A_27b all V0r_27_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_27_2E0)))))))) # label(thm_2Eset__relation_2Erange__mono) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6439 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6440 (all A_27a all V0x_2E0 all V1x_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etc_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),V1x_27_2E0)))) <-> (all V2tc_27_2E0 ((all V3a0_2E0 ((exists V4x_2E0 exists V5y_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0)))))) & s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V5y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),V3a0_2E0))) | (exists V6x_2E0 exists V7y_2E0 (s(tyop_2Epair_2Eprod(A_27a,A_27a),V3a0_2E0) = s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27a,V7y_2E0))) & (exists V8z_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6x_2E0),s(A_27a,V8z_2E0)))))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V8z_2E0),s(A_27a,V7y_2E0)))))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),V3a0_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2tc_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),V1x_27_2E0)))))))) # label(thm_2Eset__relation_2Etc__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6441 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6442 (all A_27a all V0r_2E0 all V1s_2E0 all V2s_27_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Epartial__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0)))))) # label(thm_2Eset__relation_2Epartial__order__subset) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6443 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6444 (all A_27a all V0r_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eirreflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) # label(thm_2Eset__relation_2Eirreflexive__reln__to__rel__conv__UNIV) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6445 (all A_27a all V0r_2E0 all V1tc_27_2E0 ((all V4x_2E0 all V5y_2E0 ((exists V6z_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(A_27a,V6z_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V6z_2E0),s(A_27a,V5y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V6z_2E0))),s(A_27a,V5y_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)),V1tc_27_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))) & (all V2x_2E0 all V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27a,V3y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))) -> (all V7x_2E0 all V8y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V7x_2E0),s(A_27a,V8y_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_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)),V1tc_27_2E0),s(A_27a,V7x_2E0))),s(A_27a,V8y_2E0)))))))) # label(thm_2Eset__relation_2Etc__strongind__left) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6446 (all A_27a all V0x_2E0 all V1lo_2E0 all V2X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1lo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2X_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2X_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1lo_2E0))))))) # label(thm_2Eset__relation_2Elinear__order__refl) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6447 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 s(tyop_2Eoption_2Eoption(A_27a),f2971_1_2E5(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Enum_2Enum,X3_2E0),s(tyop_2Eoption_2Eoption(A_27a),X4_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))))),f2971_1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X4_2E0)))) # label(arityeq5_2Ef2971_1_2E5_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6448 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) -> (exists V2x_2E0 p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))))))) # label(thm_2Eset__relation_2Efinite__strict__linear__order__has__minimal) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6449 (all 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)))) <-> -p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6450 (all A_27a all V0r_2E0 p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Etransitive_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))))) # label(thm_2Eset__relation_2Etc__transitive) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6451 (all A_27a all V0r_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) # label(thm_2Eset__relation_2Estrict__rrestrict) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6452 (all V0_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,V0_2E0)))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6453 (all A_27a all V0r_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2ESWAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Etc__SWAP) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6454 (all A_27a all V0r_2E0 all V1s_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2804_0_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Eset__relation_2Errestrict__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6455 (all A_27a all V0s_2E0 all V1r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0s_2E0)))))))) # label(thm_2Eset__relation_2Etc__mono) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6456 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Estrict_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Estrict_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6457 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6458 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6459 (all A_27a all V0r1_2E0 all V1r2_2E0 all V2s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) -> s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0))))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0))))) # label(thm_2Eset__relation_2Estrict__linear__order__union__acyclic) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6460 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))))) # label(thm_2Eset__relation_2Eacyclic__rrestrict) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6461 (all A_27a all A_27b all V0xy_2E0 all V1R_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0xy_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0))))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0xy_2E0))))),s(A_27b,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),V0xy_2E0)))))) # label(thm_2Eset__relation_2Ein__rel__to__reln) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6462 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Erel__to__reln_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Erel__to__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Erel__to__reln_2E1_2Emono_2EA_27a_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6463 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),f2970_0_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Enum_2Enum,X3_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))))),f2970_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Enum_2Enum,X3_2E0)))) # label(arityeq4_2Ef2970_0_2E4_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6464 (all A_27a all V0e_2E0 all V1s_2E0 all V2r1_2E0 all V3r2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r2_2E0)))))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V3r2_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Emaximal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r1_2E0)))))))) # label(thm_2Eset__relation_2Emaximal__union) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6465 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))))) # label(thm_2Eset__relation_2Estrict__linear__order) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6466 (all A_27a all V0s_2E0 all V1r_2E0 all V2x_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) -> (exists V3y_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V3y_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Etc_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0)))))))))) # label(thm_2Eset__relation_2Efinite__acyclic__has__minimal__path) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6467 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),c_2Eset__relation_2Enth__min_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eset__relation_2Enth__min_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Eset__relation_2Enth__min_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6468 (all A_27a all V0r_2E0 all V1s_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Estrict__linear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(thm_2Eset__relation_2Estrict__linear__order__acyclic) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6469 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),f2963_0_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),f2963_0_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef2963_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6470 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6471 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2802_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2802_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2802_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6472 (all A_27a all V0s_2E0 all V1r_2E0 p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))))) # label(thm_2Eset__relation_2Errestrict__SUBSET) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6473 (all A_27a all V0r_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Estrict_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),f2806_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r_2E0)))))))) # label(thm_2Eset__relation_2Estrict__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6474 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27c,X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27c,X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6475 (all A_27a all A_27b all V2e_2E0 all V0r_2E0 all V3e_27_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),f2808_0_2E3(s(A_27b,V2e_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0),s(A_27a,V3e_27_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3e_27_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3e_27_2E0),s(A_27b,V2e_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0r_2E0)))))) # label(def0_2Ethm_2Eset__relation_2Efinite__prefixes__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6476 (all A_27a all V0xs_2E0 all V1r_27_2E0 all V2r_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2r_2E0)))))))) # label(thm_2Eset__relation_2Eminimal__elements__mono) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6477 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2806_1_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,f2806_1_2E3(s(A_27a,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef2806_1_2E3_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6478 (all A_27a all V0r1_2E0 all V1r2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0r1_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eacyclic_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r2_2E0)))))) # label(thm_2Eset__relation_2Eacyclic__subset) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6479 (all A_27a all V0y_2E0 all V1x_2E0 all V2lo_2E0 all V3X_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3X_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2lo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3X_2E0)))) -> (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0y_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3X_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2lo_2E0)))))) -> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V0y_2E0),s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V2lo_2E0)))))))) # label(thm_2Eset__relation_2EIN__MIN__LO) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6480 (all A_27a all V0s_2E0 all V1r_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2Ereflexive_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2ERREFL__EXP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Ereln__to__rel_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V1r_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) # label(thm_2Eset__relation_2Ereflexive__reln__to__rel__conv) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6481 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWeakOrder_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWeakOrder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWeakOrder_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6482 (all A_27a all V0xs_2E0 all V1xss_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eper_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0xs_2E0)))) & -p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))) & (all V2xs1_2E0 all V3xs2_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3xs2_2E0) != s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs1_2E0) & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3xs2_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1xss_2E0)))) -> p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2xs1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3xs2_2E0)))))))) # label(thm_2Eset__relation_2Eper__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6483 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Euniv__reln_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Eset__relation_2Euniv__reln_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eset__relation_2Euniv__reln_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6484 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f2825_1_2E3(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),f2825_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef2825_1_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6485 (all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6486 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Ereln__to__rel_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Eset__relation_2Ereln__to__rel_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2Eset__relation_2Ereln__to__rel_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6487 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eirreflexive_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Eirreflexive_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Eirreflexive_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6488 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eset__relation_2Eper_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Eper_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Eset__relation_2Eper_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6489 (all A_27a all X0_2E0 s(tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_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_2Epred__set_2Ecountable_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6490 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),f2803_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),f2803_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef2803_0_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6491 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2EerrorStateMonad_2EUNIT_2E0),s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2EerrorStateMonad_2EUNIT_2E1(s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6492 (all A_27a all A_27b all A_27c all V0f_2E0 all V1m_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0)))))) # label(thm_2EerrorStateMonad_2EMMAP__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6493 (all A_27state all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),c_2Epair_2E_2C_2E2(s(tyop_2Eone_2Eone,X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2E_2C_2E0),s(tyop_2Eone_2Eone,X0_2E0))),s(A_27state,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6494 (all A_27a all A_27b all A_27c all V0fM_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EES__FAIL_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V0fM_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__FAIL_2E0)) # label(thm_2EerrorStateMonad_2EBIND__FAIL__L) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6495 (all A_27a all A_27b all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6496 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EUNIT_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2EI_2E0)) # label(thm_2EerrorStateMonad_2EJOIN__UNIT) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6497 (all A_27state s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2EerrorStateMonad_2EFOR_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f2980_0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2980_1_2E0)))) # label(thm_2EerrorStateMonad_2EFOR__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6498 (all A_27a all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6499 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6500 (all A_27a all A_27b all A_27state all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),f2984_1_2E2(s(A_27a,X0_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),f2984_1_2E0),s(A_27a,X0_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27state),X1_2E0)))) # label(arityeq2_2Ef2984_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6501 (all A_27a all A_27state all V4FOREACH_2E0 all V6v_2E0 all V7a_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V6v_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2981_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V7a_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOREACH_2E0))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2981_2_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOREACH_2E0),s(tyop_2Elist_2Elist(A_27a),V6v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V7a_2E0)))) # label(def3_2Ethm_2EerrorStateMonad_2EFOREACH__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6502 (all A_27a all A_27state ((all V0a_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EFOREACH_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V0a_2E0)))))) & (all V1t_2E0 all V2h_2E0 all V3a_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V3a_2E0),s(A_27a,V2h_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),f2996_0_2E2(s(tyop_2Elist_2Elist(A_27a),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V3a_2E0))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EFOREACH_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V3a_2E0)))))))) # label(thm_2EerrorStateMonad_2EFOREACH__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6503 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6504 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29_29_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_2CA_27c_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6505 (all A_27state all X0_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0)))) # label(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6506 (all A_27a all A_27state all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6507 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a))),c_2EerrorStateMonad_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EMMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27d_2CA_27b_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6508 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),f2986_2_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),f2986_2_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ef2986_2_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6509 (all A_27state all V6i_2E0 all V4FOR_2E0 all V8j_2E0 all V9a_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2980_4_2E2(s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Enum_2Enum,V8j_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V9a_2E0),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V9a_2E0),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),f2980_5_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOR_2E0),s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Enum_2Enum,V8j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V9a_2E0))))))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2980_3_2E4(s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOR_2E0),s(tyop_2Enum_2Enum,V8j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V9a_2E0)))) # label(def3_2Ethm_2EerrorStateMonad_2EFOR__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6510 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a)))),c_2EerrorStateMonad_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6511 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2980_4_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2980_4_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2980_4_2E2) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6512 (all A_27a all V3v1_2E0 s(tyop_2Eoption_2Eoption(A_27a),f2989_0_2E1(s(A_27a,V3v1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3v1_2E0)))) # label(def0_2Ethm_2EerrorStateMonad_2EES__CHOICE__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6513 (all A_27a all A_27b all A_27state all V1s1_2E0 all V4r_2E0 all V5s3_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Epair_2E_2C_2E2(s(A_27a,V4r_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),c_2Epair_2E_2C_2E2(s(A_27b,V1s1_2E0),s(A_27state,V5s3_2E0))))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),f2985_2_2E3(s(A_27b,V1s1_2E0),s(A_27a,V4r_2E0),s(A_27state,V5s3_2E0)))) # label(def0_2Ethm_2EerrorStateMonad_2EWIDEN__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6514 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6515 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),f2974_1_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))),f2974_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0)))) # label(arityeq1_2Ef2974_1_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6516 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6517 (all A_27a all A_27b all A_27d all A_27e all A_27f all A_27g all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27e_29_20mono_2EA_27f_20mono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6518 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27a_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6519 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 108.15/108.10 6520 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EIGNORE__BIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EIGNORE__BIND_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6521 (all A_27a all A_27b all A_27c all A_27d all A_27e all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c)))),c_2Eoption_2EOPTION__MCOMP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Eoption_2Eoption(A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Eoption_2Eoption(A_27c)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),X1_2E0)))) # label(arityeq2_2Ec_2Eoption_2EOPTION__MCOMP_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27e_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6522 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EJOIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EJOIN_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6523 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_2CA_27a_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6524 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),f3014_1_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),f3014_1_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ef3014_1_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6525 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6526 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2EerrorStateMonad_2EIGNORE__BIND_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2EerrorStateMonad_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EIGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6527 (all A_27a all A_27b all A_27c all A_27d all V1m_2E0 all V2n_2E0 all V3a_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1m_2E0),s(A_27b,V3a_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),V2n_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),f3003_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1m_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),V2n_2E0),s(A_27b,V3a_2E0)))) # label(def0_2Ethm_2EerrorStateMonad_2EBIND__ASSOC) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6528 (all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27state_20mono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6529 (all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6530 (all A_27c all A_27d all A_27e all A_27f all A_27g all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27f_20mono_2EA_27g_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6531 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6532 (all A_27a all A_27b all A_27c all V0k_2E0 all V1x_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),V0k_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2EerrorStateMonad_2EUNIT_2E1(s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),V0k_2E0)))) # label(thm_2EerrorStateMonad_2EBIND__LEFT__UNIT) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6533 (all A_27state all V0j_2E0 all V1i_2E0 all V2a_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EFOR_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V2a_2E0))))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,f2994_0_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0j_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V2a_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V2a_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),f2994_1_2E3(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V2a_2E0)))))))) # label(thm_2EerrorStateMonad_2EFOR__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6534 (all A_27a all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),f2981_4_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),f2981_4_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0)))) # label(arityeq3_2Ef2981_4_2E3_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6535 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2EerrorStateMonad_2Esequence_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2Elist_2EFOLDR_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),f2986_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))) # label(thm_2EerrorStateMonad_2Esequence__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6536 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),f3014_1_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),f3014_1_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ef3014_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6537 (all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X2_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6538 (all A_27state all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,A_27state),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2EerrorStateMonad_2EWRITE_2E0),s(tyop_2Emin_2Efun(A_27state,A_27state),X0_2E0))),s(A_27state,X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2EerrorStateMonad_2EWRITE_2E2(s(tyop_2Emin_2Efun(A_27state,A_27state),X0_2E0),s(A_27state,X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EWRITE_2E2_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6539 (all A_27state all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2994_1_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0),s(tyop_2Eone_2Eone,X3_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),f2994_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0))),s(tyop_2Eone_2Eone,X3_2E0)))) # label(arityeq4_2Ef2994_1_2E4_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6540 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__APPLY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EES__APPLY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EES__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6541 (all A_27a all A_27b all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2EerrorStateMonad_2ENARROW_2E3(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X1_2E0),s(A_27state,X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))))),c_2EerrorStateMonad_2ENARROW_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X1_2E0))),s(A_27state,X2_2E0)))) # label(arityeq3_2Ec_2EerrorStateMonad_2ENARROW_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6542 (all A_27state all V4FOR_2E0 all V6i_2E0 all V7v1_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),V7v1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2980_3_2E2(s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOR_2E0))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2980_2_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOR_2E0),s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),V7v1_2E0)))) # label(def4_2Ethm_2EerrorStateMonad_2EFOR__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6543 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),f2974_1_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))),f2974_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0)))) # label(arityeq3_2Ef2974_1_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6544 (all A_27a all A_27b all A_27c all V1f_2E0 all V4b_2E0 all V5s_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1f_2E0),s(A_27b,V4b_2E0))),s(A_27a,V5s_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),f2974_1_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1f_2E0),s(A_27b,V4b_2E0),s(A_27a,V5s_2E0)))) # label(def0_2Ethm_2EerrorStateMonad_2EBIND__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6545 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6546 (all A_27a all A_27b all A_27c all V1xM_2E0 all V2f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),f2991_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1xM_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1xM_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),f2991_1_2E1(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0)))))) # label(def1_2Ethm_2EerrorStateMonad_2EES__APPLY__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6547 (all A_27state all X0_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2EerrorStateMonad_2EUNIT_2E0),s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27state_20mono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6548 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6549 (all A_27c all A_27d all A_27e all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Eoption_2Eoption(A_27c))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Eoption_2Eoption(A_27c)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27d_20mono_2EA_27e_20mono_2Etyop_2Eoption_2Eoption_28A_27c_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6550 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))))),f3003_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),f3003_0_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef3003_0_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6551 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6552 (all A_27state all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_29_2Ctyop_2Emin_2Ebool_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6553 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6554 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6555 (all A_27a all A_27b all A_27c all A_27d all A_27e all A_27f all A_27g all V0g_2E0 all V1f_2E0 (s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),c_2EerrorStateMonad_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),V1f_2E0))) = s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),V1f_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2EerrorStateMonad_2EUNIT_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),V0g_2E0))) # label(thm_2EerrorStateMonad_2EMCOMP__ID) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6556 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),c_2EerrorStateMonad_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))),c_2EerrorStateMonad_2EIGNORE__BIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EIGNORE__BIND_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6557 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6558 (all A_27a all A_27b all A_27state all V0v_2E0 all V1f_2E0 all V2x_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),V1f_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),c_2Epair_2E_2C_2E2(s(A_27b,V0v_2E0),s(A_27state,V2x_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),f2984_0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2EerrorStateMonad_2ENARROW_2E3(s(A_27b,V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),V1f_2E0),s(A_27state,V2x_2E0)))) # label(thm_2EerrorStateMonad_2ENARROW__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6559 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))))),c_2EerrorStateMonad_2EmapM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),c_2EerrorStateMonad_2EmapM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EmapM_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6560 (all A_27state all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),f2980_2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2980_2_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0)))) # label(arityeq1_2Ef2980_2_2E1_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6561 (all A_27a all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),f2981_2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2981_2_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0)))) # label(arityeq3_2Ef2981_2_2E3_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6562 (all A_27a all A_27b all V0s_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2EerrorStateMonad_2EES__FAIL_2E1(s(A_27b,V0s_2E0)))) # label(thm_2EerrorStateMonad_2EES__FAIL__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6563 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6564 (all A_27a all A_27b all A_27c all A_27f all A_27g all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27f_20mono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6565 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2EerrorStateMonad_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V1g_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),f2975_0_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V1g_2E0)))))) # label(thm_2EerrorStateMonad_2EIGNORE__BIND__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6566 (all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6567 (all A_27a all A_27b all A_27c all A_27d all A_27e all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6568 (all A_27a all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2EerrorStateMonad_2EES__CHOICE_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)))),c_2EerrorStateMonad_2EES__CHOICE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ec_2EerrorStateMonad_2EES__CHOICE_2E3_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6569 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2EerrorStateMonad_2EUNIT_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6570 (all A_27state all V0R_2E0 ((all V1a_2E0 all V2j_2E0 all V3i_2E0 (s(tyop_2Enum_2Enum,V2j_2E0) != s(tyop_2Enum_2Enum,V3i_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V2j_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V1a_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V1a_2E0)))))))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),V0R_2E0)))) <-> p(s(tyop_2Emin_2Ebool,f2980_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(def0_2Ethm_2EerrorStateMonad_2EFOR__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6571 (all A_27a all A_27b all V0fM_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__FAIL_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EES__GUARD_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V0fM_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V0fM_2E0),s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EES__GUARD_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V0fM_2E0))))) # label(thm_2EerrorStateMonad_2EBIND__ESGUARD) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6572 (all A_27state all V0f_2E0 all V1x_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2EerrorStateMonad_2EWRITE_2E2(s(tyop_2Emin_2Efun(A_27state,A_27state),V0f_2E0),s(A_27state,V1x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),c_2Epair_2E_2C_2E2(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0),s(A_27state,app_2E2(s(tyop_2Emin_2Efun(A_27state,A_27state),V0f_2E0),s(A_27state,V1x_2E0)))))))) # label(thm_2EerrorStateMonad_2EWRITE__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6573 (all A_27a all A_27b all V1ms_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),f2986_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),V1ms_2E0),s(A_27b,V2x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),V1ms_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),f2986_2_2E1(s(A_27b,V2x_2E0)))))) # label(def1_2Ethm_2EerrorStateMonad_2Esequence__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6574 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1xM_2E0 all V2yM_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__APPLY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a))),c_2EerrorStateMonad_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1xM_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),V2yM_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__LIFT2_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1xM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),V2yM_2E0)))) # label(thm_2EerrorStateMonad_2EES__LIFT2__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6575 (all A_27a all A_27b all A_27state all V0f_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),f2985_0_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),V0f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2EerrorStateMonad_2EWIDEN_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),V0f_2E0)))) # label(thm_2EerrorStateMonad_2EWIDEN__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6576 (all A_27a all A_27b all A_27c all V0f_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),c_2EerrorStateMonad_2EJOIN_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2EerrorStateMonad_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0)))))))) # label(thm_2EerrorStateMonad_2EMMAP__JOIN) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6577 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6578 (all A_27a all A_27state all V4FOREACH_2E0 all V9t_2E0 all V7a_2E0 all V10u_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOREACH_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V9t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V7a_2E0))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2981_4_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOREACH_2E0),s(tyop_2Elist_2Elist(A_27a),V9t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V7a_2E0),s(tyop_2Eone_2Eone,V10u_2E0)))) # label(def1_2Ethm_2EerrorStateMonad_2EFOREACH__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6579 (all A_27a all A_27b all V0xM_2E0 all V1yM_2E0 all V2s_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2EerrorStateMonad_2EES__CHOICE_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0xM_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1yM_2E0),s(A_27b,V2s_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V0xM_2E0),s(A_27b,V2s_2E0))),s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),V1yM_2E0),s(A_27b,V2s_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),f2989_0_2E0)))) # label(thm_2EerrorStateMonad_2EES__CHOICE__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6580 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EUNIT_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2EI_2E0)) # label(thm_2EerrorStateMonad_2EJOIN__MMAP__UNIT) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6581 (all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2980_1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2980_1_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),X1_2E0)))) # label(arityeq2_2Ef2980_1_2E2_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6582 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6583 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6584 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),f2991_1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),f2991_1_2E1(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0)))) # label(arityeq1_2Ef2991_1_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6585 (all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),f2980_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2980_3_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0)))) # label(arityeq2_2Ef2980_3_2E2_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6586 (all X0_2E0 all 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)))) <-> (p(s(tyop_2Emin_2Ebool,X0_2E0)) -> p(s(tyop_2Emin_2Ebool,X1_2E0))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6587 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2Elist_2EFOLDR_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EFOLDR_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27b_29_2CA_27a_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6588 (all A_27a all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2981_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),f2981_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0)))) # label(arityeq2_2Ef2981_3_2E2_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6589 (all A_27a all A_27b all A_27state all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27state),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.11 6590 (all A_27a all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2981_1_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2981_1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0)))) # label(arityeq2_2Ef2981_1_2E2_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6591 (all A_27a all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),f2996_0_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),f2996_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0)))) # label(arityeq2_2Ef2996_0_2E2_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6592 (all A_27a all A_27b all A_27c all A_27d all A_27e all A_27f all A_27g all V0h_2E0 all V1g_2E0 all V2f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),V0h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),V2f_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),V0h_2E0)))) # label(thm_2EerrorStateMonad_2EMCOMP__ASSOC) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6593 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2EerrorStateMonad_2Esequence_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2Esequence_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2Esequence_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6594 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2EI_2E0)) # label(thm_2EerrorStateMonad_2EMMAP__ID) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6595 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27b_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6596 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6597 (all A_27a all A_27b all A_27state all V4r_2E0 all V5s1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2E_2C_2E2(s(A_27a,V4r_2E0),s(A_27state,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27state),V5s1_2E0))))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),f2984_1_2E2(s(A_27a,V4r_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),V5s1_2E0)))) # label(def0_2Ethm_2EerrorStateMonad_2ENARROW__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6598 (all A_27state all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 all X4_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2980_5_2E5(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X3_2E0),s(tyop_2Eone_2Eone,X4_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))))),f2980_5_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X3_2E0))),s(tyop_2Eone_2Eone,X4_2E0)))) # label(arityeq5_2Ef2980_5_2E5_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6599 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6600 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),f2989_0_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),f2989_0_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ef2989_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6601 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6602 (all A_27state all V1i_2E0 all V0j_2E0 all V2a_2E0 all V3u_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EFOR_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0j_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V2a_2E0))))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2994_1_2E4(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V2a_2E0),s(tyop_2Eone_2Eone,V3u_2E0)))) # label(def1_2Ethm_2EerrorStateMonad_2EFOR__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6603 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6604 (all A_27state all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6605 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6606 (all A_27a all A_27b all A_27c all V1g_2E0 all V2x_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),f2975_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V1g_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V1g_2E0)) # label(def0_2Ethm_2EerrorStateMonad_2EIGNORE__BIND__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6607 (all A_27a all A_27b all A_27state all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27state_29_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6608 (all A_27a all A_27b all V0xM_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0xM_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EerrorStateMonad_2EES__CHOICE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EerrorStateMonad_2EES__FAIL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0xM_2E0)))) # label(thm_2EerrorStateMonad_2EES__CHOICE__FAIL__LID) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6609 (all A_27a all A_27b all A_27c all A_27d all V0xM_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),c_2EerrorStateMonad_2EES__FAIL_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),c_2EerrorStateMonad_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0xM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),c_2EerrorStateMonad_2EES__FAIL_2E0))) & s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__FAIL_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EES__FAIL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0xM_2E0))))) # label(thm_2EerrorStateMonad_2EIGNORE__BIND__FAIL) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6610 (all A_27a all A_27state all X0_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EFOREACH_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2EerrorStateMonad_2EFOREACH_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EFOREACH_2E1_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6611 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29_29_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6612 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),f3014_0_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))))),f3014_0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ef3014_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6613 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6614 (all A_27a all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6615 (all A_27a all A_27state all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),f2981_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))),s(A_27a,X2_2E0))),s(tyop_2Elist_2Elist(A_27a),X3_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2981_3_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0),s(A_27a,X2_2E0),s(tyop_2Elist_2Elist(A_27a),X3_2E0)))) # label(arityeq4_2Ef2981_3_2E4_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6616 (all A_27a all A_27b all V2x_2E0 all V3xs_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),f2986_2_2E2(s(A_27b,V2x_2E0),s(tyop_2Elist_2Elist(A_27b),V3xs_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2x_2E0),s(tyop_2Elist_2Elist(A_27b),V3xs_2E0)))))) # label(def0_2Ethm_2EerrorStateMonad_2Esequence__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6617 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6618 (all A_27b all A_27c all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6619 (all A_27a all A_27state all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27state),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27state),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6620 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),f2986_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),f2986_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0)))) # label(arityeq2_2Ef2986_0_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6621 (all A_27a all A_27b all V3y_2E0 all V4ys_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3y_2E0),s(tyop_2Elist_2Elist(A_27b),V4ys_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),f3014_1_2E2(s(A_27b,V3y_2E0),s(tyop_2Elist_2Elist(A_27b),V4ys_2E0)))) # label(def0_2Ethm_2EerrorStateMonad_2EmapM__cons) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6622 (all A_27a all V0x_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6623 (all A_27state all X0_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EFOR_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2EerrorStateMonad_2EFOR_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EFOR_2E1_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6624 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X1_2E0))),s(A_27a,X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),c_2EerrorStateMonad_2EBIND_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X1_2E0),s(A_27a,X2_2E0)))) # label(arityeq3_2Ec_2EerrorStateMonad_2EBIND_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6625 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2EerrorStateMonad_2EUNIT_2E0),s(A_27c,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(A_27c,X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6626 (all A_27a all A_27c all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6627 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6628 (all A_27a all A_27state all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),f2981_4_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0))),s(tyop_2Eone_2Eone,X3_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2981_4_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0),s(tyop_2Eone_2Eone,X3_2E0)))) # label(arityeq4_2Ef2981_4_2E4_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6629 (all A_27a all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2EerrorStateMonad_2EES__FAIL_2E0),s(A_27b,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2EerrorStateMonad_2EES__FAIL_2E1(s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EES__FAIL_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6630 (all A_27a all A_27b all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27state_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6631 (all A_27b all A_27state all X0_2E0 s(A_27state,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27state),X0_2E0))) = s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),A_27state),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6632 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6633 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6634 (all A_27a all A_27b all A_27state all V1s1_2E0 all V3v_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27state),V3v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),f2985_2_2E1(s(A_27b,V1s1_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),f2985_1_2E2(s(A_27b,V1s1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27state),V3v_2E0)))) # label(def1_2Ethm_2EerrorStateMonad_2EWIDEN__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6635 (all A_27a all A_27b all A_27c all A_27d all V0f_2E0 all V1g_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0)))))) # label(thm_2EerrorStateMonad_2EMMAP__COMP) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6636 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2EerrorStateMonad_2EJOIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EJOIN_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6637 (all A_27a all A_27b all V0z_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),V0z_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),V0z_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2EI_2E0)))) # label(thm_2EerrorStateMonad_2EJOIN__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6638 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6639 (all A_27state all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))))),f2980_5_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X3_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),f2980_5_2E4(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X3_2E0)))) # label(arityeq4_2Ef2980_5_2E4_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6640 (all A_27a all A_27b all A_27state all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27state_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6641 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EerrorStateMonad_2EES__CHOICE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),c_2EerrorStateMonad_2EES__CHOICE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EES__CHOICE_2E2_2Emono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6642 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6643 (all A_27a all A_27b all A_27state all V0f_2E0 all V1s1_2E0 all V2s2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),V0f_2E0),s(A_27state,V2s2_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),f2985_1_2E1(s(A_27b,V1s1_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),f2985_0_2E3(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),V0f_2E0),s(A_27b,V1s1_2E0),s(A_27state,V2s2_2E0)))) # label(def2_2Ethm_2EerrorStateMonad_2EWIDEN__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6644 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),f2991_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),f2991_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0)))) # label(arityeq2_2Ef2991_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6645 (all A_27state all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0)))) # label(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6646 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6647 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6648 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))))),f3003_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),f3003_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),X1_2E0)))) # label(arityeq2_2Ef3003_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6649 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6650 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d)))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27d_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27d_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27d_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6651 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27d_2CA_27b_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6652 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),f2991_1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(A_27c,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),f2991_1_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ef2991_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6653 (all A_27a all A_27b all A_27c all V0g_2E0 all V1m_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V0g_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EEXT_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0)))) # label(thm_2EerrorStateMonad_2EEXT__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6654 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6655 (all A_27a all A_27b all A_27c all V0fM_2E0 all V1xM_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),V0fM_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),f2991_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1xM_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__APPLY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),V0fM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1xM_2E0)))) # label(thm_2EerrorStateMonad_2EES__APPLY__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6656 (all A_27state all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6657 (all A_27a all A_27b all A_27c all V0f_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),c_2EerrorStateMonad_2EmapM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),V0f_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),c_2EerrorStateMonad_2Esequence_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),V0f_2E0)))))) # label(thm_2EerrorStateMonad_2EmapM__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6658 (all A_27c all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ECONS_2E0),s(A_27c,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.12 6659 (all A_27a all A_27b all A_27c all V0xM_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__APPLY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V0xM_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V0xM_2E0)))) # label(thm_2EerrorStateMonad_2EAPPLY__UNIT) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6660 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6661 (all A_27a all A_27b all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),f2985_0_2E3(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X0_2E0),s(A_27b,X1_2E0),s(A_27state,X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))))),f2985_0_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X0_2E0))),s(A_27b,X1_2E0))),s(A_27state,X2_2E0)))) # label(arityeq3_2Ef2985_0_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6662 (all A_27state all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6663 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6664 (all A_27a all A_27b all A_27state all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6665 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6666 (all A_27a all A_27b all A_27c all V0g_2E0 all V1f_2E0 all V2s0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0g_2E0),s(A_27a,V2s0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),f2974_0_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1f_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),c_2EerrorStateMonad_2EBIND_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1f_2E0),s(A_27a,V2s0_2E0)))) # label(thm_2EerrorStateMonad_2EBIND__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6667 (all A_27a all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X2_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X2_2E0)))) # label(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6668 (all A_27state all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),f2980_3_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X3_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2980_3_2E4(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0),s(tyop_2Enum_2Enum,X2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X3_2E0)))) # label(arityeq4_2Ef2980_3_2E4_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6669 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_2CA_27a_29_29_29_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_2CA_27a_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6670 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2EerrorStateMonad_2EUNIT_2E2(s(A_27b,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EUNIT_2E0),s(A_27b,X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EUNIT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6671 (all A_27a all A_27b s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2Esequence_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Elist_2ENIL_2E0)))) # label(thm_2EerrorStateMonad_2Esequence__nil) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6672 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),f2975_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),f2975_0_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0)))) # label(arityeq1_2Ef2975_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6673 (all A_27a all A_27b all A_27c all A_27d all A_27e all V0g_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c)),c_2Eoption_2EOPTION__MCOMP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27e),tyop_2Eoption_2Eoption(A_27c)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),V0g_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),V1f_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(A_27c))),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),V1f_2E0)))) # label(thm_2EerrorStateMonad_2EMCOMP__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6674 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),f2974_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),f2974_0_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0)))) # label(arityeq1_2Ef2974_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6675 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6676 (all A_27a all A_27b all A_27c all V2f_2E0 all V3x_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(A_27c,V3x_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),f2991_1_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2f_2E0),s(A_27c,V3x_2E0)))) # label(def0_2Ethm_2EerrorStateMonad_2EES__APPLY__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6677 (all A_27a all A_27b all A_27c all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EmapM_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V0f_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0)))) # label(thm_2EerrorStateMonad_2EmapM__nil) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6678 (all A_27a all A_27b s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EJOIN_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),c_2EerrorStateMonad_2EJOIN_2E0)))) # label(thm_2EerrorStateMonad_2EJOIN__MAP__JOIN) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6679 (all A_27a all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2996_0_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0),s(tyop_2Eone_2Eone,X2_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),f2996_0_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))),s(tyop_2Eone_2Eone,X2_2E0)))) # label(arityeq3_2Ef2996_0_2E3_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6680 (all A_27a all A_27b all A_27state all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),f2985_1_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),f2985_1_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ef2985_1_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6681 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EmapM_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),c_2EerrorStateMonad_2EmapM_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EmapM_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6682 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ECONS_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6683 (all A_27a all X0_2E0 all 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)))) <-> s(A_27a,X1_2E0) = s(A_27a,X0_2E0))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6684 (all A_27a all A_27state all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27state,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6685 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_2CA_27a_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6686 (all A_27state all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f2980_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,f2980_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2980_0_2E1_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6687 (all A_27a all A_27b all V0k_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0k_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0k_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EUNIT_2E0)))) # label(thm_2EerrorStateMonad_2EBIND__RIGHT__UNIT) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6688 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6689 (all A_27a all A_27b all V0x_2E0 all V1x_27_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V0x_2E0),s(A_27a,V1x_27_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2EerrorStateMonad_2EUNIT_2E2(s(A_27b,V0x_2E0),s(A_27a,V1x_27_2E0)))) # label(thm_2EerrorStateMonad_2EUNIT__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6690 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),f2975_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),f2975_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef2975_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6691 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))))),f3014_0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),f3014_0_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef3014_0_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6692 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6693 (all A_27a all A_27b all V0zM_2E0 all V1yM_2E0 all V2xM_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EerrorStateMonad_2EES__CHOICE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EerrorStateMonad_2EES__CHOICE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2xM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1yM_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0zM_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EerrorStateMonad_2EES__CHOICE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2xM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EerrorStateMonad_2EES__CHOICE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1yM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0zM_2E0)))))) # label(thm_2EerrorStateMonad_2EES__CHOICE__ASSOC) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6694 (all V6i_2E0 all V8j_2E0 (s(tyop_2Enum_2Enum,V6i_2E0) = s(tyop_2Enum_2Enum,V8j_2E0) <-> p(s(tyop_2Emin_2Ebool,f2980_4_2E2(s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Enum_2Enum,V8j_2E0)))))) # label(def1_2Ethm_2EerrorStateMonad_2EFOR__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6695 (all A_27state all V4FOR_2E0 all V6i_2E0 all V8j_2E0 all V9a_2E0 all V10u_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOR_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Enum_2Enum,V8j_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V8j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V9a_2E0))))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2980_5_2E5(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOR_2E0),s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Enum_2Enum,V8j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V9a_2E0),s(tyop_2Eone_2Eone,V10u_2E0)))) # label(def2_2Ethm_2EerrorStateMonad_2EFOR__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6696 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),f2986_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),f2986_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X0_2E0)))) # label(arityeq1_2Ef2986_1_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6697 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),f2991_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),f2991_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0)))) # label(arityeq1_2Ef2991_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6698 (all A_27a all A_27b all A_27state all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),f2985_1_2E2(s(A_27b,X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27state),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),f2985_1_2E0),s(A_27b,X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27state),X1_2E0)))) # label(arityeq2_2Ef2985_1_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6699 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29_20mono_2EA_27d_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6700 (all A_27a all A_27state all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2981_2_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),f2981_2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0)))) # label(arityeq1_2Ef2981_2_2E1_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6701 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6702 (all A_27a all A_27b all A_27state all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2EerrorStateMonad_2EWIDEN_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),c_2EerrorStateMonad_2EWIDEN_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EWIDEN_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6703 (all A_27a all A_27state all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),c_2EerrorStateMonad_2EREAD_2E0),s(tyop_2Emin_2Efun(A_27state,A_27a),X0_2E0))),s(A_27state,X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2EerrorStateMonad_2EREAD_2E2(s(tyop_2Emin_2Efun(A_27state,A_27a),X0_2E0),s(A_27state,X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EREAD_2E2_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6704 (all V0t_2E0 (s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6705 (all A_27a all A_27state all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6706 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EIGNORE__BIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EIGNORE__BIND_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6707 (all V1i_2E0 all V0j_2E0 (s(tyop_2Enum_2Enum,V1i_2E0) = s(tyop_2Enum_2Enum,V0j_2E0) <-> p(s(tyop_2Emin_2Ebool,f2994_0_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0j_2E0)))))) # label(def0_2Ethm_2EerrorStateMonad_2EFOR__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6708 (all A_27a all A_27state all X0_2E0 s(tyop_2Emin_2Ebool,f2981_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f2981_0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef2981_0_2E1_2Emono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6709 (all A_27a all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) <-> s(A_27a,V0_2E0) = s(A_27a,V1_2E0))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6710 (all A_27a all A_27b all A_27c all A_27d all V0g_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),V1f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2EerrorStateMonad_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),V0g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b)))),V1f_2E0)))) # label(thm_2EerrorStateMonad_2EMCOMP__THM) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6711 (all A_27a all A_27b all A_27state all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),f2985_0_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))))),f2985_0_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),X0_2E0)))) # label(arityeq1_2Ef2985_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6712 (all A_27a all A_27b all V0xM_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0xM_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EerrorStateMonad_2EES__CHOICE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V0xM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2EerrorStateMonad_2EES__FAIL_2E0)))) # label(thm_2EerrorStateMonad_2EES__CHOICE__FAIL__RID) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6713 (all A_27a all A_27b all A_27c all V2f_2E0 all V0xs_2E0 all V3y_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EmapM_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V0xs_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),f3014_1_2E1(s(A_27b,V3y_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),f3014_0_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V0xs_2E0),s(A_27b,V3y_2E0)))) # label(def1_2Ethm_2EerrorStateMonad_2EmapM__cons) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6714 (all A_27a all A_27b all A_27c all V0x_2E0 all V1f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__APPLY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,A_27b),A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(A_27c,V0x_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V1f_2E0),s(A_27c,V0x_2E0)))))) # label(thm_2EerrorStateMonad_2EAPPLY__UNIT__UNIT) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6715 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(A_27c)),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27c_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6716 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),f2986_1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),f2986_1_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef2986_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6717 (all A_27a all A_27b all A_27c all V0xs_2E0 all V1x_2E0 all V2f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EmapM_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V1x_2E0),s(tyop_2Elist_2Elist(A_27c),V0xs_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V2f_2E0),s(A_27c,V1x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),f3014_0_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V0xs_2E0)))))) # label(thm_2EerrorStateMonad_2EmapM__cons) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6718 (all A_27a all A_27b all A_27c all V1f_2E0 all V3v_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),f2974_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1f_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),V3v_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),V3v_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),f2974_1_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1f_2E0)))))) # label(def1_2Ethm_2EerrorStateMonad_2EBIND__DEF) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6719 (all A_27a all A_27b all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EES__APPLY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__APPLY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27d,A_27b),A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EES__APPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6720 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6721 (all A_27a all A_27b all A_27c all V0k_2E0 all V1m_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0k_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1m_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a))),c_2EerrorStateMonad_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0k_2E0)))))) # label(thm_2EerrorStateMonad_2EJOIN__MAP) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6722 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),c_2EerrorStateMonad_2EUNIT_2E0),s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6723 (all A_27a all A_27b all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),f2985_2_2E3(s(A_27b,X0_2E0),s(A_27a,X1_2E0),s(A_27state,X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))))),f2985_2_2E0),s(A_27b,X0_2E0))),s(A_27a,X1_2E0))),s(A_27state,X2_2E0)))) # label(arityeq3_2Ef2985_2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6724 (all A_27b all A_27c all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2EerrorStateMonad_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2EerrorStateMonad_2EEXT_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EEXT_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6725 (all A_27state all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6726 (all A_27a all A_27b all A_27state all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),f2984_0_2E1(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state))),f2984_0_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X0_2E0)))) # label(arityeq1_2Ef2984_0_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6727 (all A_27d all A_27e all A_27f all A_27g all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))))),c_2EerrorStateMonad_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),c_2EerrorStateMonad_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27g,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27f,A_27g)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EMCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27e_20mono_2Etyop_2Epair_2Eprod_28A_27f_2CA_27g_29_20mono_2EA_27f_20mono_2EA_27g) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6728 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EMMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6729 (all A_27a all V0f_2E0 ((all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6730 (all A_27a all A_27b all A_27c all A_27d all V0k_2E0 all V1m_2E0 all V2n_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0k_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),f3003_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1m_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),V2n_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0k_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),V1m_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),V2n_2E0)))) # label(thm_2EerrorStateMonad_2EBIND__ASSOC) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6731 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EEXT_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EEXT_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EEXT_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6732 (all A_27a all A_27state s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),f2981_0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2981_1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2EerrorStateMonad_2EFOREACH_2E0)) # label(thm_2EerrorStateMonad_2EFOREACH__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6733 (all A_27a all A_27b all V0m_2E0 all V1ms_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0m_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),f2986_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),V1ms_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),f2986_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),V1ms_2E0)))) # label(def2_2Ethm_2EerrorStateMonad_2Esequence__def) # label(axiom) # label(non_clause). [assumption]. 108.15/108.13 6734 (all A_27state all V0P_2E0 ((all V1i_2E0 all V2j_2E0 all V3a_2E0 ((s(tyop_2Enum_2Enum,V1i_2E0) != s(tyop_2Enum_2Enum,V2j_2E0) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V2j_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V3a_2E0))))))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V3a_2E0)))))))))) -> (all V4v_2E0 all V5v1_2E0 all V6v2_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V4v_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V5v1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V6v2_2E0))))))))))) # label(thm_2EerrorStateMonad_2EFOR__ind) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6735 (all A_27a all A_27state all X0_2E0 s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6736 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f2994_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),f2994_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef2994_0_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6737 (all A_27a all A_27state all V0f_2E0 all V1x_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2EerrorStateMonad_2EREAD_2E2(s(tyop_2Emin_2Efun(A_27state,A_27a),V0f_2E0),s(A_27state,V1x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2E_2C_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27state,A_27a),V0f_2E0),s(A_27state,V1x_2E0))),s(A_27state,V1x_2E0)))))) # label(thm_2EerrorStateMonad_2EREAD__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6738 (all A_27a all A_27b s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2EerrorStateMonad_2EUNIT_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E0)))) # label(thm_2EerrorStateMonad_2EUNIT__CURRY) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6739 (all A_27a all A_27state all V0P_2E0 ((all V1a_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V1a_2E0))))))) & (all V2h_2E0 all V3t_2E0 all V4a_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4a_2E0)))))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4a_2E0)))))))) -> (all V5v_2E0 all V6v1_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V5v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V6v1_2E0))))))))) # label(thm_2EerrorStateMonad_2EFOREACH__ind) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6740 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),c_2EerrorStateMonad_2EES__GUARD_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EES__GUARD_2E1(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EES__GUARD_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6741 (all A_27a all A_27b all A_27state all V3v_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),V3v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)))),f2984_1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27state)),f2984_0_2E1(s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),V3v_2E0)))) # label(def1_2Ethm_2EerrorStateMonad_2ENARROW__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6742 (all A_27a all A_27state all V4FOREACH_2E0 all V5a_27_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2981_1_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOREACH_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),V5a_27_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),V5a_27_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2981_2_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOREACH_2E0)))))) # label(def4_2Ethm_2EerrorStateMonad_2EFOREACH__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6743 (all A_27a all A_27state all V0R_2E0 (p(s(tyop_2Emin_2Ebool,f2981_0_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),V0R_2E0)))) <-> (all V1h_2E0 all V2a_2E0 all V3t_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V2a_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V2a_2E0))))))) & p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),V0R_2E0)))))) # label(def0_2Ethm_2EerrorStateMonad_2EFOREACH__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6744 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a))),c_2EerrorStateMonad_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),A_27a))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EMMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6745 (all A_27a all A_27b all A_27d all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27d))),tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27d))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6746 (all A_27a all A_27b all A_27c all V0f_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2EerrorStateMonad_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)))),c_2EerrorStateMonad_2EUNIT_2E0)))) # label(thm_2EerrorStateMonad_2EMMAP__UNIT) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6747 (all A_27a all A_27c all A_27d all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))))),c_2EerrorStateMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a)))),X1_2E0)))) # label(arityeq2_2Ec_2EerrorStateMonad_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6748 (all A_27b all A_27state all X0_2E0 all X1_2E0 s(tyop_2Epair_2Eprod(A_27b,A_27state),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27state,X1_2E0)))) # label(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6749 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),f2986_2_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),f2986_2_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0)))) # label(arityeq2_2Ef2986_2_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6750 (all A_27a all A_27b all V0xM_2E0 (s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EES__GUARD_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0xM_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0xM_2E0) & s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EES__GUARD_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0xM_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__FAIL_2E0))) # label(thm_2EerrorStateMonad_2EIGNORE__BIND__ESGUARD) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6751 (all A_27a all A_27b all X0_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6752 (all A_27a all A_27b all A_27state all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),f2985_2_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))))),f2985_2_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ef2985_2_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6753 (all A_27a all V0b_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V0b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EES__FAIL_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2EerrorStateMonad_2EES__GUARD_2E1(s(tyop_2Emin_2Ebool,V0b_2E0)))) # label(thm_2EerrorStateMonad_2EES__GUARD__DEF) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6754 (all A_27a all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X2_2E0)))) # label(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6755 (all A_27a all A_27b all A_27c all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c))),A_27c)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27c)))),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6756 (all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2980_2_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X2_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),f2980_2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X2_2E0)))) # label(arityeq3_2Ef2980_2_2E3_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6757 (all A_27a all A_27state all V7a_2E0 all V4FOREACH_2E0 all V8h_2E0 all V9t_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2981_3_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V7a_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOREACH_2E0),s(A_27a,V8h_2E0),s(tyop_2Elist_2Elist(A_27a),V9t_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V7a_2E0),s(A_27a,V8h_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),f2981_4_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOREACH_2E0),s(tyop_2Elist_2Elist(A_27a),V9t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V7a_2E0)))))))) # label(def2_2Ethm_2EerrorStateMonad_2EFOREACH__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6758 (all A_27a all A_27b all A_27c all A_27d all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))))),c_2EerrorStateMonad_2EES__LIFT2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EES__LIFT2_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27a))),X2_2E0)))) # label(arityeq3_2Ec_2EerrorStateMonad_2EES__LIFT2_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6759 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,V1_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6760 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2EerrorStateMonad_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EMMAP_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6761 (all A_27a all A_27state all V1t_2E0 all V3a_2E0 all V4u_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2EerrorStateMonad_2EFOREACH_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V3a_2E0))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2996_0_2E3(s(tyop_2Elist_2Elist(A_27a),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V3a_2E0),s(tyop_2Eone_2Eone,V4u_2E0)))) # label(def0_2Ethm_2EerrorStateMonad_2EFOREACH__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6762 (all A_27a all A_27b all A_27state all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27state),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27state),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),X1_2E0)))) # label(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_29_20mono_2EA_27a_20mono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6763 (all A_27state all V4FOR_2E0 all V5a_27_2E0 s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),V5a_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),f2980_2_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOR_2E0))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),f2980_1_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V4FOR_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),V5a_27_2E0)))) # label(def5_2Ethm_2EerrorStateMonad_2EFOR__primitive__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6764 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),X1_2E0)))) # label(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27c_29_2CA_27b_29_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_29_29) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6765 (all A_27state all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),f2994_1_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),f2994_1_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0)))) # label(arityeq3_2Ef2994_1_2E3_2Emono_2EA_27state) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6766 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),f2974_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),f2974_0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)))),X0_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27a),X1_2E0)))) # label(arityeq2_2Ef2974_0_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6767 (all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0)))) # label(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6768 (all A_27a all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2EerrorStateMonad_2EUNIT_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2EerrorStateMonad_2EUNIT_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2EerrorStateMonad_2EUNIT_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6769 (all A_27a all A_27b all A_27d all A_27e all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27d,A_27e)))),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27d_2CA_27e_29_29) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6770 (all 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)))))) # label(arityeq1_2Ec_2Ebool_2E_7E_2E1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6771 (all X0_2E0 all 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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6772 (all V0m_2E0 all V1n_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f3025_0_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,V0m_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeLHI_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) # label(thm_2ElistRange_2ElistRangeLHI__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6773 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6774 (all V0x_2E0 all V1n_2E0 all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeINC_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))))) # label(thm_2ElistRange_2EMEM__listRangeINC) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6775 (all V0m_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeLHI_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ENIL_2E0)) # label(thm_2ElistRange_2ElistRangeLHI__EQ) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6776 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeLHI_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2ElistRange_2ElistRangeLHI_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2ElistRange_2ElistRangeLHI_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6777 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,f3025_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f3025_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef3025_0_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6778 (all A_27a all V0_2E0 all V1_2E0 (s(A_27a,V1_2E0) = s(A_27a,V0_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))) # label(reserved_2Elogic_2E_3D) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6779 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f3024_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f3024_0_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef3024_0_2E1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6780 (all X0_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6781 (all A_27a all A_27b all A_27c all V0f_2E0 all V1g_2E0 all V2x_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0)))) # label(reserved_2Eho_2Es__thm) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6782 (all V0t_2E0 (s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))) # label(reserved_2Eho_2Ebool__cases__ax) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6783 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f3025_0_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f3025_0_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ef3025_0_2E1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6784 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0)))) -> s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeINC_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V0n_2E0))))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeINC_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))))) # label(thm_2ElistRange_2ElistRangeINC__CONS) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6785 (all A_27a all A_27b all V0x_2E0 all V1y_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0)) # label(reserved_2Eho_2Ek__thm) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6786 (all A_27a all X0_2E0 all X1_2E0 (s(A_27a,X1_2E0) = s(A_27a,X0_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)))))) # label(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6787 (all V0lo_2E0 all V1hi_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1hi_2E0),s(tyop_2Enum_2Enum,V0lo_2E0))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeLHI_2E2(s(tyop_2Enum_2Enum,V0lo_2E0),s(tyop_2Enum_2Enum,V1hi_2E0)))))) # label(thm_2ElistRange_2ELENGTH__listRangeLHI) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6788 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (exists V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_3F) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6789 (all V0n_2E0 all V1m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0n_2E0),s(tyop_2Enum_2Enum,V1m_2E0)))) -> s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeINC_2E2(s(tyop_2Enum_2Enum,V1m_2E0),s(tyop_2Enum_2Enum,V0n_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ENIL_2E0))) # label(thm_2ElistRange_2ElistRangeINC__EMPTY) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6790 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6791 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),f3024_0_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,f3024_0_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ef3024_0_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6792 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6793 (all A_27a all V0x_2E0 s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0)))) # label(reserved_2Eho_2Ei__thm) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6794 (all X0_2E0 all X1_2E0 (p(s(tyop_2Emin_2Ebool,X1_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),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)))))) # label(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6795 (all A_27a all 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)))) # label(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6796 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) & p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_2F_5C) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6797 (all A_27a all 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))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6798 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0)))) # label(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6799 (all X0_2E0 s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Elist_2ELIST__TO__SET_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6800 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2ECONS_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0)))) # label(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6801 (all V0m_2E0 all V2i_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2i_2E0))) = s(tyop_2Enum_2Enum,f3025_0_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2i_2E0)))) # label(def0_2Ethm_2ElistRange_2ElistRangeLHI__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6802 (all V0lo_2E0 all V1i_2E0 all V2hi_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0lo_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Enum_2Enum,V2hi_2E0)))) -> s(tyop_2Enum_2Enum,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeLHI_2E2(s(tyop_2Enum_2Enum,V0lo_2E0),s(tyop_2Enum_2Enum,V2hi_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0lo_2E0),s(tyop_2Enum_2Enum,V1i_2E0))))) # label(thm_2ElistRange_2EEL__listRangeLHI) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6803 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6804 (all V0lo_2E0 all V1hi_2E0 (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0lo_2E0),s(tyop_2Enum_2Enum,V1hi_2E0)))) -> s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeLHI_2E2(s(tyop_2Enum_2Enum,V0lo_2E0),s(tyop_2Enum_2Enum,V1hi_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,V0lo_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeLHI_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0lo_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V1hi_2E0))))))) # label(thm_2ElistRange_2ElistRangeLHI__CONS) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6805 (all V0_2E0 all V1_2E0 ((p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,V0_2E0))) -> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0))) # label(reserved_2Eho_2Eboolext) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6806 (all A_27a all V0f_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) <-> (all V1x_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))))) # label(reserved_2Equant_2E_21) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6807 (all X0_2E0 s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),X0_2E0)))) # label(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6808 (all X0_2E0 all 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)))) <-> p(s(tyop_2Emin_2Ebool,X1_2E0)) | p(s(tyop_2Emin_2Ebool,X0_2E0)))) # label(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6809 (all V0m_2E0 all V2i_2E0 s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2i_2E0))) = s(tyop_2Enum_2Enum,f3024_0_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V2i_2E0)))) # label(def0_2Ethm_2ElistRange_2ElistRangeINC__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6810 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Earithmetic_2E_3C_3D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6811 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,V0_2E0)) | p(s(tyop_2Emin_2Ebool,V1_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))))) # label(reserved_2Elogic_2E_5C_2F) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6812 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6813 (all V0_2E0 all V1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V0_2E0)) -> p(s(tyop_2Emin_2Ebool,V1_2E0))))) # label(reserved_2Elogic_2E_3D_3D_3E) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6814 (all V0x_2E0 all V1n_2E0 all V2m_2E0 (p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeLHI_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,V1n_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V2m_2E0),s(tyop_2Enum_2Enum,V0x_2E0)))))) # label(thm_2ElistRange_2EMEM__listRangeLHI) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6815 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2D_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6816 (all V0lo_2E0 all V1hi_2E0 p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeLHI_2E2(s(tyop_2Enum_2Enum,V0lo_2E0),s(tyop_2Enum_2Enum,V1hi_2E0))))))) # label(thm_2ElistRange_2ElistRangeLHI__ALL__DISTINCT) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6817 (all X0_2E0 all X1_2E0 s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2Earithmetic_2E_2B_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6818 (all A_27a all A_27b all V0f_2E0 all V1g_2E0 ((all V2x_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0)))) -> s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) # label(reserved_2Eho_2Eeq__ext) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6819 (all V0lo_2E0 all V1hi_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V1hi_2E0),s(tyop_2Enum_2Enum,V0lo_2E0)))) -> s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeLHI_2E2(s(tyop_2Enum_2Enum,V0lo_2E0),s(tyop_2Enum_2Enum,V1hi_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ENIL_2E0))) # label(thm_2ElistRange_2ElistRangeLHI__EMPTY) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6820 (all V0m_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeINC_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V0m_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ECONS_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2ENIL_2E0)))) # label(thm_2ElistRange_2ElistRangeINC__SING) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6821 (all X0_2E0 all X1_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeINC_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Enum_2Enum))),c_2ElistRange_2ElistRangeINC_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0)))) # label(arityeq2_2Ec_2ElistRange_2ElistRangeINC_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6822 (all V0_2E0 (-p(s(tyop_2Emin_2Ebool,V0_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))))) # label(reserved_2Elogic_2E_7E) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6823 (all V0m_2E0 all V1n_2E0 s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2ElistRange_2ElistRangeINC_2E2(s(tyop_2Enum_2Enum,V0m_2E0),s(tyop_2Enum_2Enum,V1n_2E0))) = s(tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),f3024_0_2E1(s(tyop_2Enum_2Enum,V0m_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1n_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V0m_2E0)))))) # label(thm_2ElistRange_2ElistRangeINC__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6824 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),f3080_3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(A_27c,f3080_3_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef3080_3_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6825 (all A_27a all X0_2E0 s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2Esome_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6826 (all A_27b all V5P_2E0 all V6x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V6x_2E0))) = s(tyop_2Emin_2Ebool,f3073_0_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V6x_2E0)))) # label(def22_2Ethm_2EquantHeuristics_2EGUESS__RULES__CONJ) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6827 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f3080_8_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f3080_8_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27c,X1_2E0)))) # label(arityeq2_2Ef3080_8_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6828 (all A_27a all A_27b all V0i_2E0 all V1P_2E0 (p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) <-> ((all V2v_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0))))) <-> (all V3fv_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0)))))))))) # label(thm_2EquantHeuristics_2EGUESS__FORALL__def) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6829 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Eone_2Eone),A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Eone_2Eone),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Eone_2Eone),A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Eone_2Eone_29_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6830 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f3072_6_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f3072_6_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef3072_6_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6831 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3076_16_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3076_16_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef3076_16_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6832 (all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f3114_0_2E2(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = 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)),f3114_0_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) # label(arityeq2_2Ef3114_0_2E2) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6833 (all A_27a all A_27b all X0_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(A_27a,c_2Epair_2EFST_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0)))) # label(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6834 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3058_1_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3058_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef3058_1_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6835 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3073_1_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f3073_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef3073_1_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6836 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3069_7_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3069_7_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef3069_7_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6837 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f3076_26_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3076_26_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0)))) # label(arityeq3_2Ef3076_26_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6838 (all A_27a all A_27b all A_27c all V0iy_2E0 all V1P_2E0 (((all V2y_2E0 p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0iy_2E0),s(A_27a,V2y_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3080_0_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V2y_2E0))))))) -> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),f3080_1_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0iy_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3080_8_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0))))))) & ((all V7y_2E0 p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0iy_2E0),s(A_27a,V7y_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3080_2_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V7y_2E0))))))) -> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),f3080_3_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0iy_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3080_9_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0))))))) & ((all V17y_2E0 p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0iy_2E0),s(A_27a,V17y_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3080_6_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V17y_2E0))))))) -> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__GAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),f3080_7_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0iy_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3080_11_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0))))))) & ((all V12y_2E0 p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0iy_2E0),s(A_27a,V12y_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3080_4_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V12y_2E0))))))) -> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),f3080_5_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0iy_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3080_10_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0))))))))) # label(thm_2EquantHeuristics_2EGUESS__RULES__EXISTS______NEW__FV) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6839 (all A_27a all A_27b all V0P_2E0 all V1Q_2E0 ((all V2x_2E0 exists V3fv_2E0 s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1Q_2E0),s(A_27b,V3fv_2E0))) = s(A_27a,V2x_2E0)) -> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1Q_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))) # label(thm_2EquantHeuristics_2EGUESS__RULES__ONE__CASE______EXISTS__GAP) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6840 (all V6ARB_2E0 s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,f3065_3_2E1(s(tyop_2Eone_2Eone,V6ARB_2E0)))) # label(def2_2Ethm_2EquantHeuristics_2EGUESS__RULES__BOOL) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6841 (all V2P1_2E0 all V3P2_2E0 (p(s(tyop_2Emin_2Ebool,V3P2_2E0)) & p(s(tyop_2Emin_2Ebool,V2P1_2E0)) <-> p(s(tyop_2Emin_2Ebool,f3113_0_2E2(s(tyop_2Emin_2Ebool,V2P1_2E0),s(tyop_2Emin_2Ebool,V3P2_2E0)))))) # label(def0_2Ethm_2EquantHeuristics_2ESIMPLE__GUESS__EXISTS__AND__1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6842 (all A_27a all A_27b all V0x_2E0 (((all V2l_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V2l_2E0))) != s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0)) <-> p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0))))) & ((all V1l_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0) != s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(s(A_27a,V1l_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Esum_2EISR_2E1(s(tyop_2Esum_2Esum(A_27a,A_27b),V0x_2E0))))))) # label(thm_2EquantHeuristics_2EINL__NEQ__ELIM) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6843 (all A_27a all A_27c all V2P_2E0 all V7y_2E0 all V8x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27c,V8x_2E0))),s(A_27a,V7y_2E0))) = s(tyop_2Emin_2Ebool,f3082_2_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V7y_2E0),s(A_27c,V8x_2E0)))) # label(def8_2Ethm_2EquantHeuristics_2EGUESS__RULES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 108.21/108.14 6844 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f3104_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f3104_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef3104_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6845 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2EquantHeuristics_2EGUESS__EXISTS__GAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6846 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3072_8_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3072_8_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef3072_8_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6847 (all A_27a all V1P_2E0 all V3v_2E0 s(tyop_2Emin_2Ebool,f3100_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3v_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3v_2E0)))) # label(def0_2Ethm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__ALT__DEF) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6848 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Eone_2Eone),A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),f3084_1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Eone_2Eone),A_27b),X0_2E0))),s(A_27a,X1_2E0))) = s(A_27b,f3084_1_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Eone_2Eone),A_27b),X0_2E0),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef3084_1_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6849 (all A_27a all A_27b all V0i_2E0 all V2x_2E0 s(A_27a,V0i_2E0) = s(A_27a,f3055_0_2E2(s(A_27a,V0i_2E0),s(A_27b,V2x_2E0)))) # label(def0_2Ethm_2EquantHeuristics_2EGUESSES__UEXISTS__THM3) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6850 (all A_27a all A_27c all V0i_2E0 all V7y_2E0 all V8xxx_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0i_2E0),s(A_27a,V7y_2E0))) = s(A_27c,f3078_2_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V0i_2E0),s(A_27a,V7y_2E0),s(tyop_2Eone_2Eone,V8xxx_2E0)))) # label(def10_2Ethm_2EquantHeuristics_2EGUESS__RULES__FORALL______NEW__FV__1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6851 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3069_2_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3069_2_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef3069_2_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6852 (all A_27b all V2iK_2E0 all V18xxx_2E0 s(A_27b,f3072_11_2E2(s(A_27b,V2iK_2E0),s(tyop_2Eone_2Eone,V18xxx_2E0))) = s(A_27b,V2iK_2E0)) # label(def25_2Ethm_2EquantHeuristics_2EGUESS__RULES__DISJ) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6853 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2EquantHeuristics_2EGUESS__EXISTS__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6854 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3077_11_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f3077_11_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef3077_11_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6855 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f3075_7_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3075_7_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef3075_7_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6856 (all A_27b all X0_2E0 all X1_2E0 s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27b)),f3073_10_2E0),s(A_27b,X0_2E0))),s(tyop_2Eone_2Eone,X1_2E0))) = s(A_27b,f3073_10_2E2(s(A_27b,X0_2E0),s(tyop_2Eone_2Eone,X1_2E0)))) # label(arityeq2_2Ef3073_10_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6857 (all A_27a all A_27b all V0i_2E0 all V2x_2E0 s(A_27a,V0i_2E0) = s(A_27a,f3053_0_2E2(s(A_27a,V0i_2E0),s(A_27b,V2x_2E0)))) # label(def0_2Ethm_2EquantHeuristics_2EGUESSES__UEXISTS__THM1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6858 (all A_27a all A_27c all V1P_2E0 all V5x_2E0 (p(s(tyop_2Emin_2Ebool,f3078_1_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27c,V5x_2E0)))) <-> (all V6y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27c,V5x_2E0))),s(A_27a,V6y_2E0))))))) # label(def3_2Ethm_2EquantHeuristics_2EGUESS__RULES__FORALL______NEW__FV__1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6859 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3072_5_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3072_5_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef3072_5_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6860 (all A_27a all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ec_2EquantHeuristics_2EGUESS__FORALL__POINT_2E2_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6861 (all A_27c all X0_2E0 all X1_2E0 s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Eone_2Eone,A_27c)),f3079_8_2E0),s(A_27c,X0_2E0))),s(tyop_2Eone_2Eone,X1_2E0))) = s(A_27c,f3079_8_2E2(s(A_27c,X0_2E0),s(tyop_2Eone_2Eone,X1_2E0)))) # label(arityeq2_2Ef3079_8_2E2_2Emono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6862 (all A_27a all A_27c all V1P_2E0 all V20x_2E0 (p(s(tyop_2Emin_2Ebool,f3080_11_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27c,V20x_2E0)))) <-> (exists V21y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27c,V20x_2E0))),s(A_27a,V21y_2E0))))))) # label(def2_2Ethm_2EquantHeuristics_2EGUESS__RULES__EXISTS______NEW__FV) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6863 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f3072_21_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3072_21_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef3072_21_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6864 (all A_27b all V1P_2E0 all V4x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4x_2E0))) = s(tyop_2Emin_2Ebool,f3069_2_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4x_2E0)))) # label(def9_2Ethm_2EquantHeuristics_2EGUESS__RULES__NEG) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6865 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f3075_11_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3075_11_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) # label(arityeq2_2Ef3075_11_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6866 (all A_27b all V5P_2E0 all V26x_2E0 s(tyop_2Emin_2Ebool,f3074_17_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V26x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V26x_2E0)))) # label(def19_2Ethm_2EquantHeuristics_2EGUESS__RULES__IMP) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6867 (all A_27a all A_27b all A_27c all X0_2E0 all X1_2E0 s(A_27c,f3080_5_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),f3080_5_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0)))) # label(arityeq2_2Ef3080_5_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6868 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 all X3_2E0 s(tyop_2Emin_2Ebool,f3076_17_2E4(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),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_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),f3076_17_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))),s(A_27b,X3_2E0)))) # label(arityeq4_2Ef3076_17_2E4_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6869 (all A_27b all V5P_2E0 all V4Q_2E0 all V9x_2E0 (p(s(tyop_2Emin_2Ebool,f3073_3_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V9x_2E0)))) <-> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V9x_2E0)))) & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V9x_2E0)))))) # label(def2_2Ethm_2EquantHeuristics_2EGUESS__RULES__CONJ) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6870 (all A_27a all X0_2E0 s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),f3099_0_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f3099_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef3099_0_2E1_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6871 (all A_27b all X0_2E0 all X1_2E0 all X2_2E0 s(tyop_2Emin_2Ebool,f3074_1_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(A_27b,X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),f3074_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(A_27b,X2_2E0)))) # label(arityeq3_2Ef3074_1_2E3_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6872 (all A_27a all A_27c all V2P_2E0 all V15y_2E0 all V16x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27c,V16x_2E0))),s(A_27a,V15y_2E0))) = s(tyop_2Emin_2Ebool,f3082_6_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2P_2E0),s(A_27a,V15y_2E0),s(A_27c,V16x_2E0)))) # label(def6_2Ethm_2EquantHeuristics_2EGUESS__RULES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6873 (all X0_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),f3065_1_2E0),s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Emin_2Ebool,f3065_1_2E1(s(tyop_2Eone_2Eone,X0_2E0)))) # label(arityeq1_2Ef3065_1_2E1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6874 (all A_27b all V5P_2E0 all V22x_2E0 s(tyop_2Emin_2Ebool,f3073_13_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V22x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V22x_2E0)))) # label(def21_2Ethm_2EquantHeuristics_2EGUESS__RULES__CONJ) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6875 (all A_27a all A_27c all V1P_2E0 all V20x_2E0 ((all V21y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27c,V20x_2E0))),s(A_27a,V21y_2E0))))) <-> p(s(tyop_2Emin_2Ebool,f3077_11_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27c,V20x_2E0)))))) # label(def2_2Ethm_2EquantHeuristics_2EGUESS__RULES__FORALL______NEW__FV) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6876 (all V2P1_2E0 all V3P2_2E0 (p(s(tyop_2Emin_2Ebool,f3119_0_2E2(s(tyop_2Emin_2Ebool,V2P1_2E0),s(tyop_2Emin_2Ebool,V3P2_2E0)))) <-> (p(s(tyop_2Emin_2Ebool,V2P1_2E0)) -> p(s(tyop_2Emin_2Ebool,V3P2_2E0))))) # label(def0_2Ethm_2EquantHeuristics_2ESIMPLE__GUESS__FORALL__IMP__1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6877 (all A_27b all X0_2E0 s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),f3076_6_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3076_6_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) # label(arityeq1_2Ef3076_6_2E1_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6878 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3069_1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,f3069_1_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef3069_1_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6879 (all A_27b all V3Q_2E0 all V42x_2E0 s(tyop_2Emin_2Ebool,f3076_37_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27b,V42x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3Q_2E0),s(A_27b,V42x_2E0)))) # label(def18_2Ethm_2EquantHeuristics_2EGUESS__RULES__COND) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6880 (all A_27a all A_27b all X0_2E0 s(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(s(A_27b,X0_2E0))) = s(tyop_2Esum_2Esum(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EINR_2E0),s(A_27b,X0_2E0)))) # label(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6881 (all A_27b all V2b_2E0 all V23x_2E0 s(tyop_2Emin_2Ebool,f3076_18_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2b_2E0),s(A_27b,V23x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2b_2E0),s(A_27b,V23x_2E0)))) # label(def32_2Ethm_2EquantHeuristics_2EGUESS__RULES__COND) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6882 (all A_27a all A_27c all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f3079_13_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27c,X1_2E0))) = s(tyop_2Emin_2Ebool,f3079_13_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27c,X1_2E0)))) # label(arityeq2_2Ef3079_13_2E2_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6883 (all A_27b all V4Q_2E0 all V19x_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V19x_2E0))) = s(tyop_2Emin_2Ebool,f3072_25_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V19x_2E0)))) # label(def13_2Ethm_2EquantHeuristics_2EGUESS__RULES__DISJ) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6884 (all A_27b all V5P_2E0 all V10x_2E0 s(tyop_2Emin_2Ebool,f3072_4_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V10x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V10x_2E0)))) # label(def12_2Ethm_2EquantHeuristics_2EGUESS__RULES__DISJ) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6885 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3079_7_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f3079_7_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) # label(arityeq1_2Ef3079_7_2E1_2Emono_2EA_27a_20mono_2EA_27c) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6886 (all A_27a all A_27b all V0i_2E0 all V1P_2E0 (((all V4v_2E0 (-p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V4v_2E0)))) -> (exists V5fv_2E0 -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V5fv_2E0))))))))) <-> p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2EquantHeuristics_2EGUESS__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0)))) <-> (all V2v_2E0 (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2v_2E0)))) -> (exists V3fv_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0i_2E0),s(A_27a,V3fv_2E0)))))))))))) # label(thm_2EquantHeuristics_2EGUESS__EXISTS__FORALL__REWRITES) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6887 (all A_27b all V5P_2E0 all V13x_2E0 s(tyop_2Emin_2Ebool,f3073_7_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V13x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V13x_2E0)))) # label(def10_2Ethm_2EquantHeuristics_2EGUESS__RULES__CONJ) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6888 (all A_27b all V1P_2E0 all V13x_2E0 (p(s(tyop_2Emin_2Ebool,f3069_11_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V13x_2E0)))) <-> -p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V13x_2E0)))))) # label(def4_2Ethm_2EquantHeuristics_2EGUESS__RULES__NEG) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6889 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f3073_17_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3073_17_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef3073_17_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6890 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3072_7_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,f3072_7_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef3072_7_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6891 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f3072_20_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3072_20_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef3072_20_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6892 (all A_27b all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f3076_33_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),f3076_33_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(A_27b,X1_2E0)))) # label(arityeq2_2Ef3076_33_2E2_2Emono_2EA_27b) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6893 (all A_27a all A_27c all V1P_2E0 all V10x_2E0 ((exists V11y_2E0 p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27c,V10x_2E0))),s(A_27a,V11y_2E0))))) <-> p(s(tyop_2Emin_2Ebool,f3081_3_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27c,V10x_2E0)))))) # label(def2_2Ethm_2EquantHeuristics_2EGUESS__RULES__EXISTS______NEW__FV__1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6894 (all A_27a all A_27c all V1P_2E0 all V12y_2E0 all V13x_2E0 s(tyop_2Emin_2Ebool,f3080_4_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27a,V12y_2E0),s(A_27c,V13x_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1P_2E0),s(A_27c,V13x_2E0))),s(A_27a,V12y_2E0)))) # label(def5_2Ethm_2EquantHeuristics_2EGUESS__RULES__EXISTS______NEW__FV) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6895 (all A_27a all X0_2E0 all X1_2E0 s(tyop_2Emin_2Ebool,f3105_0_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),f3105_0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0)))) # label(arityeq2_2Ef3105_0_2E2_2Emono_2EA_27a) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6896 (all A_27b all V5P_2E0 all V4Q_2E0 all V15x_2E0 ((p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(A_27b,V15x_2E0)))) -> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V15x_2E0))))) <-> p(s(tyop_2Emin_2Ebool,f3074_9_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4Q_2E0),s(A_27b,V15x_2E0)))))) # label(def0_2Ethm_2EquantHeuristics_2EGUESS__RULES__IMP) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6897 (all A_27a all V0x_2E0 all V1l_2E0 (((exists V2e1_2E0 s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2e1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))) & (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))) <-> (exists V3e1_2E0 s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3e1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) <-> (exists V4l_27_2E0 exists V5e1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5e1_2E0),s(tyop_2Elist_2Elist(A_27a),V4l_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)))) <-> (exists V6l_27_2E0 exists V7e1_2E0 s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V7e1_2E0),s(tyop_2Elist_2Elist(A_27a),V6l_27_2E0))))) & ((exists V8l_27_2E0 exists V9e1_2E0 s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V9e1_2E0),s(tyop_2Elist_2Elist(A_27a),V8l_27_2E0)))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) <-> (exists V10l_27_2E0 exists V11e1_2E0 s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V11e1_2E0),s(tyop_2Elist_2Elist(A_27a),V10l_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) & ((exists V20l_27_2E0 exists V21e1_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V21e1_2E0),s(tyop_2Elist_2Elist(A_27a),V20l_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) & s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V20l_27_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0))) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0)))) & (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))) <-> (exists V22l_27_2E0 exists V23e1_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V22l_27_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0) & s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V23e1_2E0),s(tyop_2Elist_2Elist(A_27a),V22l_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) & ((exists V24l_27_2E0 exists V25e1_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V25e1_2E0),s(tyop_2Elist_2Elist(A_27a),V24l_27_2E0))) & s(tyop_2Enum_2Enum,V0x_2E0) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V24l_27_2E0))))) <-> s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) & (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))) = s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) <-> (exists V26l_27_2E0 exists V27e1_2E0 (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V26l_27_2E0))) = s(tyop_2Enum_2Enum,V0x_2E0) & s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V27e1_2E0),s(tyop_2Elist_2Elist(A_27a),V26l_27_2E0)))))) & (s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) <-> s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))) <-> s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) <-> s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) <-> s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)) & (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) & (s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) <-> s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0)))))))))) <-> (exists V18l_27_2E0 exists V19e1_2E0 (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V18l_27_2E0)))))) & s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V19e1_2E0),s(tyop_2Elist_2Elist(A_27a),V18l_27_2E0)))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) <-> (exists V16l_27_2E0 exists V17e1_2E0 (s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V17e1_2E0),s(tyop_2Elist_2Elist(A_27a),V16l_27_2E0))) = s(tyop_2Elist_2Elist(A_27a),V1l_2E0) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V16l_27_2E0))))))))) & ((exists V14l_27_2E0 exists V15e1_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V15e1_2E0),s(tyop_2Elist_2Elist(A_27a),V14l_27_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V14l_27_2E0)))))))) <-> p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3E_3D_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))))))) & (p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,V0x_2E0))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) <-> (exists V12l_27_2E0 exists V13e1_2E0 (s(tyop_2Elist_2Elist(A_27a),V1l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V13e1_2E0),s(tyop_2Elist_2Elist(A_27a),V12l_27_2E0))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2E_3C_3D_2E2(s(tyop_2Enum_2Enum,V0x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V12l_27_2E0))))))))))) # label(thm_2EquantHeuristics_2ELIST__LENGTH__1) # label(axiom) # label(non_clause). [assumption]. 108.21/108.15 6898 (all A_27a all A_27c all X0_2E0 s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),f3081_5_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),f3081_5_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) #Alarm clock 120.12/120.05 Prover9 interrupted 120.12/120.06 EOF