TSTP Solution File: SWW472+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW472+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:17:08 EDT 2022
% Result : Timeout 300.07s 300.42s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW472+2 : TPTP v8.1.0. Released v5.3.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 5 02:33:09 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.12/1.42 ============================== Prover9 ===============================
% 1.12/1.42 Prover9 (32) version 2009-11A, November 2009.
% 1.12/1.42 Process 16154 was started by sandbox2 on n023.cluster.edu,
% 1.12/1.42 Sun Jun 5 02:33:10 2022
% 1.12/1.42 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16001_n023.cluster.edu".
% 1.12/1.42 ============================== end of head ===========================
% 1.12/1.42
% 1.12/1.42 ============================== INPUT =================================
% 1.12/1.42
% 1.12/1.42 % Reading from file /tmp/Prover9_16001_n023.cluster.edu
% 1.12/1.42
% 1.12/1.42 set(prolog_style_variables).
% 1.12/1.42 set(auto2).
% 1.12/1.42 % set(auto2) -> set(auto).
% 1.12/1.42 % set(auto) -> set(auto_inference).
% 1.12/1.42 % set(auto) -> set(auto_setup).
% 1.12/1.42 % set(auto_setup) -> set(predicate_elim).
% 1.12/1.42 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.12/1.42 % set(auto) -> set(auto_limits).
% 1.12/1.42 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.12/1.42 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.12/1.42 % set(auto) -> set(auto_denials).
% 1.12/1.42 % set(auto) -> set(auto_process).
% 1.12/1.42 % set(auto2) -> assign(new_constants, 1).
% 1.12/1.42 % set(auto2) -> assign(fold_denial_max, 3).
% 1.12/1.42 % set(auto2) -> assign(max_weight, "200.000").
% 1.12/1.42 % set(auto2) -> assign(max_hours, 1).
% 1.12/1.42 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.12/1.42 % set(auto2) -> assign(max_seconds, 0).
% 1.12/1.42 % set(auto2) -> assign(max_minutes, 5).
% 1.12/1.42 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.12/1.42 % set(auto2) -> set(sort_initial_sos).
% 1.12/1.42 % set(auto2) -> assign(sos_limit, -1).
% 1.12/1.42 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.12/1.42 % set(auto2) -> assign(max_megs, 400).
% 1.12/1.42 % set(auto2) -> assign(stats, some).
% 1.12/1.42 % set(auto2) -> clear(echo_input).
% 1.12/1.42 % set(auto2) -> set(quiet).
% 1.12/1.42 % set(auto2) -> clear(print_initial_clauses).
% 1.12/1.42 % set(auto2) -> clear(print_given).
% 1.12/1.42 assign(lrs_ticks,-1).
% 1.12/1.42 assign(sos_limit,10000).
% 1.12/1.42 assign(order,kbo).
% 1.12/1.42 set(lex_order_vars).
% 1.12/1.42 clear(print_given).
% 1.12/1.42
% 1.12/1.42 % formulas(sos). % not echoed (354 formulas)
% 1.12/1.42
% 1.12/1.42 ============================== end of input ==========================
% 1.12/1.42
% 1.12/1.42 % From the command line: assign(max_seconds, 300).
% 1.12/1.42
% 1.12/1.42 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.12/1.42
% 1.12/1.42 % Formulas that are not ordinary clauses:
% 1.12/1.42 1 (all B_1_1 all B_2_1 is_bool(big_se1303371297_state(B_1_1,B_2_1))) # label(gsy_c_Big__Operators_Osemilattice__big_000tc__Hoare____Mirabelle____ddpglwnxwg__) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 2 (all B_1_1 is_bool(finite1710211309_state(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__commute_000tc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 3 (all B_1_1 is_bool(finite372259688_state(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__Otri) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 4 (all B_1_1 is_bool(finite1317819144e_bool(B_1_1))) # label(gsy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__Otri_001) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 5 (all B_1_1 all B_2_1 is_bool(finite774711482_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 6 (all B_1_1 all B_2_1 is_bool(finite506823037_state(B_1_1,B_2_1))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____ddpglwnxwg__O) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 7 (all B_1_1 all B_2_1 is_bool(hAPP_state_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 8 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 9 (all B_1_1 all B_2_1 is_bool(hAPP_H513860823e_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__Ostate_J_0) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 10 (all B_1_1 all B_2_1 is_bool(hAPP_nat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 11 (all B_1_1 all B_2_1 is_bool(hAPP_f1760790145l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__O) # label(hypothesis) # label(non_clause). [assumption].
% 1.12/1.42 12 (all G_2 hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),bot_bo1055319631e_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 13 (all Fun1_2 all Com_2 all Fun2_2 all Fun1_1 all Com_1 all Fun2_1 (hoare_1575745797_state(Fun1_2,Com_2,Fun2_2) = hoare_1575745797_state(Fun1_1,Com_1,Fun2_1) <-> Fun1_2 = Fun1_1 & Com_2 = Com_1 & Fun2_2 = Fun2_1)) # label(fact_1_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 14 (all G_2 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) -> hBOOL(hAPP_f1760790145l_bool(hoare_1065416081_state(G_2),Ts)))) # label(fact_2_hoare__sound) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 15 (all G_2 all G_1 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),G_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))))) # label(fact_3_cut) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 16 (all Ts all G_2 all T (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts)))))) # label(fact_4_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 17 (all G_2 all T all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),Ts))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,T),bot_bo1055319631e_bool))) & hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)))) # label(fact_5_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 18 (all Qa all G_2 all Pa all Ca all Q_2 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Q_2)),bot_bo1055319631e_bool))) -> ((all Z_1 all S (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_1),S)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_1),S)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Qa)),bot_bo1055319631e_bool)))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 19 (all Pa all G_2 all P_2 all Ca all Qa (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(P_2,Ca,Qa)),bot_bo1055319631e_bool))) -> ((all Z_1 all S (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_1),S)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_1),S)))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Qa)),bot_bo1055319631e_bool)))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 20 (all A all B all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),A_1))) -> (A != B -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1))))) # label(fact_8_insertE) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 21 (all B all A all B_1 ((-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B_1)) -> A = B) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),B_1))))) # label(fact_9_insertCI) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 22 (all Qa all Pa all G_2 all P_2 all Ca all Q_2 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(P_2,Ca,Q_2)),bot_bo1055319631e_bool))) -> ((all Z_1 all S (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_1),S)) -> (all S_1 ((all Z_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_2,Z_2),S)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_2,Z_2),S_1)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_1),S_1)))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Qa)),bot_bo1055319631e_bool)))))) # label(fact_10_conseq12) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 23 (all A -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),bot_bo1055319631e_bool))) # label(fact_11_emptyE) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 24 (all A all A_1 bot_bo1055319631e_bool != hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)) # label(fact_12_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 25 (all A all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) != bot_bo1055319631e_bool) # label(fact_13_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 26 (all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) <-> B = A)) # label(fact_14_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 27 (all A all B all Ca all D_1 (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),bot_bo1055319631e_bool)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Ca),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,D_1),bot_bo1055319631e_bool)) <-> A = Ca & B = D_1 | A = D_1 & B = Ca)) # label(fact_15_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 28 (all A all A_1 (A_1 = bot_bo1055319631e_bool -> -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)))) # label(fact_16_equals0D) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 29 (all Pa (hAPP_f921536533e_bool(collec727977250_state,Pa) = bot_bo1055319631e_bool <-> (all X_1 -hBOOL(hAPP_H513860823e_bool(Pa,X_1))))) # label(fact_17_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 30 (all Ca -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),bot_bo1055319631e_bool))) # label(fact_18_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 31 (all Pa (bot_bo1055319631e_bool = hAPP_f921536533e_bool(collec727977250_state,Pa) <-> (all X_1 -hBOOL(hAPP_H513860823e_bool(Pa,X_1))))) # label(fact_19_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 32 (all A_1 ((exists X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))) <-> A_1 != bot_bo1055319631e_bool)) # label(fact_20_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 33 (all A_1 ((all X_1 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1))) <-> A_1 = bot_bo1055319631e_bool)) # label(fact_21_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 34 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1) = A_1)) # label(fact_23_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 35 (all B all A all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),B_1))))) # label(fact_24_insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 36 (all B_1 all X_2 all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1)) -> (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1) <-> A_1 = B_1)))) # label(fact_25_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 37 (all Y_2 all A_1 all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),A_1),X_2)) <-> Y_2 = X_2 | hBOOL(hAPP_H513860823e_bool(A_1,X_2)))) # label(fact_26_insert__code) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 38 (all A all B all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),A_1))) <-> A = B | hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)))) # label(fact_27_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 39 (all X_2 all Y_2 all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1))) # label(fact_28_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 40 (all X_2 all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) # label(fact_29_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 41 (all A all Pa hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(collec727977250_state,Pa)) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(cOMBS_1248383340l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(fimplies),hAPP_f921536533e_bool(cOMBB_416661851_state(fNot),hAPP_H1645666623e_bool(cOMBC_1424981238e_bool(fequal1531560888_state),A)))),Pa))) # label(fact_30_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 42 (all A all B_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(cOMBS_1248383340l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(fdisj),hAPP_H1645666623e_bool(cOMBC_1424981238e_bool(fequal1531560888_state),A))),hAPP_f921536533e_bool(cOMBC_764456866l_bool(member1758697444_state),B_1)))) # label(fact_31_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 43 (all A all B_1 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1)))) # label(fact_32_insertI1) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 44 (all A all B (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),bot_bo1055319631e_bool) -> A = B)) # label(fact_33_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 45 (all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) -> B = A)) # label(fact_34_singletonE) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 46 (all X_2 hAPP_f2143211163_state(the_el23965208_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = X_2) # label(fact_35_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 47 (all X_2 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_36_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 48 (all X_1 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_37_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 49 (all G_2 all Pa hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,skip,Pa)),bot_bo1055319631e_bool)))) # label(fact_38_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 50 (all D_1 all R_1 all G_2 all Pa all Ca all Qa (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Qa)),bot_bo1055319631e_bool))) -> (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Qa,D_1,R_1)),bot_bo1055319631e_bool))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,semi(Ca,D_1),R_1)),bot_bo1055319631e_bool)))))) # label(fact_39_Comp) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 51 (all Y_2 -(all Fun1 all Com all Fun2 Y_2 != hoare_1575745797_state(Fun1,Com,Fun2))) # label(fact_40_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 52 (all X_2 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> -(all B_3 (A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_3) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_3)))))) # label(fact_41_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 53 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> (exists B_3 (A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_3) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),B_3)))))) # label(fact_42_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 54 (all A_1 ((all Y_1 -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Y_1),A_1))) -> A_1 = bot_bo1055319631e_bool)) # label(fact_43_equals0I) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 55 (all Qa all G_2 all Ca all Pa ((all Z_1 all S (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Pa,Z_1),S)) -> (exists P_1 exists Q_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(P_1,Ca,Q_1)),bot_bo1055319631e_bool))) & (all S_1 ((all Z_2 (hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(P_1,Z_2),S)) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Q_1,Z_2),S_1)))) -> hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(Qa,Z_1),S_1)))))))) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,hoare_1575745797_state(Pa,Ca,Qa)),bot_bo1055319631e_bool))))) # label(fact_44_conseq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 56 (all A_1 (A_1 != bot_bo1055319631e_bool <-> (exists X_1 exists B_3 (A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),B_3) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_3)))))) # label(fact_45_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 57 (all Com1_2 all Com2_2 semi(Com1_2,Com2_2) != skip) # label(fact_46_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 58 (all Com1_2 all Com2_2 skip != semi(Com1_2,Com2_2)) # label(fact_47_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 59 (all Com1_1 all Com2_1 all Com1 all Com2 (semi(Com1_1,Com2_1) = semi(Com1,Com2) <-> Com1_1 = Com1 & Com2_1 = Com2)) # label(fact_48_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 60 (all F all A all B (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)),B)) <-> A = B)) # label(fact_49_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 61 (all X_2 all F all F_1 (hBOOL(finite774711482_state(F,F_1)) -> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = X_2)) # label(fact_50_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 62 (all X_1 (hBOOL(hAPP_H513860823e_bool(bot_bo1055319631e_bool,X_1)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),bot_bo1055319631e_bool)))) # label(fact_51_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 63 (all F all A hAPP_f2143211163_state(finite1346402327_state(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) = A) # label(fact_52_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 64 (all A all G all F (G = finite1346402327_state(F) -> hAPP_f2143211163_state(G,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool)) = A)) # label(fact_53_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 65 (all F all X_2 -hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),bot_bo1055319631e_bool),X_2))) # label(fact_54_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 66 (all F all A_1 all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),A_1),X_2)) -> A_1 != bot_bo1055319631e_bool)) # label(fact_55_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 67 (all F all A all A_1 all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),A),A_1),X_2)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)),X_2))))) # label(fact_56_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 68 (all X_2 all A_1 all F all F_1 (hBOOL(finite774711482_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> (A_1 != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(F_1,A_1))))))) # label(fact_57_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 69 (all A_1 all F all F_1 (hBOOL(finite774711482_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hAPP_f2143211163_state(F_1,A_1) = hAPP_f2143211163_state(finite1346402327_state(F),A_1)))) # label(fact_58_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 70 (all A_1 all F all F_1 (hBOOL(finite774711482_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (A_1 != bot_bo1055319631e_bool -> ((all X_1 all Y_1 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),Y_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,Y_1),bot_bo1055319631e_bool))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,hAPP_f2143211163_state(F_1,A_1)),A_1))))))) # label(fact_59_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 71 (all F all A all X_3 all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),X_3)),X_2)) -> -(all A_3 all A_2 (hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),X_3) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),A_2) -> (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),A_3),A_2),X_2)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),A_2))))))) # label(fact_60_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 72 (all A_1 all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))) -> A_1 = bot_bo1055319631e_bool | A_1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))) # label(fact_61_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 73 (all X_2 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),X_2))) # label(fact_62_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 74 (all X_2 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),X_2))) # label(fact_63_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 75 (all Ca all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1))))) # label(fact_64_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 76 (all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1)) -> A_1 = B_1))) # label(fact_65_equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 77 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1))))) # label(fact_67_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 78 (all A_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A_1))) # label(fact_68_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 79 (all Qa all Pa all X_2 (hBOOL(hAPP_H513860823e_bool(Pa,X_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Pa),Qa)) -> hBOOL(hAPP_H513860823e_bool(Qa,X_2))))) # label(fact_69_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 80 (all X_2 all Pa all Qa (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Pa),Qa)) -> (hBOOL(hAPP_H513860823e_bool(Pa,X_2)) -> hBOOL(hAPP_H513860823e_bool(Qa,X_2))))) # label(fact_70_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 81 (all X_2 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) <-> hBOOL(hAPP_H513860823e_bool(A_1,X_2)))) # label(fact_71_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 82 (all Pa hAPP_f921536533e_bool(collec727977250_state,Pa) = Pa) # label(fact_72_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 83 (all A_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),A_1))) # label(fact_73_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 84 (all A_1 all B_1 (A_1 = B_1 <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1)))) # label(fact_74_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 85 (all A_1 all B_1 (A_1 = B_1 -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)))) # label(fact_75_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 86 (all A_1 all B_1 (A_1 = B_1 -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1)))) # label(fact_76_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 87 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1))))) # label(fact_77_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 88 (all B_1 all X_2 all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1))))) # label(fact_78_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 89 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1))))) # label(fact_79_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 90 (all C all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),C)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C))))) # label(fact_80_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 91 (all A_1 all B_1 (A_1 = B_1 -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1))))) # label(fact_81_equalityE) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 92 (all F all G (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) <-> (all X_1 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1)))))) # label(fact_82_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 93 (all Y_2 all X_2 ((hBOOL(X_2) <-> hBOOL(Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)))) # label(fact_83_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 94 (all X_2 all Y_2 (X_2 = Y_2 <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)))) # label(fact_84_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 95 (all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))))) # label(fact_85_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 96 (all Y_2 all X_2 ((hBOOL(X_2) <-> hBOOL(Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)))) # label(fact_86_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 97 (all X_2 all Y_2 (X_2 = Y_2 -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)))) # label(fact_87_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 98 (all X_2 all F all G (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2))))) # label(fact_88_le__funD) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 99 (all Y_2 all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) <-> (hBOOL(X_2) <-> hBOOL(Y_2))))) # label(fact_89_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.42 100 (all Y_2 all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) <-> X_2 = Y_2))) # label(fact_90_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 101 (all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))))) # label(fact_91_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 102 (all Ca all B all A ((hBOOL(A) <-> hBOOL(B)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),Ca)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),Ca))))) # label(fact_92_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 103 (all Ca all A all B (A = B -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),Ca)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),Ca))))) # label(fact_93_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 104 (all Ca all B all A ((hBOOL(A) <-> hBOOL(B)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),B)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),A))))) # label(fact_94_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 105 (all Ca all A all B (A = B -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),B)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),A))))) # label(fact_95_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 106 (all Ca all A all B (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),B)) -> ((hBOOL(B) <-> hBOOL(Ca)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),Ca))))) # label(fact_96_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 107 (all Ca all A all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B)) -> (B = Ca -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),Ca))))) # label(fact_97_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 108 (all Ca all B all A (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),A)) -> ((hBOOL(B) <-> hBOOL(Ca)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),A))))) # label(fact_98_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 109 (all Ca all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A)) -> (B = Ca -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),A))))) # label(fact_99_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 110 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) -> (hBOOL(X_2) <-> hBOOL(Y_2))))) # label(fact_100_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 111 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) -> X_2 = Y_2))) # label(fact_101_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 112 (all Z all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z))))) # label(fact_102_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 113 (all Z all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),Z)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Z))))) # label(fact_103_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 114 (all Y_2 all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) -> (hBOOL(X_2) <-> hBOOL(Y_2))))) # label(fact_104_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 115 (all Y_2 all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) -> X_2 = Y_2))) # label(fact_105_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 116 (all Z all Y_2 all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),X_2))))) # label(fact_106_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 117 (all Z all Y_2 all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),Y_2)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),X_2))))) # label(fact_107_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 118 (all X_2 all F all G (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_2)),hAPP_H513860823e_bool(G,X_2))))) # label(fact_108_le__funE) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 119 (all A hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,bot_bo1055319631e_bool),A))) # label(fact_109_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 120 (all A hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),A))) # label(fact_110_bot__least) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 121 (all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool)) <-> A = bot_bo1055319631e_bool)) # label(fact_111_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 122 (all A (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),bot_bot_bool)) <-> (hBOOL(A) <-> hBOOL(bot_bot_bool)))) # label(fact_112_bot__unique) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 123 (all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),bot_bo1055319631e_bool)) -> A = bot_bo1055319631e_bool)) # label(fact_113_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 124 (all A (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),bot_bot_bool)) -> (hBOOL(A) <-> hBOOL(bot_bot_bool)))) # label(fact_114_le__bot) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 125 (all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),bot_bo1055319631e_bool)) <-> A_1 = bot_bo1055319631e_bool)) # label(fact_115_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 126 (all B_1 all A hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1)))) # label(fact_116_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 127 (all X_2 all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),B_1)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1)) & hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)))) # label(fact_117_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 128 (all B_1 all X_2 all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))))) # label(fact_118_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 129 (all B all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,B),B_1))))) # label(fact_119_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 130 (all A all C all D (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,C),D)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),C)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),D))))) # label(fact_120_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 131 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)))) # label(fact_121_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 132 (all Ts all G_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),G_2)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts)))) # label(fact_122_asm) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 133 (all Ts all G_2 all Ts_1 (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ts),Ts_1)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))))) # label(fact_123_weaken) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 134 (all G_2 all G_1 all Ts (hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_1),Ts)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,G_1),G_2)) -> hBOOL(hAPP_f1760790145l_bool(hoare_659004819_state(G_2),Ts))))) # label(fact_124_thin) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 135 (all F all Z hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),bot_bo1055319631e_bool),Z))) # label(fact_125_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 136 (all F all Z all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),bot_bo1055319631e_bool),X_2)) -> X_2 = Z)) # label(fact_126_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 137 (all F all Z all Y_2 all X_2 all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),Y_2)) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Y_2)))))) # label(fact_127_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 138 (all Pa all A_1 all F_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F_1),A_1)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool)) -> ((all A_3 all F_2 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),F_2)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,F_2)) -> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),F_2)))))))) -> hBOOL(hAPP_f1760790145l_bool(Pa,F_1))))))) # label(fact_128_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 139 (all F all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (A_1 != bot_bo1055319631e_bool -> (exists X1 hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),A_1),X1)))))) # label(fact_129_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 140 (all B_1 all A_1 ((all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_1)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)))) # label(fact_130_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 141 (all A (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A)) <-> A = bot_bo1055319631e_bool | (exists A_2 exists A_3 (A = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),A_2) & hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_2)))))) # label(fact_131_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 142 (all Pa all F_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool)) -> ((all X_1 all F_2 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),F_2)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,F_2)) -> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),F_2))))))) -> hBOOL(hAPP_f1760790145l_bool(Pa,F_1)))))) # label(fact_132_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 143 (all F all Z all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (exists X1 hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),X1))))) # label(fact_133_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 144 (all F all G ((all X_1 hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_H513860823e_bool(F,X_1)),hAPP_H513860823e_bool(G,X_1)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)))) # label(fact_134_le__funI) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 145 (all F all A1 all A2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(finite9525415_state(F),A1),A2)) <-> (exists A_3 exists A_2 exists X_1 (A1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),A_2) & A2 = X_1 & hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),A_3),A_2),X_1)) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),A_2)))))) # label(fact_135_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 146 (all F all Z all A1 all A2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A1),A2)) <-> A1 = bot_bo1055319631e_bool & A2 = Z | (exists X_1 exists A_2 exists Y_1 (A1 = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),A_2) & A2 = hAPP_H563960305_state(hAPP_H521649881_state(F,X_1),Y_1) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_2)) & hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_2),Y_1)))))) # label(fact_136_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 147 (all B_1 all A_1 all F all F_1 (hBOOL(finite506823037_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (B_1 != bot_bo1055319631e_bool -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1)) -> hAPP_H563960305_state(hAPP_H521649881_state(F,hAPP_f2143211163_state(F_1,B_1)),hAPP_f2143211163_state(F_1,A_1)) = hAPP_f2143211163_state(F_1,A_1)))))) # label(fact_137_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 148 (all X_2 all A_1 all F all F_1 (hBOOL(finite506823037_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (A_1 != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(F_1,A_1)))))) # label(fact_138_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 149 (all Pa all F_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1)) -> (F_1 != bot_bo1055319631e_bool -> ((all X_1 hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),bot_bo1055319631e_bool)))) -> ((all X_1 all F_2 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_2)) -> (F_2 != bot_bo1055319631e_bool -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),F_2)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,F_2)) -> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_1),F_2)))))))) -> hBOOL(hAPP_f1760790145l_bool(Pa,F_1))))))) # label(fact_139_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 150 (all Qa all Pa ((all X_1 (hBOOL(hAPP_H513860823e_bool(Pa,X_1)) -> hBOOL(hAPP_H513860823e_bool(Qa,X_1)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(collec727977250_state,Pa)),hAPP_f921536533e_bool(collec727977250_state,Qa))))) # label(fact_140_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 151 (all X_2 all F all F_1 (hBOOL(finite506823037_state(F,F_1)) -> hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),X_2) = X_2)) # label(fact_141_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 152 (all X_2 all A_1 all F all F_1 (hBOOL(finite506823037_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(F_1,A_1)) = hAPP_f2143211163_state(F_1,A_1))))) # label(fact_142_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 153 (all Qa all Pa ((all X_1 (hBOOL(hAPP_H513860823e_bool(Pa,X_1)) -> hBOOL(hAPP_H513860823e_bool(Qa,X_1)))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Pa),Qa)))) # label(fact_143_predicate1I) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 154 (all Ca all F all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),hAPP_f1760790145l_bool(F,B))) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,Y_1)),hAPP_f1760790145l_bool(F,X_1))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),hAPP_f1760790145l_bool(F,A))))))) # label(fact_144_xt3) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 155 (all Ca all F all B all A (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),A)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),hAPP_b1245957081e_bool(F,B))) -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,Y_1)),hAPP_b1245957081e_bool(F,X_1)))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),hAPP_b1245957081e_bool(F,A))))))) # label(fact_145_xt3) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 156 (all Ca all F all B all A (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),A)) -> ((hBOOL(hAPP_bool_bool(F,B)) <-> hBOOL(Ca)) -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Y_1)),hAPP_bool_bool(F,X_1)))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),hAPP_bool_bool(F,A))))))) # label(fact_146_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 157 (all F all Ca all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A)) -> (hAPP_f921536533e_bool(F,B) = Ca -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Y_1)),hAPP_f921536533e_bool(F,X_1))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),hAPP_f921536533e_bool(F,A))))))) # label(fact_147_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 158 (all Ca all F all A all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B)) -> ((hBOOL(hAPP_f1760790145l_bool(F,B)) <-> hBOOL(Ca)) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,X_1)),hAPP_f1760790145l_bool(F,Y_1))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,A)),Ca)))))) # label(fact_148_ord__le__eq__subst) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 159 (all F all Ca all A all B (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),B)) -> (hAPP_b1245957081e_bool(F,B) = Ca -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,X_1)),hAPP_b1245957081e_bool(F,Y_1)))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,A)),Ca)))))) # label(fact_149_ord__le__eq__subst) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 160 (all F all Ca all A all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,B)),Ca)) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,X_1)),hAPP_f1760790145l_bool(F,Y_1))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,A)),Ca)))))) # label(fact_150_order__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 161 (all F all Ca all A all B (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),B)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,B)),Ca)) -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,X_1)),hAPP_b1245957081e_bool(F,Y_1)))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,A)),Ca)))))) # label(fact_151_order__subst2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 162 (all Ca all F all B all A ((hBOOL(A) <-> hBOOL(hAPP_f1760790145l_bool(F,B))) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),Ca)) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,X_1)),hAPP_f1760790145l_bool(F,Y_1))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),hAPP_f1760790145l_bool(F,Ca))))))) # label(fact_152_ord__eq__le__subst) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 163 (all Ca all A all F all B (A = hAPP_b1245957081e_bool(F,B) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),Ca)) -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,X_1)),hAPP_b1245957081e_bool(F,Y_1)))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_b1245957081e_bool(F,Ca))))))) # label(fact_153_ord__eq__le__subst) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 164 (all Ca all F all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,B)),A)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),B)) -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,Y_1)),hAPP_b1245957081e_bool(F,X_1)))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,Ca)),A)))))) # label(fact_154_xt2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 165 (all Ca all F all B all A (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,B)),A)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),B)) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,Y_1)),hAPP_f1760790145l_bool(F,X_1))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,Ca)),A)))))) # label(fact_155_xt2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 166 (all Ca all F all B all A ((hBOOL(A) <-> hBOOL(hAPP_bool_bool(F,B))) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),B)) -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Y_1)),hAPP_bool_bool(F,X_1)))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_bool_bool(F,Ca)),A)))))) # label(fact_156_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 167 (all Ca all A all F all B (A = hAPP_f921536533e_bool(F,B) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),B)) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Y_1)),hAPP_f921536533e_bool(F,X_1))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Ca)),A)))))) # label(fact_157_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 168 (all Ca all A all F all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_b1245957081e_bool(F,B))) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),Ca)) -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,X_1)),hAPP_b1245957081e_bool(F,Y_1)))))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),hAPP_b1245957081e_bool(F,Ca))))))) # label(fact_158_order__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 169 (all Ca all A all F all B (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),hAPP_f1760790145l_bool(F,B))) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),Ca)) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_1),Y_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,X_1)),hAPP_f1760790145l_bool(F,Y_1))))) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),hAPP_f1760790145l_bool(F,Ca))))))) # label(fact_159_order__subst1) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 170 (all A_1 all F all F_1 (hBOOL(big_se1303371297_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hAPP_f2143211163_state(F_1,A_1) = hAPP_f2143211163_state(finite1346402327_state(F),A_1)))) # label(fact_160_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 171 (all X_2 all A_1 all F all F_1 (hBOOL(finite774711482_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> (hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool -> hAPP_f2143211163_state(F_1,A_1) = X_2) & (hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F_1,A_1) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))))))))) # label(fact_161_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 172 (all X_2 all A_1 all F all F_1 (hBOOL(finite774711482_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = bot_bo1055319631e_bool -> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = X_2) & (hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) != bot_bo1055319631e_bool -> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))))))) # label(fact_162_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 173 (all B_1 all Ca all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)))))) # label(fact_163_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 174 (all Ca all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))) -> -(hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1))))) # label(fact_164_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 175 (all B_1 all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))))) # label(fact_165_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 176 (all A_1 all B_1 hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1) = hAPP_f921536533e_bool(collec727977250_state,hAPP_f921536533e_bool(cOMBS_1248383340l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(fconj),hAPP_f921536533e_bool(cOMBC_764456866l_bool(member1758697444_state),A_1))),hAPP_f921536533e_bool(cOMBB_416661851_state(fNot),hAPP_f921536533e_bool(cOMBC_764456866l_bool(member1758697444_state),B_1))))) # label(fact_166_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 177 (all Ca all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1)) & -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1)))) # label(fact_167_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 178 (all A_1 all B_1 hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)),B_1) = hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)) # label(fact_168_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 179 (all Ca all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1)))) # label(fact_169_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 180 (all Ca all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))) -> -hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1)))) # label(fact_170_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 181 (all A_1 hAPP_f921536533e_bool(minus_2076558538e_bool(bot_bo1055319631e_bool),A_1) = bot_bo1055319631e_bool) # label(fact_171_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 182 (all A_1 hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),bot_bo1055319631e_bool) = A_1) # label(fact_172_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 183 (all A_1 hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),A_1) = bot_bo1055319631e_bool) # label(fact_173_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 184 (all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1))))) # label(fact_174_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 185 (all A_1 all X_2 all B_1 ((hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1)) -> hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),B_1) = hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1)) -> hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),B_1) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))))) # label(fact_175_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 186 (all A_1 all X_2 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1)) -> hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),B_1) = hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))) # label(fact_176_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 187 (all A_1 all B_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)),A_1))) # label(fact_177_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 188 (all D all B_1 all A_1 all C (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),C)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,D),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)),hAPP_f921536533e_bool(minus_2076558538e_bool(C),D)))))) # label(fact_178_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 189 (all C all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),C)) -> hAPP_f921536533e_bool(minus_2076558538e_bool(B_1),hAPP_f921536533e_bool(minus_2076558538e_bool(C),A_1)) = A_1))) # label(fact_179_double__diff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 190 (all A_1 all A all B_1 hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1)) = hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) # label(fact_180_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 191 (all A_1 all A all B_1 hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1)) = hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))),B_1)) # label(fact_181_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.43 192 (all A all A_1 hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)) # label(fact_182_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 193 (all X_2 all A_1 (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hAPP_f921536533e_bool(minus_2076558538e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)) = A_1)) # label(fact_183_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 194 (all A all A_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = A_1)) # label(fact_184_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 195 (all A_1 all A all B_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),B_1)))) <-> hBOOL(hAPP_f1760790145l_bool(finite784854244_state,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1))))) # label(fact_185_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 196 (all A_1 all X_2 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1))) <-> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))),B_1))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1))))) # label(fact_186_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 197 (all A_1 all X_2 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1)))))) # label(fact_187_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 198 (all Pa all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,A_1)) -> ((all A_3 all A_2 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A_3),A_2)) -> (hBOOL(hAPP_f1760790145l_bool(Pa,A_2)) -> hBOOL(hAPP_f1760790145l_bool(Pa,hAPP_f921536533e_bool(minus_2076558538e_bool(A_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A_3),bot_bo1055319631e_bool)))))))) -> hBOOL(hAPP_f1760790145l_bool(Pa,bot_bo1055319631e_bool)))))) # label(fact_188_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 199 (all A_1 all B_1 all X_2 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1),X_2)) <-> hBOOL(hAPP_bool_bool(minus_minus_bool(hAPP_H513860823e_bool(A_1,X_2)),hAPP_H513860823e_bool(B_1,X_2))))) # label(fact_189_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 200 (all A_1 all B_1 all X_1 (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1),X_1)) <-> hBOOL(hAPP_bool_bool(minus_minus_bool(hAPP_H513860823e_bool(A_1,X_1)),hAPP_H513860823e_bool(B_1,X_1))))) # label(fact_190_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 201 (all A all Z all A_1 all Y_2 all F (hBOOL(finite1710211309_state(F)) -> (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),Y_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> (exists Y_3 (Y_2 = hAPP_H563960305_state(hAPP_H521649881_state(F,A),Y_3) & hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))),Y_3)))))))) # label(fact_191_comp__fun__commute_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 202 (all X_2 all Y_2 all Z all F (hBOOL(finite1710211309_state(F)) -> hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_H563960305_state(hAPP_H521649881_state(F,Y_2),Z)) = hAPP_H563960305_state(hAPP_H521649881_state(F,Y_2),hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Z)))) # label(fact_192_comp__fun__commute_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 203 (all Y_2 all Z all A_1 all X_2 all F (hBOOL(finite1710211309_state(F)) -> (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),X_2)) -> (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),Y_2)) -> Y_2 = X_2)))) # label(fact_193_comp__fun__commute_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 204 (all Z all X_2 all A_1 all V all F (hBOOL(finite1710211309_state(F)) -> (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)),V)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> -(all Y_1 (V = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Y_1) -> -hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),Y_1)))))))) # label(fact_194_comp__fun__commute_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 205 (all X_2 all Least ((all X_1 (is_bool(X_1) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Least),X_1)))) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_min_bool,X_2),Least)) <-> hBOOL(Least)))) # label(fact_195_min__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 206 (all X_2 all Least ((all X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Least),X_1))) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(ord_mi777828298e_bool,X_2),Least) = Least)) # label(fact_196_min__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 207 (all X_2 all Least ((all X_1 (is_bool(X_1) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Least),X_1)))) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_min_bool,Least),X_2)) <-> hBOOL(Least)))) # label(fact_197_min__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 208 (all X_2 all Least ((all X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Least),X_1))) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(ord_mi777828298e_bool,Least),X_2) = Least)) # label(fact_198_min__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 209 (all Z all X_2 all A_1 all F (hBOOL(finite1710211309_state(F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))))))) # label(fact_201_comp__fun__commute_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 210 (all Z all X_2 all A_1 all F (hBOOL(finite1710211309_state(F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hAPP_f2143211163_state(finite202520804_state(F,Z),A_1) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))))))) # label(fact_202_comp__fun__commute_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 211 (all F all Z hAPP_f2143211163_state(finite202520804_state(F,Z),bot_bo1055319631e_bool) = Z) # label(fact_203_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 212 (all X_2 all Z all A_1 all F (hBOOL(finite1710211309_state(F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(finite202520804_state(F,Z),A_1)) = hAPP_f2143211163_state(finite202520804_state(F,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Z)),A_1)))) # label(fact_204_comp__fun__commute_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 213 (all Z all A_1 all Y_2 all F (hBOOL(finite1710211309_state(F)) -> (hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),Y_2)) -> hAPP_f2143211163_state(finite202520804_state(F,Z),A_1) = Y_2))) # label(fact_205_comp__fun__commute_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 214 (all Z all X_2 all A_1 all F (hBOOL(finite1710211309_state(F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f2143211163_state(finite202520804_state(F,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Z)),A_1))))) # label(fact_206_comp__fun__commute_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 215 (all Z all X_2 all A_1 all F (hBOOL(finite1710211309_state(F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(finite202520804_state(F,Z),A_1)))))) # label(fact_207_comp__fun__commute_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 216 (all X_2 all A_1 all F all F_1 (hBOOL(finite774711482_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f2143211163_state(finite202520804_state(F,X_2),A_1))))) # label(fact_208_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 217 (all A all A_1 all F all F_1 (hBOOL(finite506823037_state(F,F_1)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hAPP_f2143211163_state(F_1,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),A_1)) = hAPP_f2143211163_state(finite202520804_state(F,A),A_1)))) # label(fact_209_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 218 (all Z all A_1 all F (hBOOL(finite1710211309_state(F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hBOOL(hAPP_H513860823e_bool(hAPP_f921536533e_bool(hAPP_H727730819e_bool(finite1935632226_state(F),Z),A_1),hAPP_f2143211163_state(finite202520804_state(F,Z),A_1)))))) # label(fact_210_comp__fun__commute_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 219 (all Z all X_2 all A_1 all F (hBOOL(finite372259688_state(F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),hAPP_f2143211163_state(finite202520804_state(F,Z),A_1))))) # label(fact_211_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 220 (all Z all X_2 all A_1 all F (hBOOL(finite1317819144e_bool(F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hAPP_f921536533e_bool(finite512563852e_bool(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(F,X_2),hAPP_f921536533e_bool(finite512563852e_bool(F,Z),A_1))))) # label(fact_212_comp__fun__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 221 (all Z all X_2 all A_1 all F (hBOOL(finite372259688_state(F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hAPP_f2143211163_state(finite202520804_state(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f2143211163_state(finite202520804_state(F,hAPP_H563960305_state(hAPP_H521649881_state(F,X_2),Z)),A_1)))) # label(fact_213_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 222 (all Z all X_2 all A_1 all F (hBOOL(finite1317819144e_bool(F)) -> (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> hAPP_f921536533e_bool(finite512563852e_bool(F,Z),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = hAPP_f921536533e_bool(finite512563852e_bool(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(F,X_2),Z)),A_1)))) # label(fact_214_comp__fun__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 223 (all X_2 all Z all F (hBOOL(finite1317819144e_bool(F)) -> hAPP_f921536533e_bool(hAPP_H727730819e_bool(F,X_2),hAPP_f921536533e_bool(hAPP_H727730819e_bool(F,X_2),Z)) = hAPP_f921536533e_bool(hAPP_H727730819e_bool(F,X_2),Z))) # label(fact_215_comp__fun__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 224 (all F all A all A_1 ((hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> big_co272093296te_nat(F,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = hAPP_nat_nat(minus_minus_nat(big_co272093296te_nat(F,A_1)),hAPP_H716259088te_nat(F,A))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> big_co272093296te_nat(F,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))) = big_co272093296te_nat(F,A_1)))) # label(fact_217_setsum__diff1__nat) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 225 (all F all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),A_1)) -> big_co272093296te_nat(F,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),B_1)) = hAPP_nat_nat(minus_minus_nat(big_co272093296te_nat(F,A_1)),big_co272093296te_nat(F,B_1))))) # label(fact_218_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 226 (all G all H all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> ((all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hAPP_H716259088te_nat(G,X_1) = hAPP_H716259088te_nat(H,X_1))) -> big_co272093296te_nat(G,A_1) = big_co272093296te_nat(H,A_1)))) # label(fact_219_setsum_Ocong) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 227 (all X_2 all Least ((all X_1 (is_bool(X_1) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Least),X_1)))) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_max_bool,X_2),Least)) <-> hBOOL(X_2)))) # label(fact_220_max__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 228 (all X_2 all Least ((all X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Least),X_1))) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(ord_ma295552312e_bool,X_2),Least) = X_2)) # label(fact_221_max__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 229 (all X_2 all Least ((all X_1 (is_bool(X_1) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Least),X_1)))) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_max_bool,Least),X_2)) <-> hBOOL(X_2)))) # label(fact_222_max__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 230 (all X_2 all Least ((all X_1 hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Least),X_1))) -> hAPP_f921536533e_bool(hAPP_f1583986009e_bool(ord_ma295552312e_bool,Least),X_2) = X_2)) # label(fact_223_max__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 231 (all G all X_2 all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> big_co272093296te_nat(G,A_1) = plus_plus_nat(hAPP_H716259088te_nat(G,X_2),big_co272093296te_nat(G,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))))))) # label(fact_226_setsum_Oremove) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 232 (all F all A all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),A_1)) -> big_co272093296te_nat(F,A_1) = plus_plus_nat(hAPP_H716259088te_nat(F,A),big_co272093296te_nat(F,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),bot_bo1055319631e_bool))))))) # label(fact_227_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 233 (all G all X_2 all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> big_co272093296te_nat(G,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = plus_plus_nat(hAPP_H716259088te_nat(G,X_2),big_co272093296te_nat(G,A_1))))) # label(fact_228_setsum_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 234 (all F all A all F_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,F_1)) -> (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,A),F_1)) -> big_co272093296te_nat(F,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,A),F_1)) = plus_plus_nat(hAPP_H716259088te_nat(F,A),big_co272093296te_nat(F,F_1))))) # label(fact_229_setsum__insert) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 235 (all G all X_2 all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> big_co272093296te_nat(G,hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),A_1)) = plus_plus_nat(hAPP_H716259088te_nat(G,X_2),big_co272093296te_nat(G,hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool)))))) # label(fact_230_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 236 (all F all G all A_1 ((all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hAPP_H716259088te_nat(F,X_1) = hAPP_H716259088te_nat(G,X_1))) -> big_co272093296te_nat(F,A_1) = big_co272093296te_nat(G,A_1))) # label(fact_231_setsum__cong2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 237 (all F all G all A_1 all B_1 (A_1 = B_1 -> ((all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_1)) -> hAPP_H716259088te_nat(F,X_1) = hAPP_H716259088te_nat(G,X_1))) -> big_co272093296te_nat(F,A_1) = big_co272093296te_nat(G,B_1)))) # label(fact_232_setsum__cong) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 238 (all H all G all A_1 all B_1 (A_1 = B_1 -> ((all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),B_1)) -> hAPP_H716259088te_nat(H,X_1) = hAPP_H716259088te_nat(G,X_1))) -> big_co272093296te_nat(H,A_1) = big_co272093296te_nat(G,B_1)))) # label(fact_233_setsum_OF__cong) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 239 (all A -hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),bot_bo1055319631e_bool))) # label(fact_234_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 240 (all A -hBOOL(hAPP_bool_bool(ord_less_bool(A),bot_bot_bool))) # label(fact_235_not__less__bot) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 241 (all A (A != bot_bo1055319631e_bool <-> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(bot_bo1055319631e_bool),A)))) # label(fact_236_bot__less) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 242 (all A (-(hBOOL(A) <-> hBOOL(bot_bot_bool)) <-> hBOOL(hAPP_bool_bool(ord_less_bool(bot_bot_bool),A)))) # label(fact_237_bot__less) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 243 (all A_1 -hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),bot_bo1055319631e_bool))) # label(fact_238_not__psubset__empty) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 244 (all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) & A_1 != B_1)) # label(fact_239_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 245 (all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) <-> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1)) | A_1 = B_1)) # label(fact_240_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 246 (all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)))) # label(fact_241_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 247 (all C all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B_1),C)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),C))))) # label(fact_242_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 248 (all C all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B_1),C)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),C))))) # label(fact_243_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 249 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) -> -hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2)))) # label(fact_244_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 250 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) -> -hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2)))) # label(fact_245_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 251 (all Z all Y_2 all X_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2)) -> (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Z),Y_2)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Z),X_2))))) # label(fact_246_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 252 (all Z all Y_2 all X_2 (hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(ord_less_bool(Z),Y_2)) -> hBOOL(hAPP_bool_bool(ord_less_bool(Z),X_2))))) # label(fact_247_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 253 (all Z all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) -> (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),Z)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Z))))) # label(fact_248_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 254 (all Z all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) -> (hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),Z)) -> hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Z))))) # label(fact_249_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 255 (all Ca all B all A (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A)) -> (B = Ca -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),A))))) # label(fact_250_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 256 (all Ca all B all A (hBOOL(hAPP_bool_bool(ord_less_bool(B),A)) -> ((hBOOL(B) <-> hBOOL(Ca)) -> hBOOL(hAPP_bool_bool(ord_less_bool(Ca),A))))) # label(fact_251_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 257 (all Ca all A all B (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),B)) -> (B = Ca -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),Ca))))) # label(fact_252_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 258 (all Ca all A all B (hBOOL(hAPP_bool_bool(ord_less_bool(A),B)) -> ((hBOOL(B) <-> hBOOL(Ca)) -> hBOOL(hAPP_bool_bool(ord_less_bool(A),Ca))))) # label(fact_253_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 259 (all Ca all A all B (A = B -> (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),B)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),A))))) # label(fact_254_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 260 (all Ca all B all A ((hBOOL(A) <-> hBOOL(B)) -> (hBOOL(hAPP_bool_bool(ord_less_bool(Ca),B)) -> hBOOL(hAPP_bool_bool(ord_less_bool(Ca),A))))) # label(fact_255_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 261 (all Ca all A all B (A = B -> (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),Ca)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),Ca))))) # label(fact_256_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 262 (all Ca all B all A ((hBOOL(A) <-> hBOOL(B)) -> (hBOOL(hAPP_bool_bool(ord_less_bool(B),Ca)) -> hBOOL(hAPP_bool_bool(ord_less_bool(A),Ca))))) # label(fact_257_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 263 (all B all A (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A)) -> -hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),B)))) # label(fact_258_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 264 (all B all A (hBOOL(hAPP_bool_bool(ord_less_bool(B),A)) -> -hBOOL(hAPP_bool_bool(ord_less_bool(A),B)))) # label(fact_259_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 265 (all A all B (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),B)) -> -hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A)))) # label(fact_260_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 266 (all A all B (hBOOL(hAPP_bool_bool(ord_less_bool(A),B)) -> -hBOOL(hAPP_bool_bool(ord_less_bool(B),A)))) # label(fact_261_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 267 (all Pa all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) -> (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2)) -> hBOOL(Pa)))) # label(fact_262_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 268 (all Pa all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) -> (hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2)) -> hBOOL(Pa)))) # label(fact_263_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 269 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) -> Y_2 != X_2)) # label(fact_264_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 270 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) -> (hBOOL(Y_2) <-> -hBOOL(X_2)))) # label(fact_265_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 271 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) -> X_2 != Y_2)) # label(fact_266_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 272 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) -> (hBOOL(X_2) <-> -hBOOL(Y_2)))) # label(fact_267_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 273 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) -> -hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2)))) # label(fact_268_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 274 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) -> -hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2)))) # label(fact_269_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 275 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) -> -hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2)))) # label(fact_270_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 276 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) -> -hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2)))) # label(fact_271_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 277 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) -> X_2 != Y_2)) # label(fact_272_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 278 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) -> -(hBOOL(X_2) <-> hBOOL(Y_2)))) # label(fact_273_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 279 (all X_2 -hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),X_2))) # label(fact_274_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 280 (all X_2 -hBOOL(hAPP_bool_bool(ord_less_bool(X_2),X_2))) # label(fact_275_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 281 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) & -(hBOOL(X_2) <-> hBOOL(Y_2)))) # label(fact_276_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 282 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) & X_2 != Y_2)) # label(fact_277_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 283 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) <-> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) & -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)))) # label(fact_278_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 284 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) & -hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)))) # label(fact_279_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 285 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) <-> hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) | (hBOOL(X_2) <-> hBOOL(Y_2)))) # label(fact_280_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 286 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) <-> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) | X_2 = Y_2)) # label(fact_281_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 287 (all B all A (-(hBOOL(A) <-> hBOOL(B)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),B)) -> hBOOL(hAPP_bool_bool(ord_less_bool(A),B))))) # label(fact_282_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 288 (all A all B (A != B -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),B))))) # label(fact_283_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 289 (all B all A (-(hBOOL(A) <-> hBOOL(B)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),A)) -> hBOOL(hAPP_bool_bool(ord_less_bool(B),A))))) # label(fact_284_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 290 (all A all B (A != B -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A))))) # label(fact_285_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 291 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)))) # label(fact_286_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 292 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)))) # label(fact_287_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 293 (all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) -> hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) | (hBOOL(X_2) <-> hBOOL(Y_2)))) # label(fact_288_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 294 (all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) | X_2 = Y_2)) # label(fact_289_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 295 (all A all B (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,A),B)) -> (-(hBOOL(A) <-> hBOOL(B)) -> hBOOL(hAPP_bool_bool(ord_less_bool(A),B))))) # label(fact_290_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 296 (all A all B (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A),B)) -> (A != B -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A),B))))) # label(fact_291_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 297 (all B all A (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,B),A)) -> (-(hBOOL(A) <-> hBOOL(B)) -> hBOOL(hAPP_bool_bool(ord_less_bool(B),A))))) # label(fact_292_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 298 (all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,B),A)) -> (A != B -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A))))) # label(fact_293_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 299 (all Z all X_2 all Y_2 (hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Y_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z)) -> hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Z))))) # label(fact_294_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 300 (all Z all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Y_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),Z)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Z))))) # label(fact_295_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 301 (all Z all Y_2 all X_2 (hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z),Y_2)) -> hBOOL(hAPP_bool_bool(ord_less_bool(Z),X_2))))) # label(fact_296_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 302 (all Z all Y_2 all X_2 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),X_2)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Z),Y_2)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Z),X_2))))) # label(fact_297_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 303 (all Z all X_2 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) -> (hBOOL(hAPP_bool_bool(ord_less_bool(Y_2),Z)) -> hBOOL(hAPP_bool_bool(ord_less_bool(X_2),Z))))) # label(fact_298_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 304 (all Z all X_2 all Y_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,X_2),Y_2)) -> (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_2),Z)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(X_2),Z))))) # label(fact_299_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 305 (all Z all Y_2 all X_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) -> (hBOOL(hAPP_bool_bool(ord_less_bool(Z),Y_2)) -> hBOOL(hAPP_bool_bool(ord_less_bool(Z),X_2))))) # label(fact_300_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 306 (all Z all Y_2 all X_2 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_2),X_2)) -> (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Z),Y_2)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Z),X_2))))) # label(fact_301_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 307 (all F all G (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(F),G)) <-> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,F),G)) & -hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,G),F)))) # label(fact_302_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 308 (all A_1 all X_2 all B_1 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),B_1))) <-> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(minus_2076558538e_bool(A_1),hAPP_f921536533e_bool(hAPP_H727730819e_bool(insert1835143293_state,X_2),bot_bo1055319631e_bool))),B_1))) & (-hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_2),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,A_1),B_1)))))) # label(fact_303_psubset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 309 (all F all G all A_1 (hBOOL(hAPP_f1760790145l_bool(finite784854244_state,A_1)) -> (A_1 != bot_bo1055319631e_bool -> ((all X_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,X_1),A_1)) -> hBOOL(hAPP_nat_bool(ord_less_nat(hAPP_H716259088te_nat(F,X_1)),hAPP_H716259088te_nat(G,X_1))))) -> hBOOL(hAPP_nat_bool(ord_less_nat(big_co272093296te_nat(F,A_1)),big_co272093296te_nat(G,A_1))))))) # label(fact_304_setsum__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 310 (all C all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B_1),C)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),C))))) # label(fact_305_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 311 (all Ca all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),A_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,Ca),B_1))))) # label(fact_306_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.44 312 (all A_1 all B_1 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(A_1),B_1)) -> (exists B_2 hBOOL(hAPP_f1760790145l_bool(hAPP_H248360617l_bool(member1758697444_state,B_2),hAPP_f921536533e_bool(minus_2076558538e_bool(B_1),A_1)))))) # label(fact_307_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 313 (all Ca all F all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,B)),A)) -> (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),B)) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(F,Y_1)),hAPP_f921536533e_bool(F,X_1))))) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(F,Ca)),A)))))) # label(fact_308_xt6) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 314 (all Ca all F all B all A (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,B)),A)) -> (hBOOL(hAPP_bool_bool(ord_less_bool(Ca),B)) -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(ord_less_bool(Y_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_b1245957081e_bool(F,Y_1)),hAPP_b1245957081e_bool(F,X_1)))))) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_b1245957081e_bool(F,Ca)),A)))))) # label(fact_309_xt6) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 315 (all Ca all F all B all A (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(B),A)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),hAPP_f921536533e_bool(F,B))) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Y_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(F,Y_1)),hAPP_f921536533e_bool(F,X_1))))) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),hAPP_f921536533e_bool(F,A))))))) # label(fact_310_xt5) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 316 (all Ca all F all B all A (hBOOL(hAPP_bool_bool(ord_less_bool(B),A)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),hAPP_b1245957081e_bool(F,B))) -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(ord_less_bool(Y_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_b1245957081e_bool(F,Y_1)),hAPP_b1245957081e_bool(F,X_1)))))) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(Ca),hAPP_b1245957081e_bool(F,A))))))) # label(fact_311_xt5) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 317 (all Ca all F all B all A (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(F,B)),A)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),B)) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_f921536533e_bool(F,Y_1)),hAPP_f921536533e_bool(F,X_1))))) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_f921536533e_bool(F,Ca)),A)))))) # label(fact_312_xt4) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 318 (all Ca all F all B all A (hBOOL(hAPP_bool_bool(ord_less_bool(hAPP_f1760790145l_bool(F,B)),A)) -> (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Ca),B)) -> ((all X_1 all Y_1 (hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,Y_1),X_1)) -> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1760790145l_bool(F,Y_1)),hAPP_f1760790145l_bool(F,X_1))))) -> hBOOL(hAPP_bool_bool(ord_less_bool(hAPP_f1760790145l_bool(F,Ca)),A)))))) # label(fact_313_xt4) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 319 (all Ca all F all B all A (hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_b1245957081e_bool(F,B)),A)) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),B)) -> ((all X_1 all Y_1 (is_bool(X_1) & is_bool(Y_1) -> (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1)) -> hBOOL(hAPP_f1760790145l_bool(hAPP_f854625363l_bool(ord_le1720872323e_bool,hAPP_b1245957081e_bool(F,Y_1)),hAPP_b1245957081e_bool(F,X_1)))))) -> hBOOL(hAPP_f1760790145l_bool(ord_le260787855e_bool(hAPP_b1245957081e_bool(F,Ca)),A)))))) # label(fact_314_xt4) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 320 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 321 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 322 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 323 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 324 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 325 (all Q all P (-hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 326 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 327 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 328 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 329 (all Q all P (hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)))) # label(help_fimplies_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 330 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)))) # label(help_fimplies_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 331 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) | -hBOOL(P) | hBOOL(Q))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 332 (all X all Y (-hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 333 (all X all Y (X != Y | hBOOL(hAPP_H513860823e_bool(hAPP_H1645666623e_bool(fequal1531560888_state,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 334 (all P all Q (is_bool(P) -> hAPP_H513860823e_bool(hAPP_b1245957081e_bool(cOMBK_1079618832_state,P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____ddpglwnxwg__) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 335 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(cOMBB_416661851_state(P),Q),R) = hAPP_bool_bool(P,hAPP_H513860823e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 336 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(cOMBS_1248383340l_bool(P),Q),R) = hAPP_bool_bool(hAPP_H226398757l_bool(P,R),hAPP_H513860823e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 337 (all P all Q all R hAPP_H226398757l_bool(hAPP_f1558728829l_bool(cOMBB_1382207997_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H513860823e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 338 (all P all Q all R hAPP_H513860823e_bool(hAPP_H1645666623e_bool(cOMBC_1424981238e_bool(P),Q),R) = hAPP_H513860823e_bool(hAPP_H1645666623e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com__) # label(axiom) # label(non_clause). [assumption].
% 1.12/1.45 339 (all P all Q all R hAPP_H513860823e_bool(hAPP_f921536533e_bool(cOMBC_764456866l_bool(P),Q),R) = hAPP_f1760790145l_bool(hAPP_H248360617l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____ddpglwnxwg__Otriple_Itc__Com___002) # label(axiom) # label(non_clause). [assumption].
% 2.45/2.76
% 2.45/2.76 ============================== end of process non-clausal formulas ===
% 2.45/2.76
% 2.45/2.76 ============================== PROCESS INITIAL CLAUSES ===============
% 2.45/2.76
% 2.45/2.76 ============================== PREDICATE ELIMINATION =================
% 2.45/2.76
% 2.45/2.76 ============================== end predicate elimination =============
% 2.45/2.76
% 2.45/2.76 Auto_denials: (non-Horn, no changes).
% 2.45/2.76
% 2.45/2.76 Term ordering decisions:
% 2.45/2.76 Function symbol KB weights: ord_le1720872323e_bool=1. insert1835143293_state=1. ord_less_eq_bool=1. bot_bo1055319631e_bool=1. member1758697444_state=1. finite784854244_state=1. bot_bot_bool=1. collec727977250_state=1. ord_max_bool=1. ord_min_bool=1. fconj=1. fdisj=1. fequal1531560888_state=1. fimplies=1. fFalse=1. fNot=1. ord_ma295552312e_bool=1. ord_mi777828298e_bool=1. c=1. cOMBK_1079618832_state=1. fTrue=1. bool=1. p=1. q=1. skip=1. the_el23965208_state=1. hAPP_f1760790145l_bool=1. hAPP_f921536533e_bool=1. hAPP_bool_bool=1. hAPP_f854625363l_bool=1. hAPP_H727730819e_bool=1. hAPP_b589554111l_bool=1. hAPP_H248360617l_bool=1. hAPP_H513860823e_bool=1. hAPP_b1245957081e_bool=1. hAPP_f2143211163_state=1. big_co272093296te_nat=1. hAPP_H521649881_state=1. hAPP_H563960305_state=1. finite202520804_state=1. hAPP_H716259088te_nat=1. hAPP_state_bool=1. hAPP_s1806633685e_bool=1. finite774711482_state=1. semi=1. finite506823037_state=1. hAPP_H1645666623e_bool=1. plus_plus_nat=1. finite512563852e_bool=1. hAPP_f1558728829l_bool=1. hAPP_f1583986009e_bool=1. hAPP_nat_bool=1. big_se1303371297_state=1. hAPP_H226398757l_bool=1. hAPP_nat_nat=1. f15=1. f16=1. f27=1. f30=1. f31=1. f34=1. f35=1. f37=1. f44=1. f45=1. f46=1. f47=1. f48=1. f81=1. f82=1. f85=1. f86=1. f87=1. f88=1. f90=1. f91=1. f92=1. f93=1. f98=1. ord_le260787855e_bool=1. ord_less_bool=1. minus_2076558538e_bool=1. hoare_659004819_state=1. finite1935632226_state=1. finite1710211309_state=1. finite9525415_state=1. finite1317819144e_bool=1. cOMBB_1382207997_state=1. cOMBC_764456866l_bool=1. cOMBS_1248383340l_bool=1. finite1346402327_state=1. minus_minus_bool=1. cOMBB_416661851_state=1. cOMBC_1424981238e_bool=1. finite372259688_state=1. ord_less_nat=1. hoare_1065416081_state=1. minus_minus_nat=1. hoare_Mirabelle_MGT=1. max_bool=1. max_fu30884092e_bool=1. min_bool=1. min_fu513160078e_bool=1. undefined_bool=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f17=1. f21=1. f22=1. f32=1. f33=1. hoare_1575745797_state=1. f23=1. f24=1. f28=1. f29=1. f36=1. f38=1. f39=1. f40=1. f89=1. f94=1. f97=1. f18=1. f19=1. f25=1. f26=1. f41=1. f42=1. f43=1. f49=1. f50=1. f51=1. f52=1. f53=1. f54=1. f55=1. f56=1. f57=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f70=1. f71=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f95=1. f96=1. f99=1. f100=1. f101=1. f102=1. f103=1. f104=1. f105=1. f106=1. f107=1. f108=1. f109=1. f110=1. f111=1. f112=1. f1=1. f2=1. f3=1. f4=1. f83=1. f84=1. f5=1. f6=1. f7=1. f20=1.
% 2.45/2.76
% 2.45/2.76 ============================== end of process initial clauses ========
% 2.45/2.76
% 2.45/2.76 ============================== CLAUSES FOR SEARCH ====================
% 2.45/2.76
% 2.45/2.76 ============================== end of clauses for search =============
% 2.45/2.76
% 2.45/2.76 ============================== SEARCH ================================
% 2.45/2.76
% 2.45/2.76 % Starting search at 0.23 seconds.
% 2.45/2.76
% 2.45/2.76 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 36 (0.00 of 0.87 sec).
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=76.000, iters=3747
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=50.000, iters=3429
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=48.000, iters=3386
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=46.000, iters=3336
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=43.000, iters=3363
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=40.000, iters=3425
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=37.000, iters=3343
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=36.000, iters=3343
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=34.000, iters=3398
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=33.000, iters=3652
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=31.000, iters=3444
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=30.000, iters=3496
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=29.000, iters=3380
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=28.000, iters=3388
% 2.45/2.76
% 2.45/2.76 Low Water (keep): wt=27.000, iters=3425
% 2.45/2.76
% 2.45/2.76 Low WaCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------