TSTP Solution File: SWW470+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW470+1 : 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 01:17:05 EDT 2022
% Result : Theorem 4.35s 4.65s
% Output : Refutation 4.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW470+1 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 5 03:05:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.82/1.13 ============================== Prover9 ===============================
% 0.82/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.13 Process 4157 was started by sandbox on n023.cluster.edu,
% 0.82/1.13 Sun Jun 5 03:05:10 2022
% 0.82/1.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4004_n023.cluster.edu".
% 0.82/1.13 ============================== end of head ===========================
% 0.82/1.13
% 0.82/1.13 ============================== INPUT =================================
% 0.82/1.13
% 0.82/1.13 % Reading from file /tmp/Prover9_4004_n023.cluster.edu
% 0.82/1.13
% 0.82/1.13 set(prolog_style_variables).
% 0.82/1.13 set(auto2).
% 0.82/1.13 % set(auto2) -> set(auto).
% 0.82/1.13 % set(auto) -> set(auto_inference).
% 0.82/1.13 % set(auto) -> set(auto_setup).
% 0.82/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.13 % set(auto) -> set(auto_limits).
% 0.82/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.13 % set(auto) -> set(auto_denials).
% 0.82/1.13 % set(auto) -> set(auto_process).
% 0.82/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.13 % set(auto2) -> assign(stats, some).
% 0.82/1.13 % set(auto2) -> clear(echo_input).
% 0.82/1.13 % set(auto2) -> set(quiet).
% 0.82/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.13 % set(auto2) -> clear(print_given).
% 0.82/1.13 assign(lrs_ticks,-1).
% 0.82/1.13 assign(sos_limit,10000).
% 0.82/1.13 assign(order,kbo).
% 0.82/1.13 set(lex_order_vars).
% 0.82/1.13 clear(print_given).
% 0.82/1.13
% 0.82/1.13 % formulas(sos). % not echoed (144 formulas)
% 0.82/1.13
% 0.82/1.13 ============================== end of input ==========================
% 0.82/1.13
% 0.82/1.13 % From the command line: assign(max_seconds, 300).
% 0.82/1.13
% 0.82/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.13
% 0.82/1.13 % Formulas that are not ordinary clauses:
% 0.82/1.13 1 (all B_1_1 all B_2 is_bool(finite520909254iple_a(B_1_1,B_2))) # label(gsy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____jfehddehev__Otriple) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 2 (all B_1_1 all B_2 is_bool(finite1948426435iple_a(B_1_1,B_2))) # label(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____jfehddehev__O) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 3 (all B_1_1 all B_2 is_bool(hAPP_state_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__Com__Ostate_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 4 (all B_1_1 all B_2 (is_bool(B_2) -> is_bool(hAPP_bool_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 5 (all B_1_1 all B_2 is_bool(hAPP_H1927961489a_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_000tc__HOL__) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 6 (all B_1_1 all B_2 is_bool(hAPP_f1753944735l_bool(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_Mtc) # label(hypothesis) # label(non_clause). [assumption].
% 0.82/1.13 7 (all Ga hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),bot_bo1687970473a_bool))) # label(fact_0_empty) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 8 (all Fun1_2 all Com_2 all Fun2_2 all Fun1_1 all Com_1 all Fun2_1 (hoare_1050552211iple_a(Fun1_2,Com_2,Fun2_2) = hoare_1050552211iple_a(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].
% 0.82/1.13 9 (all Ga all G_1 all Ts (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(G_1),Ts)) -> (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),G_1)) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),Ts))))) # label(fact_2_cut) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 10 (all Ts all Ga all T (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,T),bot_bo1687970473a_bool))) -> (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),Ts)) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,T),Ts)))))) # label(fact_3_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 11 (all Ga all Pa all Ca all Q_1 all C ((hBOOL(C) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,hAPP_f340725611e_bool(cOMBB_1348041619bool_a(cOMBC_231445413l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),Pa))),C),Ca,Q_1)),bot_bo1687970473a_bool))))) # label(fact_4_constant) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 12 (all Ga all Ca all Q_1 all Pa ((all Z_1 all S (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S)) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,fequal_state),S)),Ca,cOMBK_1458035955bool_a(hAPP_a2036067514e_bool(Q_1,Z_1)))),bot_bo1687970473a_bool))))) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool))))) # label(fact_5_escape) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 13 (all Q_1 all Ga all Pa all Ca all Q_3 (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_3)),bot_bo1687970473a_bool))) -> ((all Z_1 all S (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_3,Z_1),S)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S)))) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))))) # label(fact_6_conseq2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 14 (all Pa all Ga all P_2 all Ca all Q_1 (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_2,Ca,Q_1)),bot_bo1687970473a_bool))) -> ((all Z_1 all S (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_2,Z_1),S)))) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))))) # label(fact_7_conseq1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 15 (all Q_1 all Pa all Ga all P_2 all Ca all Q_3 (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_2,Ca,Q_3)),bot_bo1687970473a_bool))) -> ((all Z_1 all S (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S)) -> (all S_1 ((all Z_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_2,Z_2),S)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_3,Z_2),S_1)))) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)))))) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool)))))) # label(fact_8_conseq12) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 16 (all A_3 all Ba all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Ba),A))) -> (A_3 != Ba -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A))))) # label(fact_9_insertE) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 17 (all Ba all A_3 all B_1 ((-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),B_1)) -> A_3 = Ba) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Ba),B_1))))) # label(fact_10_insertCI) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 18 (all A_3 -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),bot_bo1687970473a_bool))) # label(fact_11_emptyE) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 19 (all A_3 collec1266446174iple_a(hAPP_H562195827a_bool(fequal1878252616iple_a,A_3)) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool)) # label(fact_12_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 20 (all A_3 collec1266446174iple_a(hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),A_3)) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool)) # label(fact_13_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 21 (all Pa all A_3 ((hBOOL(hAPP_H1927961489a_bool(Pa,A_3)) -> collec1266446174iple_a(hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fconj),hAPP_H562195827a_bool(fequal1878252616iple_a,A_3))),Pa)) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool)) & (-hBOOL(hAPP_H1927961489a_bool(Pa,A_3)) -> collec1266446174iple_a(hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fconj),hAPP_H562195827a_bool(fequal1878252616iple_a,A_3))),Pa)) = bot_bo1687970473a_bool))) # label(fact_14_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 22 (all Pa all A_3 ((hBOOL(hAPP_H1927961489a_bool(Pa,A_3)) -> collec1266446174iple_a(hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fconj),hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),A_3))),Pa)) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool)) & (-hBOOL(hAPP_H1927961489a_bool(Pa,A_3)) -> collec1266446174iple_a(hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fconj),hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),A_3))),Pa)) = bot_bo1687970473a_bool))) # label(fact_15_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 23 (all A_3 all A (A = bot_bo1687970473a_bool -> -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A)))) # label(fact_16_equals0D) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 24 (all Pa (collec1266446174iple_a(Pa) = bot_bo1687970473a_bool <-> (all X_2 -hBOOL(hAPP_H1927961489a_bool(Pa,X_2))))) # label(fact_17_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 25 (all Ca -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,Ca),bot_bo1687970473a_bool))) # label(fact_18_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 26 (all Pa (bot_bo1687970473a_bool = collec1266446174iple_a(Pa) <-> (all X_2 -hBOOL(hAPP_H1927961489a_bool(Pa,X_2))))) # label(fact_19_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 27 (all A ((exists X_2 hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A))) <-> A != bot_bo1687970473a_bool)) # label(fact_20_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 28 (all A ((all X_2 -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A))) <-> A = bot_bo1687970473a_bool)) # label(fact_21_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 29 (all A_3 all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A)) -> hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) = A)) # label(fact_23_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 30 (all Ba all A_3 all B_1 (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),B_1)) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Ba),B_1))))) # label(fact_24_insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 31 (all B_1 all X_1 all A (-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_1),A)) -> (-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_1),B_1)) -> (hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),A) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),B_1) <-> A = B_1)))) # label(fact_25_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 32 (all Y_2 all A all X_1 (hBOOL(hAPP_H1927961489a_bool(hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Y_2),A),X_1)) <-> Y_2 = X_1 | hBOOL(hAPP_H1927961489a_bool(A,X_1)))) # label(fact_26_insert__code) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 33 (all A_3 all Ba all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Ba),A))) <-> A_3 = Ba | hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A)))) # label(fact_27_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 34 (all X_1 all Y_2 all A hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Y_2),A)) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Y_2),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),A))) # label(fact_28_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 35 (all X_1 all A hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),A)) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),A)) # label(fact_29_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 36 (all A_3 all Pa hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),collec1266446174iple_a(Pa)) = collec1266446174iple_a(hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fimplies),hAPP_f1400872321a_bool(cOMBB_650444389iple_a(fNot),hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),A_3)))),Pa))) # label(fact_30_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 37 (all A_3 all B_1 hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),B_1) = collec1266446174iple_a(hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fdisj),hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),A_3))),hAPP_f1400872321a_bool(hAPP_f945663555a_bool(cOMBC_2067518550l_bool,member564727580iple_a),B_1)))) # label(fact_31_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 38 (all A_3 all B_1 hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),B_1)))) # label(fact_32_insertI1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 39 (all X_2 all Xa hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_2),Xa) = collec1266446174iple_a(hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fdisj),hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),X_2))),hAPP_f1400872321a_bool(hAPP_f945663555a_bool(cOMBC_2067518550l_bool,member564727580iple_a),Xa)))) # label(fact_33_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 40 (all A_3 all Ba (hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Ba),bot_bo1687970473a_bool) -> A_3 = Ba)) # label(fact_34_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 41 (all Ba all A_3 (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,Ba),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool))) -> Ba = A_3)) # label(fact_35_singletonE) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 42 (all A_3 all Ba all Ca all D (hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Ba),bot_bo1687970473a_bool)) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Ca),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,D),bot_bo1687970473a_bool)) <-> A_3 = Ca & Ba = D | A_3 = D & Ba = Ca)) # label(fact_36_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 43 (all Ba all A_3 (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,Ba),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool))) <-> Ba = A_3)) # label(fact_37_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 44 (all A_3 all A hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A) != bot_bo1687970473a_bool) # label(fact_38_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 45 (all A_3 all A bot_bo1687970473a_bool != hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A)) # label(fact_39_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 46 (all X_1 hAPP_f1826273671iple_a(the_el287271400iple_a,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),bot_bo1687970473a_bool)) = X_1) # label(fact_40_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 47 (all X_1 (hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_41_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 48 (all X_2 (hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X_2)) <-> hBOOL(bot_bot_bool))) # label(fact_42_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 49 (all Ga all Pa hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,skip,Pa)),bot_bo1687970473a_bool)))) # label(fact_43_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 50 (all D all R_1 all Ga all Pa all Ca all Q_1 (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool))) -> (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Q_1,D,R_1)),bot_bo1687970473a_bool))) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,semi(Ca,D),R_1)),bot_bo1687970473a_bool)))))) # label(fact_44_Comp) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 51 (all Y_2 -(all Fun1 all Com all Fun2 Y_2 != hoare_1050552211iple_a(Fun1,Com,Fun2))) # label(fact_45_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 52 (all X_1 all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_1),A)) -> -(all B (A = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),B) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_1),B)))))) # label(fact_46_Set_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 53 (all Com1_2 all Com2_2 semi(Com1_2,Com2_2) != skip) # label(fact_47_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 54 (all Com1_2 all Com2_2 skip != semi(Com1_2,Com2_2)) # label(fact_48_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 55 (all X_3 hAPP_f1826273671iple_a(the_el287271400iple_a,X_3) = hAPP_f1826273671iple_a(the_Ho1745054714iple_a,hAPP_f1447988451a_bool(cOMBB_545742339iple_a(hAPP_f1945881407l_bool(fequal1765155200a_bool,X_3)),hAPP_f1170963427a_bool(hAPP_f1874567875a_bool(cOMBC_1089176504a_bool,insert1871499715iple_a),bot_bo1687970473a_bool)))) # label(fact_49_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 56 (all A_3 all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A)) -> (exists B (A = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),B) & -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),B)))))) # label(fact_50_mk__disjoint__insert) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 57 (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_51_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 58 (all X_1 hAPP_f1826273671iple_a(the_Ho1745054714iple_a,hAPP_H562195827a_bool(fequal1878252616iple_a,X_1)) = X_1) # label(fact_52_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 59 (all A_3 hAPP_f1826273671iple_a(the_Ho1745054714iple_a,hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),A_3)) = A_3) # label(fact_53_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 60 (all X_1 all Y_2 all Pa ((hBOOL(Pa) -> X_1 = hAPP_f1826273671iple_a(the_Ho1745054714iple_a,hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fconj),hAPP_f1400872321a_bool(cOMBB_650444389iple_a(hAPP_b589554111l_bool(fimplies,Pa)),hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),X_1)))),hAPP_f1400872321a_bool(cOMBB_650444389iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),Y_2))))) & (-hBOOL(Pa) -> Y_2 = hAPP_f1826273671iple_a(the_Ho1745054714iple_a,hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fconj),hAPP_f1400872321a_bool(cOMBB_650444389iple_a(hAPP_b589554111l_bool(fimplies,Pa)),hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),X_1)))),hAPP_f1400872321a_bool(cOMBB_650444389iple_a(hAPP_b589554111l_bool(fimplies,hAPP_bool_bool(fNot,Pa))),hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,fequal1878252616iple_a),Y_2))))))) # label(fact_54_If__def) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 61 (all A ((all Y_1 -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,Y_1),A))) -> A = bot_bo1687970473a_bool)) # label(fact_55_equals0I) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 62 (all Pa all A_3 (hBOOL(hAPP_H1927961489a_bool(Pa,A_3)) -> ((all X_2 (hBOOL(hAPP_H1927961489a_bool(Pa,X_2)) -> X_2 = A_3)) -> hAPP_f1826273671iple_a(the_Ho1745054714iple_a,Pa) = A_3))) # label(fact_56_the__equality) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 63 (all Pa all A_3 (hBOOL(hAPP_H1927961489a_bool(Pa,A_3)) -> ((all X_2 (hBOOL(hAPP_H1927961489a_bool(Pa,X_2)) -> X_2 = A_3)) -> hBOOL(hAPP_H1927961489a_bool(Pa,hAPP_f1826273671iple_a(the_Ho1745054714iple_a,Pa)))))) # label(fact_57_theI) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 64 (all A_3 all Pa ((exists X_2 (hBOOL(hAPP_H1927961489a_bool(Pa,X_2)) & (all Y_1 (hBOOL(hAPP_H1927961489a_bool(Pa,Y_1)) -> Y_1 = X_2)))) -> (hBOOL(hAPP_H1927961489a_bool(Pa,A_3)) -> hAPP_f1826273671iple_a(the_Ho1745054714iple_a,Pa) = A_3))) # label(fact_58_the1__equality) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 65 (all Pa ((exists X_2 (hBOOL(hAPP_H1927961489a_bool(Pa,X_2)) & (all Y_1 (hBOOL(hAPP_H1927961489a_bool(Pa,Y_1)) -> Y_1 = X_2)))) -> hBOOL(hAPP_H1927961489a_bool(Pa,hAPP_f1826273671iple_a(the_Ho1745054714iple_a,Pa))))) # label(fact_59_theI_H) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 66 (all Q_1 all Ga all Ca all Pa ((all Z_1 all S (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S)) -> (exists P_1 exists Q_2 (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool))) & (all S_1 ((all Z_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)))) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)))))))) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool))))) # label(fact_60_conseq) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 67 (all A (A != bot_bo1687970473a_bool <-> (exists X_2 exists B (A = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_2),B) & -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),B)))))) # label(fact_61_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 68 (all F_1 all A_3 all Ba (hBOOL(hAPP_H1927961489a_bool(finite388748825iple_a(F_1,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool)),Ba)) <-> A_3 = Ba)) # label(fact_62_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 69 (all X_1 all F_1 all F (hBOOL(finite520909254iple_a(F_1,F)) -> hAPP_f1826273671iple_a(F,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),bot_bo1687970473a_bool)) = X_1)) # label(fact_63_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 70 (all X_2 (hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X_2)) <-> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),bot_bo1687970473a_bool)))) # label(fact_64_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 71 (all F_1 all X_1 -hBOOL(hAPP_H1927961489a_bool(finite388748825iple_a(F_1,bot_bo1687970473a_bool),X_1))) # label(fact_65_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 72 (all F_1 all A all X_1 (hBOOL(hAPP_H1927961489a_bool(finite388748825iple_a(F_1,A),X_1)) -> A != bot_bo1687970473a_bool)) # label(fact_66_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 73 (all F_1 all A_3 all A all X_1 (hBOOL(hAPP_H1927961489a_bool(finite1734202118iple_a(F_1,A_3,A),X_1)) -> (-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_3),A)) -> hBOOL(hAPP_H1927961489a_bool(finite388748825iple_a(F_1,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A)),X_1))))) # label(fact_67_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 74 (all X_1 all A all F_1 all F (hBOOL(finite520909254iple_a(F_1,F)) -> (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A)) -> (-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_1),A)) -> (A != bot_bo1687970473a_bool -> hAPP_f1826273671iple_a(F,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),A)) = hAPP_H401672213iple_a(hAPP_H568064713iple_a(F_1,X_1),hAPP_f1826273671iple_a(F,A))))))) # label(fact_68_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 75 (all F_1 all A hAPP_f1826273671iple_a(finite233325225iple_a(F_1),A) = hAPP_f1826273671iple_a(the_Ho1745054714iple_a,finite388748825iple_a(F_1,A))) # label(fact_69_fold1__def) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.13 76 (all Q_1 all Pa (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,collec1266446174iple_a(Pa))) | hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,collec1266446174iple_a(Q_1))) -> hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,collec1266446174iple_a(hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fconj),Pa)),Q_1)))))) # label(fact_70_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 77 (all A_3 all A (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A)) -> hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A))))) # label(fact_72_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 78 (all X_1 all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_1),A)) <-> hBOOL(hAPP_H1927961489a_bool(A,X_1)))) # label(fact_73_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 79 (all Pa collec1266446174iple_a(Pa) = Pa) # label(fact_74_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 80 (all A all F_1 all F (hBOOL(finite520909254iple_a(F_1,F)) -> (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A)) -> hAPP_f1826273671iple_a(F,A) = hAPP_f1826273671iple_a(finite233325225iple_a(F_1),A)))) # label(fact_75_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 81 (all F_1 all Z hBOOL(hAPP_H1927961489a_bool(finite1734202118iple_a(F_1,Z,bot_bo1687970473a_bool),Z))) # label(fact_76_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 82 (all F_1 all Z all X_1 (hBOOL(hAPP_H1927961489a_bool(finite1734202118iple_a(F_1,Z,bot_bo1687970473a_bool),X_1)) -> X_1 = Z)) # label(fact_77_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 83 (all F_1 all Z all Y_2 all X_1 all A (-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_1),A)) -> (hBOOL(hAPP_H1927961489a_bool(finite1734202118iple_a(F_1,Z,A),Y_2)) -> hBOOL(hAPP_H1927961489a_bool(finite1734202118iple_a(F_1,Z,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),A)),hAPP_H401672213iple_a(hAPP_H568064713iple_a(F_1,X_1),Y_2)))))) # label(fact_78_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 84 (all Pa all Q_1 (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,collec1266446174iple_a(hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,hAPP_f13210641l_bool(cOMBB_633860163iple_a(fdisj),Pa)),Q_1)))) <-> hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,collec1266446174iple_a(Pa))) & hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,collec1266446174iple_a(Q_1))))) # label(fact_79_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 85 (all A_3 all A (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),A))) <-> hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A)))) # label(fact_80_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 86 (all A_3 all G all F_1 (G = finite233325225iple_a(F_1) -> hAPP_f1826273671iple_a(G,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool)) = A_3)) # label(fact_81_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 87 (all F_1 all A_3 hAPP_f1826273671iple_a(finite233325225iple_a(F_1),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool)) = A_3) # label(fact_82_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 88 (all A all F_1 all F (hBOOL(finite520909254iple_a(F_1,F)) -> (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A)) -> (A != bot_bo1687970473a_bool -> ((all X_2 all Y_1 hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hAPP_H401672213iple_a(hAPP_H568064713iple_a(F_1,X_2),Y_1)),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_2),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,Y_1),bot_bo1687970473a_bool))))) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hAPP_f1826273671iple_a(F,A)),A))))))) # label(fact_83_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 89 (all F_1 all A_3 all X_3 all X_1 (hBOOL(hAPP_H1927961489a_bool(finite388748825iple_a(F_1,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),X_3)),X_1)) -> -(all A_2 all A_1 (hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),X_3) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_2),A_1) -> (hBOOL(hAPP_H1927961489a_bool(finite1734202118iple_a(F_1,A_2,A_1),X_1)) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_2),A_1))))))) # label(fact_84_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 90 (all F_1 all A (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A)) -> (A != bot_bo1687970473a_bool -> (exists X1 hBOOL(hAPP_H1927961489a_bool(finite388748825iple_a(F_1,A),X1)))))) # label(fact_85_finite__nonempty__imp__fold1Set) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 91 (all Pa all F (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,F)) -> (hBOOL(hAPP_f1753944735l_bool(Pa,bot_bo1687970473a_bool)) -> ((all X_2 all F_2 (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,F_2)) -> (-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),F_2)) -> (hBOOL(hAPP_f1753944735l_bool(Pa,F_2)) -> hBOOL(hAPP_f1753944735l_bool(Pa,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_2),F_2))))))) -> hBOOL(hAPP_f1753944735l_bool(Pa,F)))))) # label(fact_86_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 92 (all A_3 (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A_3)) <-> A_3 = bot_bo1687970473a_bool | (exists A_1 exists A_2 (A_3 = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_2),A_1) & hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A_1)))))) # label(fact_87_finite_Osimps) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 93 (all F_1 all Z all A (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A)) -> (exists X1 hBOOL(hAPP_H1927961489a_bool(finite1734202118iple_a(F_1,Z,A),X1))))) # label(fact_88_finite__imp__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 94 (all F_1 all A1 all A2 (hBOOL(hAPP_H1927961489a_bool(finite388748825iple_a(F_1,A1),A2)) <-> (exists A_2 exists A_1 exists X_2 (A1 = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_2),A_1) & A2 = X_2 & hBOOL(hAPP_H1927961489a_bool(finite1734202118iple_a(F_1,A_2,A_1),X_2)) & -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_2),A_1)))))) # label(fact_89_fold1Set_Osimps) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 95 (all F_1 all Z all A1 all A2 (hBOOL(hAPP_H1927961489a_bool(finite1734202118iple_a(F_1,Z,A1),A2)) <-> A1 = bot_bo1687970473a_bool & A2 = Z | (exists X_2 exists A_1 exists Y_1 (A1 = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_2),A_1) & A2 = hAPP_H401672213iple_a(hAPP_H568064713iple_a(F_1,X_2),Y_1) & -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A_1)) & hBOOL(hAPP_H1927961489a_bool(finite1734202118iple_a(F_1,Z,A_1),Y_1)))))) # label(fact_90_fold__graph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 96 (all X_1 all A all F_1 all F (hBOOL(finite1948426435iple_a(F_1,F)) -> (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A)) -> (A != bot_bo1687970473a_bool -> hAPP_f1826273671iple_a(F,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_1),A)) = hAPP_H401672213iple_a(hAPP_H568064713iple_a(F_1,X_1),hAPP_f1826273671iple_a(F,A)))))) # label(fact_91_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 97 (all Pa all F (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,F)) -> (F != bot_bo1687970473a_bool -> ((all X_2 hBOOL(hAPP_f1753944735l_bool(Pa,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_2),bot_bo1687970473a_bool)))) -> ((all X_2 all F_2 (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,F_2)) -> (F_2 != bot_bo1687970473a_bool -> (-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),F_2)) -> (hBOOL(hAPP_f1753944735l_bool(Pa,F_2)) -> hBOOL(hAPP_f1753944735l_bool(Pa,hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,X_2),F_2)))))))) -> hBOOL(hAPP_f1753944735l_bool(Pa,F))))))) # label(fact_92_finite__ne__induct) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 98 (all X_1 all F_1 all F (hBOOL(finite1948426435iple_a(F_1,F)) -> hAPP_H401672213iple_a(hAPP_H568064713iple_a(F_1,X_1),X_1) = X_1)) # label(fact_93_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 99 (all X_1 all A all F_1 all F (hBOOL(finite1948426435iple_a(F_1,F)) -> (hBOOL(hAPP_f1753944735l_bool(finite506133020iple_a,A)) -> (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_1),A)) -> hAPP_H401672213iple_a(hAPP_H568064713iple_a(F_1,X_1),hAPP_f1826273671iple_a(F,A)) = hAPP_f1826273671iple_a(F,A))))) # label(fact_94_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 100 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 101 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 102 (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].
% 0.82/1.14 103 (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].
% 0.82/1.14 104 (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].
% 0.82/1.14 105 (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].
% 0.82/1.14 106 (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].
% 0.82/1.14 107 (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].
% 0.82/1.14 108 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 109 (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].
% 0.82/1.14 110 (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].
% 0.82/1.14 111 (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].
% 0.82/1.14 112 (all X all Y (-hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 113 (all X all Y (X != Y | hBOOL(hAPP_state_bool(hAPP_s1806633685e_bool(fequal_state,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Com__Ostate_T) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 114 (all P all Q (is_bool(P) -> hAPP_state_bool(cOMBK_bool_state(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 115 (all P all Q hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 116 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(cOMBB_160679318_state(P),Q),R) = hAPP_bool_bool(P,hAPP_state_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 117 (all P all Q all R hAPP_state_bool(hAPP_b2019457360e_bool(hAPP_f167292325e_bool(cOMBC_231445413l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 118 (all P all Q all R hAPP_state_bool(hAPP_f1759915619e_bool(hAPP_f644196280e_bool(cOMBS_1378840469l_bool,P),Q),R) = hAPP_bool_bool(hAPP_s58564346l_bool(P,R),hAPP_state_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Ostate_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 119 (all P all Q all R hAPP_state_bool(hAPP_s1806633685e_bool(hAPP_f817621513e_bool(cOMBC_2027030106e_bool,P),Q),R) = hAPP_state_bool(hAPP_s1806633685e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Ostate_000tc__Com__Ostate_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 120 (all X all Y (-hBOOL(hAPP_H1927961489a_bool(hAPP_H562195827a_bool(fequal1878252616iple_a,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 121 (all X all Y (X != Y | hBOOL(hAPP_H1927961489a_bool(hAPP_H562195827a_bool(fequal1878252616iple_a,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 122 (all P all Q all R hAPP_a2036067514e_bool(hAPP_b540892988e_bool(hAPP_f1824947087e_bool(cOMBC_41962815e_bool,P),Q),R) = hAPP_b2019457360e_bool(hAPP_a723219176e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__HOL__Obool_000tc__fun_Itc__Com__Ostate_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 123 (all P all Q (is_bool(P) -> hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 124 (all P all Q all R hAPP_s58564346l_bool(hAPP_f1259673775l_bool(cOMBB_188601460_state(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_state_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].
% 0.82/1.14 125 (all X all Y (-hBOOL(hAPP_f1753944735l_bool(hAPP_f1945881407l_bool(fequal1765155200a_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 126 (all X all Y (X != Y | hBOOL(hAPP_f1753944735l_bool(hAPP_f1945881407l_bool(fequal1765155200a_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 127 (all P all Q all R hAPP_H1927961489a_bool(hAPP_f1400872321a_bool(cOMBB_650444389iple_a(P),Q),R) = hAPP_bool_bool(P,hAPP_H1927961489a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 128 (all P all Q all R hAPP_H1927961489a_bool(hAPP_f1400872321a_bool(hAPP_f1104866853a_bool(cOMBS_213702372l_bool,P),Q),R) = hAPP_bool_bool(hAPP_H1877746411l_bool(P,R),hAPP_H1927961489a_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 129 (all P all Q all R hAPP_a2036067514e_bool(hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,P),Q),R) = hAPP_f1759915619e_bool(hAPP_a1200519163e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 130 (all P all Q all R hAPP_H1877746411l_bool(hAPP_f13210641l_bool(cOMBB_633860163iple_a(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_H1927961489a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_001) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.14 131 (all P all Q all R hAPP_a849909144l_bool(hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(P),Q),R) = hAPP_f1259673775l_bool(P,hAPP_a2036067514e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000tc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.21 132 (all P all Q all R hAPP_H1927961489a_bool(hAPP_H562195827a_bool(hAPP_f1915402821a_bool(cOMBC_2049287834a_bool,P),Q),R) = hAPP_H1927961489a_bool(hAPP_H562195827a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.21 133 (all P all Q all R hAPP_a723219176e_bool(hAPP_f340725611e_bool(cOMBB_1348041619bool_a(P),Q),R) = hAPP_f167292325e_bool(P,hAPP_a849909144l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.21 134 (all P all Q all R hAPP_H1927961489a_bool(hAPP_f1447988451a_bool(cOMBB_545742339iple_a(P),Q),R) = hAPP_f1753944735l_bool(P,hAPP_H562195827a_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.21 135 (all P all Q all R hAPP_H1927961489a_bool(hAPP_f1400872321a_bool(hAPP_f945663555a_bool(cOMBC_2067518550l_bool,P),Q),R) = hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_002) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.21 136 (all P all Q all R hAPP_a1200519163e_bool(hAPP_f963367678e_bool(cOMBB_145932198bool_a(P),Q),R) = hAPP_f644196280e_bool(P,hAPP_a849909144l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Ostate_Mtc__fun_Itc__HOL__Obool_Mtc__H_003) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.21 137 (all P all Q all R hAPP_H562195827a_bool(hAPP_f1170963427a_bool(hAPP_f1874567875a_bool(cOMBC_1089176504a_bool,P),Q),R) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_004) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.21
% 0.85/1.21 ============================== end of process non-clausal formulas ===
% 0.85/1.21
% 0.85/1.21 ============================== PROCESS INITIAL CLAUSES ===============
% 0.85/1.21
% 0.85/1.21 ============================== PREDICATE ELIMINATION =================
% 0.85/1.21
% 0.85/1.21 ============================== end predicate elimination =============
% 0.85/1.21
% 0.85/1.21 Auto_denials: (non-Horn, no changes).
% 0.85/1.21
% 0.85/1.21 Term ordering decisions:
% 0.85/1.21 Function symbol KB weights: insert1871499715iple_a=1. bot_bo1687970473a_bool=1. member564727580iple_a=1. finite506133020iple_a=1. fequal1878252616iple_a=1. cOMBS_213702372l_bool=1. the_Ho1745054714iple_a=1. fconj=1. cOMBC_2049287834a_bool=1. fdisj=1. fimplies=1. bot_bot_bool=1. fNot=1. cOMBC_2067518550l_bool=1. cOMBC_231445413l_bool=1. cOMBC_41962815e_bool=1. fFalse=1. fequal1765155200a_bool=1. fequal_state=1. cOMBC_1089176504a_bool=1. cOMBC_2027030106e_bool=1. fTrue=1. the_el287271400iple_a=1. cOMBC_892787026e_bool=1. cOMBS_1378840469l_bool=1. skip=1. b=1. c=1. g=1. p=1. hAPP_f1400872321a_bool=1. hAPP_f1753944735l_bool=1. hAPP_H1816261935a_bool=1. hAPP_H1927961489a_bool=1. hAPP_H1926610125l_bool=1. hAPP_f1826273671iple_a=1. hAPP_state_bool=1. hAPP_H562195827a_bool=1. hAPP_a2036067514e_bool=1. hAPP_bool_bool=1. hAPP_b589554111l_bool=1. hAPP_f1104866853a_bool=1. hAPP_f13210641l_bool=1. hAPP_f1915402821a_bool=1. finite388748825iple_a=1. hAPP_H401672213iple_a=1. hAPP_H568064713iple_a=1. semi=1. finite520909254iple_a=1. hAPP_s1806633685e_bool=1. finite1948426435iple_a=1. hAPP_a849909144l_bool=1. hAPP_b540892988e_bool=1. hAPP_f1509969235l_bool=1. hAPP_f1759915619e_bool=1. hAPP_f1824947087e_bool=1. hAPP_f1945881407l_bool=1. hAPP_f340725611e_bool=1. hAPP_f945663555a_bool=1. hAPP_s58564346l_bool=1. hAPP_H1877746411l_bool=1. hAPP_a1200519163e_bool=1. hAPP_a723219176e_bool=1. hAPP_b2019457360e_bool=1. hAPP_f1170963427a_bool=1. hAPP_f1259673775l_bool=1. hAPP_f1447988451a_bool=1. hAPP_f167292325e_bool=1. hAPP_f1874567875a_bool=1. hAPP_f644196280e_bool=1. hAPP_f817621513e_bool=1. hAPP_f1261923407e_bool=1. hAPP_f762886889e_bool=1. hAPP_f963367678e_bool=1. f17=1. f18=1. f20=1. f21=1. f23=1. f33=1. f34=1. f35=1. f45=1. f46=1. f47=1. hoare_472868247rivs_a=1. collec1266446174iple_a=1. cOMBB_633860163iple_a=1. cOMBB_650444389iple_a=1. finite233325225iple_a=1. cOMBB_1348041619bool_a=1. cOMBB_1355796797bool_a=1. cOMBB_188601460_state=1. cOMBK_1458035955bool_a=1. cOMBB_545742339iple_a=1. cOMBK_1150238960iple_a=1. cOMBB_145932198bool_a=1. cOMBB_160679318_state=1. cOMBK_bool_state=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f19=1. f27=1. f28=1. f36=1. f37=1. hoare_1050552211iple_a=1. finite1734202118iple_a=1. f22=1. f29=1. f30=1. f38=1. f39=1. f40=1. f41=1. f1=1. f2=1. f24=1. f25=1. f31=1. f32=1. f42=1. f43=1. f44=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f26=1.
% 4.35/4.65
% 4.35/4.65 ============================== end of process initial clauses ========
% 4.35/4.65
% 4.35/4.65 ============================== CLAUSES FOR SEARCH ====================
% 4.35/4.65
% 4.35/4.65 ============================== end of clauses for search =============
% 4.35/4.65
% 4.35/4.65 ============================== SEARCH ================================
% 4.35/4.65
% 4.35/4.65 % Starting search at 0.10 seconds.
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=42.000, iters=3354
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=36.000, iters=3384
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=30.000, iters=3354
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=28.000, iters=3396
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=26.000, iters=3346
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=25.000, iters=3395
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=24.000, iters=3340
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=23.000, iters=3355
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=22.000, iters=3690
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=21.000, iters=3358
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=20.000, iters=3349
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=19.000, iters=3421
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=18.000, iters=3384
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=17.000, iters=3342
% 4.35/4.65
% 4.35/4.65 Low Water (keep): wt=16.000, iters=3336
% 4.35/4.65
% 4.35/4.65 ============================== PROOF =================================
% 4.35/4.65 % SZS status Theorem
% 4.35/4.65 % SZS output start Refutation
% 4.35/4.65
% 4.35/4.65 % Proof 1 at 3.46 (+ 0.09) seconds.
% 4.35/4.65 % Length of proof is 40.
% 4.35/4.65 % Level of proof is 8.
% 4.35/4.65 % Maximum clause weight is 29.000.
% 4.35/4.65 % Given clauses 2235.
% 4.35/4.65
% 4.35/4.65 19 (all A_3 collec1266446174iple_a(hAPP_H562195827a_bool(fequal1878252616iple_a,A_3)) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A_3),bot_bo1687970473a_bool)) # label(fact_12_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 4.35/4.65 26 (all Pa (bot_bo1687970473a_bool = collec1266446174iple_a(Pa) <-> (all X_2 -hBOOL(hAPP_H1927961489a_bool(Pa,X_2))))) # label(fact_19_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 4.35/4.65 47 (all X_1 (hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X_1)) <-> hBOOL(bot_bot_bool))) # label(fact_41_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 4.35/4.65 66 (all Q_1 all Ga all Ca all Pa ((all Z_1 all S (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Pa,Z_1),S)) -> (exists P_1 exists Q_2 (hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(P_1,Ca,Q_2)),bot_bo1687970473a_bool))) & (all S_1 ((all Z_2 (hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(P_1,Z_2),S)) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_2,Z_2),S_1)))) -> hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(Q_1,Z_1),S_1)))))))) -> hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(Ga),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(Pa,Ca,Q_1)),bot_bo1687970473a_bool))))) # label(fact_60_conseq) # label(axiom) # label(non_clause). [assumption].
% 4.35/4.65 79 (all Pa collec1266446174iple_a(Pa) = Pa) # label(fact_74_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 4.35/4.65 114 (all P all Q (is_bool(P) -> hAPP_state_bool(cOMBK_bool_state(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom) # label(non_clause). [assumption].
% 4.35/4.65 115 (all P all Q hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) # label(axiom) # label(non_clause). [assumption].
% 4.35/4.65 123 (all P all Q (is_bool(P) -> hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__) # label(axiom) # label(non_clause). [assumption].
% 4.35/4.65 140 is_bool(bot_bot_bool) # label(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool) # label(axiom). [assumption].
% 4.35/4.65 141 is_bool(fFalse) # label(gsy_c_fFalse) # label(hypothesis). [assumption].
% 4.35/4.65 169 collec1266446174iple_a(hAPP_H562195827a_bool(fequal1878252616iple_a,A)) = hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A),bot_bo1687970473a_bool) # label(fact_12_singleton__conv2) # label(axiom). [clausify(19)].
% 4.35/4.65 170 hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A),bot_bo1687970473a_bool) = collec1266446174iple_a(hAPP_H562195827a_bool(fequal1878252616iple_a,A)). [copy(169),flip(a)].
% 4.35/4.65 183 collec1266446174iple_a(A) = bot_bo1687970473a_bool | hBOOL(hAPP_H1927961489a_bool(A,f11(A))) # label(fact_19_empty__Collect__eq) # label(axiom). [clausify(26)].
% 4.35/4.65 190 bot_bo1687970473a_bool = collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)) # label(fact_22_empty__def) # label(axiom). [assumption].
% 4.35/4.65 229 hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,A)) | -hBOOL(bot_bot_bool) # label(fact_41_bot__apply) # label(axiom). [clausify(47)].
% 4.35/4.65 230 hBOOL(hAPP_H1927961489a_bool(collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse)),A)) | -hBOOL(bot_bot_bool). [copy(229),rewrite([190(1)])].
% 4.35/4.65 262 hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(A,f24(B,C,D,A)),f25(B,C,D,A))) | hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(C),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(A,D,B)),bot_bo1687970473a_bool))) # label(fact_60_conseq) # label(axiom). [clausify(66)].
% 4.35/4.65 263 hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(A,f24(B,C,D,A)),f25(B,C,D,A))) | hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(C),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(A,D,B)),collec1266446174iple_a(cOMBK_1150238960iple_a(fFalse))))). [copy(262),rewrite([190(10)])].
% 4.35/4.65 300 collec1266446174iple_a(A) = A # label(fact_74_Collect__def) # label(axiom). [clausify(79)].
% 4.35/4.65 384 -hBOOL(fFalse) # label(help_fFalse_1_1_U) # label(axiom). [assumption].
% 4.35/4.65 392 -is_bool(A) | hAPP_state_bool(cOMBK_bool_state(A),B) = A # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Ostate_U) # label(axiom). [clausify(114)].
% 4.35/4.65 393 hAPP_a2036067514e_bool(cOMBK_1458035955bool_a(A),B) = A # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_J_000t__a_U) # label(axiom). [clausify(115)].
% 4.35/4.65 404 -is_bool(A) | hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(A),B) = A # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__) # label(axiom). [clausify(123)].
% 4.35/4.65 422 -hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),bot_bo1687970473a_bool))) # label(conj_0) # label(negated_conjecture). [assumption].
% 4.35/4.65 423 -hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))),cOMBK_1150238960iple_a(fFalse)))). [copy(422),rewrite([190(25),300(27)])].
% 4.35/4.65 441 cOMBK_1150238960iple_a(fFalse) = A | hBOOL(hAPP_H1927961489a_bool(A,f11(A))). [back_rewrite(183),rewrite([300(1),190(1),300(3)]),flip(a)].
% 4.35/4.65 447 hAPP_f1400872321a_bool(hAPP_H1816261935a_bool(insert1871499715iple_a,A),cOMBK_1150238960iple_a(fFalse)) = hAPP_H562195827a_bool(fequal1878252616iple_a,A). [back_rewrite(170),rewrite([190(3),300(5),300(8)])].
% 4.35/4.65 471 hBOOL(hAPP_state_bool(hAPP_a2036067514e_bool(A,f24(B,C,D,A)),f25(B,C,D,A))) | hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(C),hAPP_H562195827a_bool(fequal1878252616iple_a,hoare_1050552211iple_a(A,D,B)))). [back_rewrite(263),rewrite([300(12),447(12)])].
% 4.35/4.65 476 hBOOL(hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),A)) | -hBOOL(bot_bot_bool). [back_rewrite(230),rewrite([300(3)])].
% 4.35/4.65 514 -hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_H562195827a_bool(fequal1878252616iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(fFalse)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))). [back_rewrite(423),rewrite([447(27)])].
% 4.35/4.65 628 hAPP_state_bool(cOMBK_bool_state(bot_bot_bool),A) = bot_bot_bool. [resolve(392,a,140,a)].
% 4.35/4.65 673 hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(fFalse),A) = fFalse. [resolve(404,a,141,a)].
% 4.35/4.65 674 hAPP_H1927961489a_bool(cOMBK_1150238960iple_a(bot_bot_bool),A) = bot_bot_bool. [resolve(404,a,140,a)].
% 4.35/4.65 677 -hBOOL(bot_bot_bool). [back_rewrite(476),rewrite([673(3)]),unit_del(a,384)].
% 4.35/4.65 1126 hBOOL(hAPP_state_bool(A,f25(B,C,D,cOMBK_1458035955bool_a(A)))) | hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(C),hAPP_H562195827a_bool(fequal1878252616iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(A),D,B)))). [para(393(a,1),471(a,1,1))].
% 4.35/4.65 1625 cOMBK_1150238960iple_a(fFalse) = cOMBK_1150238960iple_a(bot_bot_bool). [para(674(a,1),441(b,1)),unit_del(b,677)].
% 4.35/4.65 1998 fFalse = bot_bot_bool. [back_rewrite(673),rewrite([1625(2),674(3)]),flip(a)].
% 4.35/4.65 2078 -hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(g),hAPP_H562195827a_bool(fequal1878252616iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),c,hAPP_f762886889e_bool(hAPP_f1261923407e_bool(cOMBC_892787026e_bool,hAPP_f963367678e_bool(cOMBB_145932198bool_a(cOMBS_1378840469l_bool),hAPP_f1509969235l_bool(cOMBB_1355796797bool_a(cOMBB_188601460_state(fconj)),p))),hAPP_f1759915619e_bool(cOMBB_160679318_state(fNot),b)))))). [back_rewrite(514),rewrite([1998(4)])].
% 4.35/4.65 12376 hBOOL(hAPP_f1753944735l_bool(hoare_472868247rivs_a(A),hAPP_H562195827a_bool(fequal1878252616iple_a,hoare_1050552211iple_a(cOMBK_1458035955bool_a(cOMBK_bool_state(bot_bot_bool)),B,C)))). [para(628(a,1),1126(a,1)),unit_del(a,677)].
% 4.35/4.65 12377 $F. [resolve(12376,a,2078,a)].
% 4.35/4.65
% 4.35/4.65 % SZS output end Refutation
% 4.35/4.65 ============================== end of proof ==========================
% 4.35/4.65
% 4.35/4.65 ============================== STATISTICS ============================
% 4.35/4.65
% 4.35/4.65 Given=2235. Generated=136025. Kept=12156. proofs=1.
% 4.35/4.65 Usable=2145. Sos=8650. Demods=710. Limbo=0, Disabled=1578. Hints=0.
% 4.35/4.65 Megabytes=40.07.
% 4.35/4.65 User_CPU=3.46, System_CPU=0.09, Wall_clock=4.
% 4.35/4.65
% 4.35/4.65 ============================== end of statistics =====================
% 4.35/4.65
% 4.35/4.65 ============================== end of search =========================
% 4.35/4.65
% 4.35/4.65 THEOREM PROVED
% 4.35/4.65 % SZS status Theorem
% 4.35/4.65
% 4.35/4.65 Exiting with 1 proof.
% 4.35/4.65
% 4.35/4.65 Process 4157 exit (max_proofs) Sun Jun 5 03:05:14 2022
% 4.35/4.65 Prover9 interrupted
%------------------------------------------------------------------------------