TSTP Solution File: SWW471+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW471+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 01:17:06 EDT 2022
% Result : Timeout 300.08s 300.39s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW471+1 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Mon Jun 6 04:04:53 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.96/1.30 ============================== Prover9 ===============================
% 0.96/1.30 Prover9 (32) version 2009-11A, November 2009.
% 0.96/1.30 Process 30216 was started by sandbox on n027.cluster.edu,
% 0.96/1.30 Mon Jun 6 04:04:54 2022
% 0.96/1.30 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30063_n027.cluster.edu".
% 0.96/1.30 ============================== end of head ===========================
% 0.96/1.30
% 0.96/1.30 ============================== INPUT =================================
% 0.96/1.30
% 0.96/1.30 % Reading from file /tmp/Prover9_30063_n027.cluster.edu
% 0.96/1.30
% 0.96/1.30 set(prolog_style_variables).
% 0.96/1.30 set(auto2).
% 0.96/1.30 % set(auto2) -> set(auto).
% 0.96/1.30 % set(auto) -> set(auto_inference).
% 0.96/1.30 % set(auto) -> set(auto_setup).
% 0.96/1.30 % set(auto_setup) -> set(predicate_elim).
% 0.96/1.30 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.96/1.30 % set(auto) -> set(auto_limits).
% 0.96/1.30 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.96/1.30 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.96/1.30 % set(auto) -> set(auto_denials).
% 0.96/1.30 % set(auto) -> set(auto_process).
% 0.96/1.30 % set(auto2) -> assign(new_constants, 1).
% 0.96/1.30 % set(auto2) -> assign(fold_denial_max, 3).
% 0.96/1.30 % set(auto2) -> assign(max_weight, "200.000").
% 0.96/1.30 % set(auto2) -> assign(max_hours, 1).
% 0.96/1.30 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.96/1.30 % set(auto2) -> assign(max_seconds, 0).
% 0.96/1.30 % set(auto2) -> assign(max_minutes, 5).
% 0.96/1.30 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.96/1.30 % set(auto2) -> set(sort_initial_sos).
% 0.96/1.30 % set(auto2) -> assign(sos_limit, -1).
% 0.96/1.30 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.96/1.30 % set(auto2) -> assign(max_megs, 400).
% 0.96/1.30 % set(auto2) -> assign(stats, some).
% 0.96/1.30 % set(auto2) -> clear(echo_input).
% 0.96/1.30 % set(auto2) -> set(quiet).
% 0.96/1.30 % set(auto2) -> clear(print_initial_clauses).
% 0.96/1.30 % set(auto2) -> clear(print_given).
% 0.96/1.30 assign(lrs_ticks,-1).
% 0.96/1.30 assign(sos_limit,10000).
% 0.96/1.30 assign(order,kbo).
% 0.96/1.30 set(lex_order_vars).
% 0.96/1.30 clear(print_given).
% 0.96/1.30
% 0.96/1.30 % formulas(sos). % not echoed (259 formulas)
% 0.96/1.30
% 0.96/1.30 ============================== end of input ==========================
% 0.96/1.30
% 0.96/1.30 % From the command line: assign(max_seconds, 300).
% 0.96/1.30
% 0.96/1.30 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.96/1.30
% 0.96/1.30 % Formulas that are not ordinary clauses:
% 0.96/1.30 1 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2)))) # label(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 2 (all B_1_1 all B_2 (is_pname(B_2) -> is_fun_pname_bool(cOMBC_1149511130e_bool(B_1_1,B_2)))) # label(gsy_c_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 3 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun_pname_bool(cOMBC_1058051404l_bool(B_1_1,B_2)))) # label(gsy_c_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 4 (all B_1_1 (is_bool(B_1_1) -> is_fun_pname_bool(cOMBK_bool_pname(B_1_1)))) # label(gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 5 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2)))) # label(gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 6 (all B_1_1 all B_2 is_bool(hoare_472868247rivs_a(B_1_1,B_2))) # label(gsy_c_Hoare__Mirabelle__jfehddehev_Ohoare__derivs_000t__a) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 7 (all B_1_1 all B_2 is_bool(hoare_810701593lids_a(B_1_1,B_2))) # label(gsy_c_Hoare__Mirabelle__jfehddehev_Ohoare__valids_000t__a) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 8 (all B_1_1 all B_2 (is_bool(B_1_1) & is_bool(B_2) -> is_bool(semila1168014441p_bool(B_1_1,B_2)))) # label(gsy_c_Lattices_Osemilattice__sup__class_Osup_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 9 (all B_1_1 all B_2 (is_fun_pname_bool(B_1_1) & is_fun_pname_bool(B_2) -> is_fun_pname_bool(semila278973382e_bool(B_1_1,B_2)))) # label(gsy_c_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__Com__Opname_Mtc__HO) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 10 (all B_1_1 all B_2 all B_3 is_bool(evalc(B_1_1,B_2,B_3))) # label(gsy_c_Natural_Oevalc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 11 (all B_1_1 (is_fun_pname_bool(B_1_1) -> is_fun_pname_bool(collect_pname(B_1_1)))) # label(gsy_c_Set_OCollect_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 12 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_fun_pname_bool(image_pname_pname(B_1_1,B_2)))) # label(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 13 (all B_1_1 all B_2 is_fun_pname_bool(image_1474161344_pname(B_1_1,B_2))) # label(gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_000tc_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 14 (all B_1_1 all B_2 (is_pname(B_1_1) & is_fun_pname_bool(B_2) -> is_fun_pname_bool(insert_pname(B_1_1,B_2)))) # label(gsy_c_Set_Oinsert_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 15 (all B_1_1 all B_2 (is_pname(B_2) -> is_pname(hAPP_pname_pname(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 16 (all B_1_1 all B_2 (is_fun_pname_bool(B_1_1) & is_pname(B_2) -> is_bool(hAPP_pname_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 17 (all B_1_1 all B_2 (is_pname(B_2) -> is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 18 (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].
% 0.96/1.30 19 (all B_1_1 all B_2 is_pname(hAPP_H82695184_pname(B_1_1,B_2))) # label(gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_000tc__Com__) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 20 (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(hypothesis) # label(non_clause). [assumption].
% 0.96/1.30 21 (all B_1_1 all B_2 (is_fun_pname_bool(B_2) -> is_bool(hAPP_f1664156314l_bool(B_1_1,B_2)))) # label(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 22 (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].
% 0.96/1.30 23 (all Fun1_2 all Com_2 all Fun2_2 all Fun1_1 all Com_1 all Fun2_1 (hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Fun1_2),Com_2),Fun2_2) = hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Fun1_1),Com_1),Fun2_1) <-> Fun1_2 = Fun1_1 & Com_2 = Com_1 & Fun2_2 = Fun2_1)) # label(fact_0_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 24 (all Ga all Ts (hBOOL(hoare_810701593lids_a(Ga,Ts)) <-> (all N ((all X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),Ga)) -> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(N),X)))) -> (all X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),Ts)) -> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(N),X)))))))) # label(fact_1_hoare__valids__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 25 (all Ga all Pa all Qa all Procsa (hBOOL(hoare_472868247rivs_a(semila2005279307a_bool(Ga,image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,Pa),body),Qa),Procsa)),image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,Pa),cOMBB_923936821_pname(the_com,body_1)),Qa),Procsa))) -> hBOOL(hoare_472868247rivs_a(Ga,image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,Pa),body),Qa),Procsa))))) # label(fact_2_hoare__derivs_OBody) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 26 (all C all A all B_1 (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),semila2005279307a_bool(A,B_1))) -> (-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),A)) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),B_1))))) # label(fact_3_UnE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 27 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),semila278973382e_bool(A,B_1))) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1))))) # label(fact_4_UnE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 28 (all A all B_1 all X_2 (hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(A,B_1),X_2)) -> (-hBOOL(hAPP_H1927961489a_bool(A,X_2)) -> hBOOL(hAPP_H1927961489a_bool(B_1,X_2))))) # label(fact_5_sup1E) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 29 (all A all B_1 all X_2 (hBOOL(hAPP_pname_bool(semila278973382e_bool(A,B_1),X_2)) -> (-hBOOL(hAPP_pname_bool(A,X_2)) -> hBOOL(hAPP_pname_bool(B_1,X_2))))) # label(fact_6_sup1E) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 30 (all A all B_1 all X_2 ((-hBOOL(hAPP_H1927961489a_bool(B_1,X_2)) -> hBOOL(hAPP_H1927961489a_bool(A,X_2))) -> hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(A,B_1),X_2)))) # label(fact_7_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 31 (all A all B_1 all X_2 ((-hBOOL(hAPP_pname_bool(B_1,X_2)) -> hBOOL(hAPP_pname_bool(A,X_2))) -> hBOOL(hAPP_pname_bool(semila278973382e_bool(A,B_1),X_2)))) # label(fact_8_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 32 (all A all C all B_1 ((-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),B_1)) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),A))) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),semila2005279307a_bool(A,B_1))))) # label(fact_9_UnCI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 33 (all A all C all B_1 ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A))) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),semila278973382e_bool(A,B_1))))) # label(fact_10_UnCI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 34 (all A all B all F all X_2 (B = hAPP_p1261697242iple_a(F,X_2) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,B),image_505679754iple_a(F,A)))))) # label(fact_11_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 35 (all A all B all F all X_2 (B = hAPP_H82695184_pname(F,X_2) -> (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),image_1474161344_pname(F,A)))))) # label(fact_12_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 36 (all F all A all B_1 image_505679754iple_a(F,semila278973382e_bool(A,B_1)) = semila2005279307a_bool(image_505679754iple_a(F,A),image_505679754iple_a(F,B_1))) # label(fact_13_image__Un) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 37 (all F all A all B_1 image_1474161344_pname(F,semila2005279307a_bool(A,B_1)) = semila278973382e_bool(image_1474161344_pname(F,A),image_1474161344_pname(F,B_1))) # label(fact_14_image__Un) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 38 (all F all G all X (hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(F,G),X)) <-> hBOOL(semila1168014441p_bool(hAPP_H1927961489a_bool(F,X),hAPP_H1927961489a_bool(G,X))))) # label(fact_15_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 39 (all F all G all X (hBOOL(hAPP_pname_bool(semila278973382e_bool(F,G),X)) <-> hBOOL(semila1168014441p_bool(hAPP_pname_bool(F,X),hAPP_pname_bool(G,X))))) # label(fact_16_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 40 (all F all G all X_2 (hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(F,G),X_2)) <-> hBOOL(semila1168014441p_bool(hAPP_H1927961489a_bool(F,X_2),hAPP_H1927961489a_bool(G,X_2))))) # label(fact_17_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 41 (all F all G all X_2 (hBOOL(hAPP_pname_bool(semila278973382e_bool(F,G),X_2)) <-> hBOOL(semila1168014441p_bool(hAPP_pname_bool(F,X_2),hAPP_pname_bool(G,X_2))))) # label(fact_18_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 42 (all Ga all G_1 all Ts (hBOOL(hoare_472868247rivs_a(G_1,Ts)) -> (hBOOL(hoare_472868247rivs_a(Ga,G_1)) -> hBOOL(hoare_472868247rivs_a(Ga,Ts))))) # label(fact_19_cut) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 43 (all X_2 all Y_1 all Z semila2005279307a_bool(semila2005279307a_bool(X_2,Y_1),Z) = semila2005279307a_bool(X_2,semila2005279307a_bool(Y_1,Z))) # label(fact_20_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 44 (all X_2 all Y_1 all Z semila278973382e_bool(semila278973382e_bool(X_2,Y_1),Z) = semila278973382e_bool(X_2,semila278973382e_bool(Y_1,Z))) # label(fact_21_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 45 (all X_2 all Y_1 all Z (hBOOL(semila1168014441p_bool(semila1168014441p_bool(X_2,Y_1),Z)) <-> hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(Y_1,Z))))) # label(fact_22_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 46 (all X_2 all Y_1 all Z semila2005279307a_bool(semila2005279307a_bool(X_2,Y_1),Z) = semila2005279307a_bool(X_2,semila2005279307a_bool(Y_1,Z))) # label(fact_23_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 47 (all X_2 all Y_1 all Z semila278973382e_bool(semila278973382e_bool(X_2,Y_1),Z) = semila278973382e_bool(X_2,semila278973382e_bool(Y_1,Z))) # label(fact_24_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 48 (all X_2 all Y_1 all Z (hBOOL(semila1168014441p_bool(semila1168014441p_bool(X_2,Y_1),Z)) <-> hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(Y_1,Z))))) # label(fact_25_inf__sup__aci_I6_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 49 (all A_1 all B all C semila2005279307a_bool(semila2005279307a_bool(A_1,B),C) = semila2005279307a_bool(A_1,semila2005279307a_bool(B,C))) # label(fact_26_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 50 (all A_1 all B all C semila278973382e_bool(semila278973382e_bool(A_1,B),C) = semila278973382e_bool(A_1,semila278973382e_bool(B,C))) # label(fact_27_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 51 (all A_1 all B all C (hBOOL(semila1168014441p_bool(semila1168014441p_bool(A_1,B),C)) <-> hBOOL(semila1168014441p_bool(A_1,semila1168014441p_bool(B,C))))) # label(fact_28_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 52 (all X_2 all Y_1 all Z semila2005279307a_bool(X_2,semila2005279307a_bool(Y_1,Z)) = semila2005279307a_bool(Y_1,semila2005279307a_bool(X_2,Z))) # label(fact_29_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 53 (all X_2 all Y_1 all Z semila278973382e_bool(X_2,semila278973382e_bool(Y_1,Z)) = semila278973382e_bool(Y_1,semila278973382e_bool(X_2,Z))) # label(fact_30_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 54 (all X_2 all Y_1 all Z (hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(Y_1,Z))) <-> hBOOL(semila1168014441p_bool(Y_1,semila1168014441p_bool(X_2,Z))))) # label(fact_31_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 55 (all X_2 all Y_1 all Z semila2005279307a_bool(X_2,semila2005279307a_bool(Y_1,Z)) = semila2005279307a_bool(Y_1,semila2005279307a_bool(X_2,Z))) # label(fact_32_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 56 (all X_2 all Y_1 all Z semila278973382e_bool(X_2,semila278973382e_bool(Y_1,Z)) = semila278973382e_bool(Y_1,semila278973382e_bool(X_2,Z))) # label(fact_33_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 57 (all X_2 all Y_1 all Z (hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(Y_1,Z))) <-> hBOOL(semila1168014441p_bool(Y_1,semila1168014441p_bool(X_2,Z))))) # label(fact_34_inf__sup__aci_I7_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 58 (all B all A_1 all C semila2005279307a_bool(B,semila2005279307a_bool(A_1,C)) = semila2005279307a_bool(A_1,semila2005279307a_bool(B,C))) # label(fact_35_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 59 (all B all A_1 all C semila278973382e_bool(B,semila278973382e_bool(A_1,C)) = semila278973382e_bool(A_1,semila278973382e_bool(B,C))) # label(fact_36_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 60 (all B all A_1 all C (hBOOL(semila1168014441p_bool(B,semila1168014441p_bool(A_1,C))) <-> hBOOL(semila1168014441p_bool(A_1,semila1168014441p_bool(B,C))))) # label(fact_37_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 61 (all X_2 all Y_1 semila2005279307a_bool(X_2,semila2005279307a_bool(X_2,Y_1)) = semila2005279307a_bool(X_2,Y_1)) # label(fact_38_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 62 (all X_2 all Y_1 semila278973382e_bool(X_2,semila278973382e_bool(X_2,Y_1)) = semila278973382e_bool(X_2,Y_1)) # label(fact_39_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 63 (all X_2 all Y_1 (hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(X_2,Y_1))) <-> hBOOL(semila1168014441p_bool(X_2,Y_1)))) # label(fact_40_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 64 (all X_2 all Y_1 semila2005279307a_bool(X_2,semila2005279307a_bool(X_2,Y_1)) = semila2005279307a_bool(X_2,Y_1)) # label(fact_41_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 65 (all X_2 all Y_1 semila278973382e_bool(X_2,semila278973382e_bool(X_2,Y_1)) = semila278973382e_bool(X_2,Y_1)) # label(fact_42_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 66 (all X_2 all Y_1 (hBOOL(semila1168014441p_bool(X_2,semila1168014441p_bool(X_2,Y_1))) <-> hBOOL(semila1168014441p_bool(X_2,Y_1)))) # label(fact_43_inf__sup__aci_I8_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 67 (all A_1 all B semila2005279307a_bool(A_1,semila2005279307a_bool(A_1,B)) = semila2005279307a_bool(A_1,B)) # label(fact_44_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 68 (all A_1 all B semila278973382e_bool(A_1,semila278973382e_bool(A_1,B)) = semila278973382e_bool(A_1,B)) # label(fact_45_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 69 (all A_1 all B (hBOOL(semila1168014441p_bool(A_1,semila1168014441p_bool(A_1,B))) <-> hBOOL(semila1168014441p_bool(A_1,B)))) # label(fact_46_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 70 (all X_2 all Y_1 semila2005279307a_bool(X_2,Y_1) = semila2005279307a_bool(Y_1,X_2)) # label(fact_47_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 71 (all X_2 all Y_1 semila278973382e_bool(X_2,Y_1) = semila278973382e_bool(Y_1,X_2)) # label(fact_48_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 72 (all X_2 all Y_1 (hBOOL(semila1168014441p_bool(X_2,Y_1)) <-> hBOOL(semila1168014441p_bool(Y_1,X_2)))) # label(fact_49_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 73 (all X_2 all Y_1 semila2005279307a_bool(X_2,Y_1) = semila2005279307a_bool(Y_1,X_2)) # label(fact_50_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 74 (all X_2 all Y_1 semila278973382e_bool(X_2,Y_1) = semila278973382e_bool(Y_1,X_2)) # label(fact_51_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 75 (all X_2 all Y_1 (hBOOL(semila1168014441p_bool(X_2,Y_1)) <-> hBOOL(semila1168014441p_bool(Y_1,X_2)))) # label(fact_52_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 76 (all A_1 all B semila2005279307a_bool(A_1,B) = semila2005279307a_bool(B,A_1)) # label(fact_53_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 77 (all A_1 all B semila278973382e_bool(A_1,B) = semila278973382e_bool(B,A_1)) # label(fact_54_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 78 (all A_1 all B (hBOOL(semila1168014441p_bool(A_1,B)) <-> hBOOL(semila1168014441p_bool(B,A_1)))) # label(fact_55_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 79 (all X_2 semila2005279307a_bool(X_2,X_2) = X_2) # label(fact_56_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 80 (all X_2 (is_fun_pname_bool(X_2) -> semila278973382e_bool(X_2,X_2) = X_2)) # label(fact_57_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 81 (all X_2 (hBOOL(semila1168014441p_bool(X_2,X_2)) <-> hBOOL(X_2))) # label(fact_58_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 82 (all A_1 semila2005279307a_bool(A_1,A_1) = A_1) # label(fact_59_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 83 (all A_1 (is_fun_pname_bool(A_1) -> semila278973382e_bool(A_1,A_1) = A_1)) # label(fact_60_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 84 (all A_1 (hBOOL(semila1168014441p_bool(A_1,A_1)) <-> hBOOL(A_1))) # label(fact_61_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 85 (all B all F all X_2 all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A)) -> (B = hAPP_H82695184_pname(F,X_2) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),image_1474161344_pname(F,A)))))) # label(fact_62_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 86 (all B all F all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (B = hAPP_p1261697242iple_a(F,X_2) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,B),image_505679754iple_a(F,A)))))) # label(fact_63_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 87 (all F all X_2 all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_H82695184_pname(F,X_2)),image_1474161344_pname(F,A))))) # label(fact_64_imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 88 (all F all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,hAPP_p1261697242iple_a(F,X_2)),image_505679754iple_a(F,A))))) # label(fact_65_imageI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 89 (all Z all F all A (is_pname(Z) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Z),image_1474161344_pname(F,A))) <-> (exists X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A)) & Z = hAPP_H82695184_pname(F,X)))))) # label(fact_66_image__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 90 (all Z all F all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,Z),image_505679754iple_a(F,A))) <-> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) & Z = hAPP_p1261697242iple_a(F,X))))) # label(fact_67_image__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 91 (all A all C all B_1 (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),B_1)) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),semila2005279307a_bool(A,B_1))))) # label(fact_68_UnI2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 92 (all A all C all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),semila278973382e_bool(A,B_1))))) # label(fact_69_UnI2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 93 (all B_1 all C all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),A)) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),semila2005279307a_bool(A,B_1))))) # label(fact_70_UnI1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 94 (all B_1 all C all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),semila278973382e_bool(A,B_1))))) # label(fact_71_UnI1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 95 (all A all B_1 all X_2 (hBOOL(hAPP_H1927961489a_bool(B_1,X_2)) -> hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(A,B_1),X_2)))) # label(fact_72_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 96 (all A all B_1 all X_2 (hBOOL(hAPP_pname_bool(B_1,X_2)) -> hBOOL(hAPP_pname_bool(semila278973382e_bool(A,B_1),X_2)))) # label(fact_73_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 97 (all B_1 all A all X_2 (hBOOL(hAPP_H1927961489a_bool(A,X_2)) -> hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(A,B_1),X_2)))) # label(fact_74_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 98 (all B_1 all A all X_2 (hBOOL(hAPP_pname_bool(A,X_2)) -> hBOOL(hAPP_pname_bool(semila278973382e_bool(A,B_1),X_2)))) # label(fact_75_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 99 (all Pa all A all B_1 ((all X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),semila2005279307a_bool(A,B_1))) -> hBOOL(hAPP_H1927961489a_bool(Pa,X)))) <-> (all X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A)) -> hBOOL(hAPP_H1927961489a_bool(Pa,X)))) & (all X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),B_1)) -> hBOOL(hAPP_H1927961489a_bool(Pa,X)))))) # label(fact_76_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 100 (all Pa all A all B_1 ((all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),semila278973382e_bool(A,B_1))) -> hBOOL(hAPP_pname_bool(Pa,X))))) <-> (all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) -> hBOOL(hAPP_pname_bool(Pa,X))))) & (all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_1)) -> hBOOL(hAPP_pname_bool(Pa,X))))))) # label(fact_77_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 101 (all Pa all A all B_1 ((exists X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),semila2005279307a_bool(A,B_1))) & hBOOL(hAPP_H1927961489a_bool(Pa,X)))) <-> (exists X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A)) & hBOOL(hAPP_H1927961489a_bool(Pa,X)))) | (exists X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),B_1)) & hBOOL(hAPP_H1927961489a_bool(Pa,X)))))) # label(fact_78_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 102 (all Pa all A all B_1 ((exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),semila278973382e_bool(A,B_1))) & hBOOL(hAPP_pname_bool(Pa,X)))) <-> (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)) & hBOOL(hAPP_pname_bool(Pa,X)))) | (exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),B_1)) & hBOOL(hAPP_pname_bool(Pa,X)))))) # label(fact_79_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 103 (all A all B_1 all C_2 semila2005279307a_bool(semila2005279307a_bool(A,B_1),C_2) = semila2005279307a_bool(A,semila2005279307a_bool(B_1,C_2))) # label(fact_80_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 104 (all A all B_1 all C_2 semila278973382e_bool(semila278973382e_bool(A,B_1),C_2) = semila278973382e_bool(A,semila278973382e_bool(B_1,C_2))) # label(fact_81_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 105 (all C all A all B_1 (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),semila2005279307a_bool(A,B_1))) <-> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),A)) | hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),B_1)))) # label(fact_82_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 106 (all C all A all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),semila278973382e_bool(A,B_1))) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),A)) | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),B_1)))) # label(fact_83_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 107 (all A all B_1 all C_2 semila2005279307a_bool(A,semila2005279307a_bool(B_1,C_2)) = semila2005279307a_bool(B_1,semila2005279307a_bool(A,C_2))) # label(fact_84_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 108 (all A all B_1 all C_2 semila278973382e_bool(A,semila278973382e_bool(B_1,C_2)) = semila278973382e_bool(B_1,semila278973382e_bool(A,C_2))) # label(fact_85_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 109 (all A all B_1 semila2005279307a_bool(A,semila2005279307a_bool(A,B_1)) = semila2005279307a_bool(A,B_1)) # label(fact_86_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 110 (all A all B_1 semila278973382e_bool(A,semila278973382e_bool(A,B_1)) = semila278973382e_bool(A,B_1)) # label(fact_87_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 111 (all A all B_1 semila2005279307a_bool(A,B_1) = semila2005279307a_bool(B_1,A)) # label(fact_88_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 112 (all A all B_1 semila278973382e_bool(A,B_1) = semila278973382e_bool(B_1,A)) # label(fact_89_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 113 (all A all B_1 semila2005279307a_bool(A,B_1) = collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fdisj,cOMBC_2067518550l_bool(member564727580iple_a,A)),cOMBC_2067518550l_bool(member564727580iple_a,B_1)))) # label(fact_90_Un__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 114 (all A all B_1 semila278973382e_bool(A,B_1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,cOMBC_1058051404l_bool(member_pname,A)),cOMBC_1058051404l_bool(member_pname,B_1)))) # label(fact_91_Un__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 115 (all A semila2005279307a_bool(A,A) = A) # label(fact_92_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 116 (all A (is_fun_pname_bool(A) -> semila278973382e_bool(A,A) = A)) # label(fact_93_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 117 (all F all G all A image_505679754iple_a(F,image_1474161344_pname(G,A)) = image_29267653iple_a(cOMBB_548833416iple_a(F,G),A)) # label(fact_94_image__image) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 118 (all F all G all A image_1474161344_pname(F,image_505679754iple_a(G,A)) = image_pname_pname(cOMBB_1314377293_pname(F,G),A)) # label(fact_95_image__image) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 119 (all R_1 all S_1 all X (hBOOL(hAPP_H1927961489a_bool(semila2005279307a_bool(cOMBC_2067518550l_bool(member564727580iple_a,R_1),cOMBC_2067518550l_bool(member564727580iple_a,S_1)),X)) <-> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),semila2005279307a_bool(R_1,S_1))))) # label(fact_96_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 120 (all R_1 all S_1 all X (hBOOL(hAPP_pname_bool(semila278973382e_bool(cOMBC_1058051404l_bool(member_pname,R_1),cOMBC_1058051404l_bool(member_pname,S_1)),X)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),semila278973382e_bool(R_1,S_1))))) # label(fact_97_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 121 (all Pa all Qa collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fdisj,Pa),Qa)) = semila2005279307a_bool(collec1266446174iple_a(Pa),collec1266446174iple_a(Qa))) # label(fact_98_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 122 (all Pa all Qa collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Qa)) = semila278973382e_bool(collect_pname(Pa),collect_pname(Qa))) # label(fact_99_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.30 123 (all B all F all A (is_pname(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),image_1474161344_pname(F,A))) -> -(all X (B = hAPP_H82695184_pname(F,X) -> -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A))))))) # label(fact_100_imageE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 124 (all B all F all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,B),image_505679754iple_a(F,A))) -> -(all X (is_pname(X) -> (B = hAPP_p1261697242iple_a(F,X) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A))))))) # label(fact_101_imageE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 125 (all N_2 all Pa all Pn_1 all Qa (hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(N_2),hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Pa),hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn_1))),Qa))) <-> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(suc(N_2)),hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa))))) # label(fact_102_Body__triple__valid__Suc) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 126 (all Y_1 -(all Fun1 all Com all Fun2 Y_1 != hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Fun1),Com),Fun2))) # label(fact_103_triple_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 127 (all Pn_1 all Ga all Pa all Qa all Procsa (hBOOL(hoare_472868247rivs_a(semila2005279307a_bool(Ga,image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,Pa),body),Qa),Procsa)),image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,Pa),cOMBB_923936821_pname(the_com,body_1)),Qa),Procsa))) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn_1),Procsa)) -> hBOOL(hoare_472868247rivs_a(Ga,insert1871499715iple_a(hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,hAPP_p635540397e_bool(Pa,Pn_1)),hAPP_pname_com(body,Pn_1)),hAPP_p635540397e_bool(Qa,Pn_1)),bot_bo1687970473a_bool)))))) # label(fact_104_Body1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 128 (all F all G all M all N_1 (M = N_1 -> ((all X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),N_1)) -> hAPP_H82695184_pname(F,X) = hAPP_H82695184_pname(G,X))) -> image_1474161344_pname(F,M) = image_1474161344_pname(G,N_1)))) # label(fact_105_image__cong) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 129 (all F all G all M all N_1 (M = N_1 -> ((all X (is_pname(X) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),N_1)) -> hAPP_p1261697242iple_a(F,X) = hAPP_p1261697242iple_a(G,X)))) -> image_505679754iple_a(F,M) = image_505679754iple_a(G,N_1)))) # label(fact_106_image__cong) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 130 (all Pa all Pn_1 all Qa hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(zero_zero_nat),hAPP_f1148670082iple_a(hAPP_c1572710133iple_a(hAPP_f841604374iple_a(hoare_1050552211iple_a,Pa),hAPP_pname_com(body,Pn_1)),Qa)))) # label(fact_107_Body__triple__valid__0) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 131 (all Pname_1 all Pname (is_pname(Pname_1) & is_pname(Pname) -> (hAPP_pname_com(body,Pname_1) = hAPP_pname_com(body,Pname) <-> Pname_1 = Pname))) # label(fact_108_com_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 132 (all Pn all S0 all S1 (hBOOL(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,Pn)),S0,S1)) -> hBOOL(evalc(hAPP_pname_com(body,Pn),S0,S1)))) # label(fact_109_evalc_OBody) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 133 (all A_1 -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),bot_bo1687970473a_bool))) # label(fact_110_emptyE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 134 (all A_1 -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),bot_bo844097828e_bool))) # label(fact_111_emptyE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 135 (all A_1 all B all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),insert1871499715iple_a(B,A))) -> (A_1 != B -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),A))))) # label(fact_112_insertE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 136 (all A_1 all B all A (is_pname(A_1) & is_pname(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B,A))) -> (A_1 != B -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)))))) # label(fact_113_insertE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 137 (all B all A_1 all B_1 ((-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),B_1)) -> A_1 = B) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),insert1871499715iple_a(B,B_1))))) # label(fact_114_insertCI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 138 (all B all A_1 all B_1 ((-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B_1)) -> A_1 = B) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B,B_1))))) # label(fact_115_insertCI) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 139 (all P all S all S1 (hBOOL(evalc(hAPP_pname_com(body,P),S,S1)) -> hBOOL(evalc(hAPP_option_com_com(the_com,hAPP_p799580910on_com(body_1,P)),S,S1)))) # label(fact_116_evalc__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 140 (all A_1 all A bot_bo1687970473a_bool != insert1871499715iple_a(A_1,A)) # label(fact_117_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 141 (all A_1 all A bot_bo844097828e_bool != insert_pname(A_1,A)) # label(fact_118_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 142 (all A_1 all A insert1871499715iple_a(A_1,A) != bot_bo1687970473a_bool) # label(fact_119_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 143 (all A_1 all A insert_pname(A_1,A) != bot_bo844097828e_bool) # label(fact_120_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 144 (all X (hBOOL(hAPP_H1927961489a_bool(bot_bo1687970473a_bool,X)) <-> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),bot_bo1687970473a_bool)))) # label(fact_121_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 145 (all X (hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X)) <-> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),bot_bo844097828e_bool)))) # label(fact_122_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 146 (all A_1 all B_1 hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),insert1871499715iple_a(A_1,B_1)))) # label(fact_125_insertI1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 147 (all A_1 all B_1 hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(A_1,B_1)))) # label(fact_126_insertI1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 148 (all A ((all X -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A))) <-> A = bot_bo1687970473a_bool)) # label(fact_127_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 149 (all A (is_fun_pname_bool(A) -> ((all X (is_pname(X) -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)))) <-> A = bot_bo844097828e_bool))) # label(fact_128_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 150 (all A_1 collec1266446174iple_a(hAPP_H562195827a_bool(fequal1878252616iple_a,A_1)) = insert1871499715iple_a(A_1,bot_bo1687970473a_bool)) # label(fact_129_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 151 (all A_1 collect_pname(hAPP_p61793385e_bool(fequal_pname,A_1)) = insert_pname(A_1,bot_bo844097828e_bool)) # label(fact_130_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 152 (all A ((exists X hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),A))) <-> A != bot_bo1687970473a_bool)) # label(fact_131_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 153 (all A (is_fun_pname_bool(A) -> ((exists X (is_pname(X) & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X),A)))) <-> A != bot_bo844097828e_bool))) # label(fact_132_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 154 (all A_1 collec1266446174iple_a(cOMBC_2049287834a_bool(fequal1878252616iple_a,A_1)) = insert1871499715iple_a(A_1,bot_bo1687970473a_bool)) # label(fact_133_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 155 (all A_1 collect_pname(cOMBC_1149511130e_bool(fequal_pname,A_1)) = insert_pname(A_1,bot_bo844097828e_bool)) # label(fact_134_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 156 (all Pa all A_1 ((hBOOL(hAPP_H1927961489a_bool(Pa,A_1)) -> collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fconj,hAPP_H562195827a_bool(fequal1878252616iple_a,A_1)),Pa)) = insert1871499715iple_a(A_1,bot_bo1687970473a_bool)) & (-hBOOL(hAPP_H1927961489a_bool(Pa,A_1)) -> collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fconj,hAPP_H562195827a_bool(fequal1878252616iple_a,A_1)),Pa)) = bot_bo1687970473a_bool))) # label(fact_135_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 157 (all Pa all A_1 ((hBOOL(hAPP_pname_bool(Pa,A_1)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_1)),Pa)) = insert_pname(A_1,bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(Pa,A_1)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,A_1)),Pa)) = bot_bo844097828e_bool))) # label(fact_136_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 158 (all Pa all A_1 ((hBOOL(hAPP_H1927961489a_bool(Pa,A_1)) -> collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fconj,cOMBC_2049287834a_bool(fequal1878252616iple_a,A_1)),Pa)) = insert1871499715iple_a(A_1,bot_bo1687970473a_bool)) & (-hBOOL(hAPP_H1927961489a_bool(Pa,A_1)) -> collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fconj,cOMBC_2049287834a_bool(fequal1878252616iple_a,A_1)),Pa)) = bot_bo1687970473a_bool))) # label(fact_137_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 159 (all Pa all A_1 ((hBOOL(hAPP_pname_bool(Pa,A_1)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,cOMBC_1149511130e_bool(fequal_pname,A_1)),Pa)) = insert_pname(A_1,bot_bo844097828e_bool)) & (-hBOOL(hAPP_pname_bool(Pa,A_1)) -> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,cOMBC_1149511130e_bool(fequal_pname,A_1)),Pa)) = bot_bo844097828e_bool))) # label(fact_138_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 160 (all Pa (bot_bo844097828e_bool = collect_pname(Pa) <-> (all X (is_pname(X) -> -hBOOL(hAPP_pname_bool(Pa,X)))))) # label(fact_139_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 161 (all Pa (bot_bo1687970473a_bool = collec1266446174iple_a(Pa) <-> (all X -hBOOL(hAPP_H1927961489a_bool(Pa,X))))) # label(fact_140_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 162 (all C -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,C),bot_bo1687970473a_bool))) # label(fact_141_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 163 (all C -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C),bot_bo844097828e_bool))) # label(fact_142_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 164 (all X_2 all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A)) <-> hBOOL(hAPP_H1927961489a_bool(A,X_2)))) # label(fact_143_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 165 (all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) <-> hBOOL(hAPP_pname_bool(A,X_2)))) # label(fact_144_mem__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 166 (all Pa (is_fun_pname_bool(Pa) -> collect_pname(Pa) = Pa)) # label(fact_145_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 167 (all Pa collec1266446174iple_a(Pa) = Pa) # label(fact_146_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 168 (all A_1 all B_1 insert1871499715iple_a(A_1,B_1) = collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fdisj,cOMBC_2049287834a_bool(fequal1878252616iple_a,A_1)),cOMBC_2067518550l_bool(member564727580iple_a,B_1)))) # label(fact_147_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 169 (all A_1 all B_1 insert_pname(A_1,B_1) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,cOMBC_1149511130e_bool(fequal_pname,A_1)),cOMBC_1058051404l_bool(member_pname,B_1)))) # label(fact_148_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 170 (all A_1 all A insert1871499715iple_a(A_1,A) = semila2005279307a_bool(insert1871499715iple_a(A_1,bot_bo1687970473a_bool),A)) # label(fact_149_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 171 (all A_1 all A insert_pname(A_1,A) = semila278973382e_bool(insert_pname(A_1,bot_bo844097828e_bool),A)) # label(fact_150_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 172 (all A_1 all Pa insert1871499715iple_a(A_1,collec1266446174iple_a(Pa)) = collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fimplies,cOMBB_650444389iple_a(fNot,cOMBC_2049287834a_bool(fequal1878252616iple_a,A_1))),Pa))) # label(fact_151_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 173 (all A_1 all Pa insert_pname(A_1,collect_pname(Pa)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,cOMBC_1149511130e_bool(fequal_pname,A_1))),Pa))) # label(fact_152_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 174 (all B all A_1 (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,B),insert1871499715iple_a(A_1,bot_bo1687970473a_bool))) <-> B = A_1)) # label(fact_153_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 175 (all B all A_1 (is_pname(B) & is_pname(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),insert_pname(A_1,bot_bo844097828e_bool))) <-> B = A_1))) # label(fact_154_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 176 (all X_2 all A insert1871499715iple_a(X_2,insert1871499715iple_a(X_2,A)) = insert1871499715iple_a(X_2,A)) # label(fact_155_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 177 (all X_2 all A insert_pname(X_2,insert_pname(X_2,A)) = insert_pname(X_2,A)) # label(fact_156_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 178 (all X_2 all Y_1 all A insert1871499715iple_a(X_2,insert1871499715iple_a(Y_1,A)) = insert1871499715iple_a(Y_1,insert1871499715iple_a(X_2,A))) # label(fact_157_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 179 (all X_2 all Y_1 all A insert_pname(X_2,insert_pname(Y_1,A)) = insert_pname(Y_1,insert_pname(X_2,A))) # label(fact_158_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 180 (all A_1 all B all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),insert1871499715iple_a(B,A))) <-> A_1 = B | hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),A)))) # label(fact_159_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 181 (all A_1 all B all A (is_pname(A_1) & is_pname(B) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B,A))) <-> A_1 = B | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))))) # label(fact_160_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 182 (all Pa (collect_pname(Pa) = bot_bo844097828e_bool <-> (all X (is_pname(X) -> -hBOOL(hAPP_pname_bool(Pa,X)))))) # label(fact_161_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 183 (all Pa (collec1266446174iple_a(Pa) = bot_bo1687970473a_bool <-> (all X -hBOOL(hAPP_H1927961489a_bool(Pa,X))))) # label(fact_162_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 184 (all A_1 all B all C all D (insert1871499715iple_a(A_1,insert1871499715iple_a(B,bot_bo1687970473a_bool)) = insert1871499715iple_a(C,insert1871499715iple_a(D,bot_bo1687970473a_bool)) <-> A_1 = C & B = D | A_1 = D & B = C)) # label(fact_163_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 185 (all A_1 all B all C all D (is_pname(A_1) & is_pname(B) & is_pname(C) & is_pname(D) -> (insert_pname(A_1,insert_pname(B,bot_bo844097828e_bool)) = insert_pname(C,insert_pname(D,bot_bo844097828e_bool)) <-> A_1 = C & B = D | A_1 = D & B = C))) # label(fact_164_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 186 (all Y_1 all A all X_2 (hBOOL(hAPP_H1927961489a_bool(insert1871499715iple_a(Y_1,A),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_H1927961489a_bool(A,X_2)))) # label(fact_165_insert__code) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 187 (all Y_1 all A all X_2 (is_pname(Y_1) & is_pname(X_2) -> (hBOOL(hAPP_pname_bool(insert_pname(Y_1,A),X_2)) <-> Y_1 = X_2 | hBOOL(hAPP_pname_bool(A,X_2))))) # label(fact_166_insert__code) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 188 (all X all Xa insert1871499715iple_a(X,Xa) = collec1266446174iple_a(cOMBS_213702372l_bool(cOMBB_633860163iple_a(fdisj,cOMBC_2049287834a_bool(fequal1878252616iple_a,X)),cOMBC_2067518550l_bool(member564727580iple_a,Xa)))) # label(fact_167_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 189 (all X all Xa insert_pname(X,Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,cOMBC_1149511130e_bool(fequal_pname,X)),cOMBC_1058051404l_bool(member_pname,Xa)))) # label(fact_168_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 190 (all B_1 all X_2 all A (-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A)) -> (-hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),B_1)) -> (insert1871499715iple_a(X_2,A) = insert1871499715iple_a(X_2,B_1) <-> A = B_1)))) # label(fact_169_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 191 (all B_1 all X_2 all A (is_fun_pname_bool(B_1) & is_fun_pname_bool(A) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> (-hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_1)) -> (insert_pname(X_2,A) = insert_pname(X_2,B_1) <-> A = B_1))))) # label(fact_170_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 192 (all A_1 all A (A = bot_bo1687970473a_bool -> -hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),A)))) # label(fact_171_equals0D) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 193 (all A_1 all A (A = bot_bo844097828e_bool -> -hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)))) # label(fact_172_equals0D) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 194 (all B all A_1 all B_1 (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),B_1)) -> hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),insert1871499715iple_a(B,B_1))))) # label(fact_173_insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 195 (all B all A_1 all B_1 (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B_1)) -> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B,B_1))))) # label(fact_174_insertI2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 196 (all A_1 all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,A_1),A)) -> insert1871499715iple_a(A_1,A) = A)) # label(fact_175_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 197 (all A_1 all A (is_fun_pname_bool(A) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) -> insert_pname(A_1,A) = A))) # label(fact_176_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 198 (all Ts all Ga all T_1 (hBOOL(hoare_472868247rivs_a(Ga,insert1871499715iple_a(T_1,bot_bo1687970473a_bool))) -> (hBOOL(hoare_472868247rivs_a(Ga,Ts)) -> hBOOL(hoare_472868247rivs_a(Ga,insert1871499715iple_a(T_1,Ts)))))) # label(fact_177_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 199 (all B all A_1 (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,B),insert1871499715iple_a(A_1,bot_bo1687970473a_bool))) -> B = A_1)) # label(fact_178_singletonE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 200 (all B all A_1 (is_pname(B) & is_pname(A_1) -> (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B),insert_pname(A_1,bot_bo844097828e_bool))) -> B = A_1))) # label(fact_179_singletonE) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 201 (all Ga all T_1 all Ts (hBOOL(hoare_472868247rivs_a(Ga,insert1871499715iple_a(T_1,Ts))) -> hBOOL(hoare_472868247rivs_a(Ga,insert1871499715iple_a(T_1,bot_bo1687970473a_bool))) & hBOOL(hoare_472868247rivs_a(Ga,Ts)))) # label(fact_180_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 202 (all A_1 all B (insert1871499715iple_a(A_1,bot_bo1687970473a_bool) = insert1871499715iple_a(B,bot_bo1687970473a_bool) -> A_1 = B)) # label(fact_181_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 203 (all A_1 all B (is_pname(A_1) & is_pname(B) -> (insert_pname(A_1,bot_bo844097828e_bool) = insert_pname(B,bot_bo844097828e_bool) -> A_1 = B))) # label(fact_182_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 204 (all U all C_1 all S all T (hBOOL(evalc(C_1,S,T)) -> (hBOOL(evalc(C_1,S,U)) -> U = T))) # label(fact_183_com__det) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 205 (all C all A ((A = bot_bo1687970473a_bool -> image_1474161344_pname(cOMBK_1932526739iple_a(C),A) = bot_bo844097828e_bool) & (A != bot_bo1687970473a_bool -> image_1474161344_pname(cOMBK_1932526739iple_a(C),A) = insert_pname(C,bot_bo844097828e_bool)))) # label(fact_184_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 206 (all C all A (is_fun_pname_bool(A) -> (A = bot_bo844097828e_bool -> image_505679754iple_a(cOMBK_753524681_pname(C),A) = bot_bo1687970473a_bool) & (A != bot_bo844097828e_bool -> image_505679754iple_a(cOMBK_753524681_pname(C),A) = insert1871499715iple_a(C,bot_bo1687970473a_bool)))) # label(fact_185_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 207 (all C all X_2 all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A)) -> image_1474161344_pname(cOMBK_1932526739iple_a(C),A) = insert_pname(C,bot_bo844097828e_bool))) # label(fact_186_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 208 (all C all X_2 all A (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X_2),A)) -> image_29267653iple_a(cOMBK_1548232270iple_a(C),A) = insert1871499715iple_a(C,bot_bo1687970473a_bool))) # label(fact_187_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 209 (all C all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> image_pname_pname(cOMBK_pname_pname(C),A) = insert_pname(C,bot_bo844097828e_bool))) # label(fact_188_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 210 (all C all X_2 all A (hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) -> image_505679754iple_a(cOMBK_753524681_pname(C),A) = insert1871499715iple_a(C,bot_bo1687970473a_bool))) # label(fact_189_image__constant) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 211 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 212 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 213 (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].
% 0.96/1.31 214 (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].
% 0.96/1.31 215 (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].
% 0.96/1.31 216 (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].
% 0.96/1.31 217 (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].
% 0.96/1.31 218 (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].
% 0.96/1.31 219 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 220 (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].
% 0.96/1.31 221 (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].
% 0.96/1.31 222 (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].
% 0.96/1.31 223 (all X_1 all Y (is_pname(X_1) & is_pname(Y) -> -hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__Com__Opname_T) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 224 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__Com__Opname_T) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 225 (all P all Q (is_bool(P) -> hAPP_pname_bool(cOMBK_bool_pname(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 226 (all P all Q (is_pname(P) -> hAPP_pname_pname(cOMBK_pname_pname(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 227 (all P all Q all R hAPP_pname_bool(cOMBB_647938656_pname(P,Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 228 (all P all Q all R hAPP_pname_bool(cOMBS_568398431l_bool(P,Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 229 (all P all Q all R hAPP_pname_bool(cOMBC_1149511130e_bool(P,Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 230 (all X_1 all Y (-hBOOL(hAPP_H1927961489a_bool(hAPP_H562195827a_bool(fequal1878252616iple_a,X_1),Y)) | X_1 = Y)) # label(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 231 (all X_1 all Y (X_1 != Y | hBOOL(hAPP_H1927961489a_bool(hAPP_H562195827a_bool(fequal1878252616iple_a,X_1),Y)))) # label(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 232 (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].
% 0.96/1.31 233 (all P all Q all R hAPP_pname_com(cOMBB_923936821_pname(P,Q),R) = hAPP_option_com_com(P,hAPP_p799580910on_com(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 234 (all P all Q (is_pname(P) -> hAPP_H82695184_pname(cOMBK_1932526739iple_a(P),Q) = P)) # label(help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 235 (all P all Q hAPP_p1261697242iple_a(cOMBK_753524681_pname(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 236 (all P all Q all R hAPP_p393069232l_bool(cOMBB_675860798_pname(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_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].
% 0.96/1.31 237 (all P all Q all R hAPP_pname_bool(cOMBC_1058051404l_bool(P,Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 238 (all P all Q all R hAPP_H1927961489a_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].
% 0.96/1.31 239 (all P all Q all R hAPP_H1927961489a_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].
% 0.96/1.31 240 (all P all Q all R hAPP_pname_pname(cOMBB_1314377293_pname(P,Q),R) = hAPP_H82695184_pname(P,hAPP_p1261697242iple_a(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 241 (all P all Q hAPP_H401672213iple_a(cOMBK_1548232270iple_a(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_It__a_J_00_001) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 242 (all P all Q all R hAPP_H1877746411l_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_002) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 243 (all P all Q all R hAPP_H1927961489a_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].
% 0.96/1.31 244 (all P all Q all R hAPP_H401672213iple_a(cOMBB_548833416iple_a(P,Q),R) = hAPP_p1261697242iple_a(P,hAPP_H82695184_pname(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 245 (all P all Q all R hAPP_p1261697242iple_a(cOMBS_1258869540iple_a(P,Q),R) = hAPP_f1148670082iple_a(hAPP_p510058747iple_a(P,R),hAPP_p635540397e_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__fun_It__a_Mtc__fun_Itc__Com__Osta) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 246 (all P all Q all R hAPP_H1927961489a_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_003) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 247 (all P all Q all R hAPP_p510058747iple_a(cOMBS_121941143iple_a(P,Q),R) = hAPP_c1572710133iple_a(hAPP_p297245038iple_a(P,R),hAPP_pname_com(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__Com__Ocom_000tc__fun_Itc__fun_It_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 248 (all P all Q all R hAPP_p297245038iple_a(cOMBB_1500441031_pname(P,Q),R) = hAPP_f841604374iple_a(P,hAPP_p635540397e_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__fun_Itc__Com__Ostate_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.31 249 (all N ((all X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),semila2005279307a_bool(g,image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,p),body),q),procs)))) -> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(N),X)))) -> (all X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,p),cOMBB_923936821_pname(the_com,body_1)),q),procs))) -> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(N),X)))))) # label(conj_0) # label(hypothesis) # label(non_clause). [assumption].
% 2.78/3.15 250 -((all X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),g)) -> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(n),X)))) -> (all X (hBOOL(hAPP_f1753944735l_bool(hAPP_H1926610125l_bool(member564727580iple_a,X),image_505679754iple_a(cOMBS_1258869540iple_a(cOMBS_121941143iple_a(cOMBB_1500441031_pname(hoare_1050552211iple_a,p),body),q),procs))) -> hBOOL(hAPP_H1927961489a_bool(hoare_426900819alid_a(n),X))))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.78/3.15
% 2.78/3.15 ============================== end of process non-clausal formulas ===
% 2.78/3.15
% 2.78/3.15 ============================== PROCESS INITIAL CLAUSES ===============
% 2.78/3.15
% 2.78/3.15 ============================== PREDICATE ELIMINATION =================
% 2.78/3.15
% 2.78/3.15 ============================== end predicate elimination =============
% 2.78/3.15
% 2.78/3.15 Auto_denials: (non-Horn, no changes).
% 2.78/3.15
% 2.78/3.15 Term ordering decisions:
% 2.78/3.15 Function symbol KB weights: member_pname=1. member564727580iple_a=1. bot_bo844097828e_bool=1. bot_bo1687970473a_bool=1. hoare_1050552211iple_a=1. body=1. fconj=1. fdisj=1. fequal1878252616iple_a=1. fequal_pname=1. body_1=1. the_com=1. fimplies=1. procs=1. fFalse=1. p=1. q=1. fNot=1. fTrue=1. g=1. pname=1. bool=1. n=1. zero_zero_nat=1. c1=1. hAPP_f1664156314l_bool=1. hAPP_p338031245l_bool=1. hAPP_f1753944735l_bool=1. hAPP_H1926610125l_bool=1. semila278973382e_bool=1. hAPP_pname_bool=1. semila2005279307a_bool=1. hAPP_H1927961489a_bool=1. semila1168014441p_bool=1. insert1871499715iple_a=1. insert_pname=1. image_505679754iple_a=1. image_1474161344_pname=1. hAPP_c1572710133iple_a=1. hAPP_f1148670082iple_a=1. hAPP_f841604374iple_a=1. hAPP_bool_bool=1. hoare_472868247rivs_a=1. hAPP_H82695184_pname=1. hAPP_p1261697242iple_a=1. hAPP_pname_com=1. cOMBS_568398431l_bool=1. hAPP_b589554111l_bool=1. cOMBB_1500441031_pname=1. cOMBB_633860163iple_a=1. cOMBB_675860798_pname=1. cOMBC_1058051404l_bool=1. cOMBS_121941143iple_a=1. cOMBS_1258869540iple_a=1. cOMBS_213702372l_bool=1. cOMBC_2067518550l_bool=1. cOMBC_1149511130e_bool=1. cOMBC_2049287834a_bool=1. hAPP_p61793385e_bool=1. hAPP_H562195827a_bool=1. hoare_810701593lids_a=1. cOMBB_923936821_pname=1. hAPP_option_com_com=1. hAPP_p799580910on_com=1. hAPP_p635540397e_bool=1. cOMBB_647938656_pname=1. hAPP_pname_pname=1. image_pname_pname=1. cOMBB_1314377293_pname=1. cOMBB_548833416iple_a=1. cOMBB_650444389iple_a=1. hAPP_H1877746411l_bool=1. hAPP_H401672213iple_a=1. hAPP_p297245038iple_a=1. hAPP_p393069232l_bool=1. hAPP_p510058747iple_a=1. image_29267653iple_a=1. fun=1. f2=1. f3=1. collect_pname=1. collec1266446174iple_a=1. hoare_426900819alid_a=1. cOMBK_1932526739iple_a=1. cOMBK_753524681_pname=1. cOMBK_bool_pname=1. cOMBK_1150238960iple_a=1. cOMBK_1548232270iple_a=1. cOMBK_pname_pname=1. suc=1. undefi17486888e_bool=1. undefined_pname=1. f20=1. f21=1. f22=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. evalc=1. f1=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f23=1. f24=1.
% 2.78/3.15
% 2.78/3.15 ============================== end of process initial clauses ========
% 2.78/3.15
% 2.78/3.15 ============================== CLAUSES FOR SEARCH ====================
% 2.78/3.15
% 2.78/3.15 ============================== end of clauses for search =============
% 2.78/3.15
% 2.78/3.15 ============================== SEARCH ================================
% 2.78/3.15
% 2.78/3.15 % Starting search at 0.15 seconds.
% 2.78/3.15
% 2.78/3.15 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 57 (0.00 of 1.18 sec).
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=47.000, iters=3427
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=43.000, iters=3391
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=34.000, iters=3551
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=31.000, iters=3422
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=28.000, iters=3397
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=26.000, iters=3388
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=25.000, iters=3363
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=24.000, iters=3342
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=22.000, iters=3348
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=21.000, iters=3354
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=19.000, iters=3406
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=18.000, iters=3362
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=16.000, iters=3359
% 2.78/3.15
% 2.78/3.15 Low Water (keep): wt=14.000, iters=3352
% 2.78/3.15
% 2.78/3.15 LowCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------